From 73ca6243b31e225e9fd5b75a96cbc82d62557de6 Mon Sep 17 00:00:00 2001
From: "caryclark@google.com"
 <caryclark@google.com@2bbb7eff-a529-9590-31e7-b0007b416f81>
Date: Thu, 17 Jan 2013 21:02:47 +0000
Subject: [PATCH] shape ops work in progress

mostly working on cubic/cubic intersect

git-svn-id: http://skia.googlecode.com/svn/trunk@7266 2bbb7eff-a529-9590-31e7-b0007b416f81
---
 experimental/Intersection/CubicBezierClip.cpp      |    4 +-
 experimental/Intersection/CubicIntersection.cpp    |  130 ++
 .../Intersection/CubicIntersection_Test.cpp        |  209 ++
 .../Intersection/CubicIntersection_TestData.cpp    |    1 -
 .../Intersection/CubicIntersection_TestData.h      |    5 +-
 experimental/Intersection/CubicReduceOrder.cpp     |   19 +-
 experimental/Intersection/CubicToQuadratics.cpp    |  128 +-
 .../Intersection/CubicToQuadratics_Test.cpp        |  117 +-
 experimental/Intersection/CubicUtilities.cpp       |   28 +-
 experimental/Intersection/CubicUtilities.h         |    7 +-
 experimental/Intersection/CurveIntersection.h      |    6 +-
 experimental/Intersection/DataTypes.cpp            |    7 -
 experimental/Intersection/DataTypes.h              |   26 +-
 experimental/Intersection/DataTypes_Test.h         |    7 +
 experimental/Intersection/EdgeWalker.cpp           |    2 +-
 experimental/Intersection/Intersection_Tests.cpp   |    6 +-
 experimental/Intersection/Intersection_Tests.h     |    6 +-
 experimental/Intersection/Intersections.cpp        |   99 +
 experimental/Intersection/Intersections.h          |  129 +-
 .../Intersection/LineCubicIntersection.cpp         |  277 +--
 .../Intersection/LineCubicIntersection_Test.cpp    |    6 +-
 experimental/Intersection/LineIntersection.cpp     |   20 +-
 experimental/Intersection/LineIntersection.h       |    5 +-
 experimental/Intersection/LineParameters.h         |   12 +-
 .../Intersection/LineParameteters_Test.cpp         |    6 +-
 experimental/Intersection/QuadraticImplicit.cpp    |  345 +++-
 .../Intersection/QuadraticIntersection_Test.cpp    |   51 +-
 .../Intersection/QuadraticIntersection_TestData.h  |    5 +-
 experimental/Intersection/QuadraticUtilities.h     |    8 +-
 experimental/Intersection/QuarticRoot.cpp          |   60 +-
 experimental/Intersection/QuarticRoot_Test.cpp     |   15 +-
 experimental/Intersection/Simplify.cpp             |  202 +-
 experimental/Intersection/SimplifyNew_Test.cpp     |   44 +-
 experimental/Intersection/TSearch.h                |   29 +
 experimental/Intersection/op.htm                   |   29 +-
 experimental/Intersection/qc.htm                   | 2079 ++++++++++++++++++++
 36 files changed, 3674 insertions(+), 455 deletions(-)
 create mode 100644 experimental/Intersection/DataTypes_Test.h
 create mode 100644 experimental/Intersection/qc.htm

diff --git a/experimental/Intersection/CubicBezierClip.cpp b/experimental/Intersection/CubicBezierClip.cpp
index d0141e9..825a7b9 100644
--- a/experimental/Intersection/CubicBezierClip.cpp
+++ b/experimental/Intersection/CubicBezierClip.cpp
@@ -26,7 +26,8 @@ bool bezier_clip(const Cubic& cubic1, const Cubic& cubic2, double& minT, double&
     }
 
     double distance[2];
-    endLine.controlPtDistance(cubic1, distance);
+    distance[0] = endLine.controlPtDistance(cubic1, 1);
+    distance[1] = endLine.controlPtDistance(cubic1, 2);
 
     // find fat line
     double top = distance[0];
@@ -87,4 +88,3 @@ bool bezier_clip(const Cubic& cubic1, const Cubic& cubic2, double& minT, double&
 
     return minT < maxT; // returns false if distance shows no intersection
 }
-
diff --git a/experimental/Intersection/CubicIntersection.cpp b/experimental/Intersection/CubicIntersection.cpp
index fcd4119..d5a5bde 100644
--- a/experimental/Intersection/CubicIntersection.cpp
+++ b/experimental/Intersection/CubicIntersection.cpp
@@ -159,3 +159,133 @@ bool intersect(const Cubic& c1, const Cubic& c2, Intersections& i) {
     return c.intersect();
 }
 
+#include "CubicUtilities.h"
+
+// this flavor approximates the cubics with quads to find the intersecting ts
+// OPTIMIZE: if this strategy proves successful, the quad approximations, or the ts used
+// to create the approximations, could be stored in the cubic segment
+// fixme: this strategy needs to add short line segments on either end, or similarly extend the 
+// initial and final quadratics
+bool intersect2(const Cubic& c1, const Cubic& c2, Intersections& i) {
+    SkTDArray<double> ts1;
+    double precision1 = calcPrecision(c1);
+    cubic_to_quadratics(c1, precision1, ts1);
+    SkTDArray<double> ts2;
+    double precision2 = calcPrecision(c2);
+    cubic_to_quadratics(c2, precision2, ts2);
+    double t1Start = 0;
+    int ts1Count = ts1.count();
+    for (int i1 = 0; i1 <= ts1Count; ++i1) {
+        const double t1 = i1 < ts1Count ? ts1[i1] : 1;
+        Cubic part1;
+        sub_divide(c1, t1Start, t1, part1);
+        Quadratic q1;
+        demote_cubic_to_quad(part1, q1);
+  //      start here;
+        // should reduceOrder be looser in this use case if quartic is going to blow up on an
+        // extremely shallow quadratic?
+        // maybe quadratics to lines need the same sort of recursive solution that I hope to find
+        // for cubics to quadratics ...
+        Quadratic s1;
+        int o1 = reduceOrder(q1, s1);
+        double t2Start = 0;
+        int ts2Count = ts2.count();
+        for (int i2 = 0; i2 <= ts2Count; ++i2) {
+            const double t2 = i2 < ts2Count ? ts2[i2] : 1;
+            Cubic part2;
+            sub_divide(c2, t2Start, t2, part2);
+            Quadratic q2;
+            demote_cubic_to_quad(part2, q2);
+            Quadratic s2;
+            double o2 = reduceOrder(q2, s2);
+            Intersections locals;
+            if (o1 == 3 && o2 == 3) {
+                intersect2(q1, q2, locals);
+            } else if (o1 <= 2 && o2 <= 2) {
+                i.fUsed = intersect((const _Line&) s1, (const _Line&) s2, i.fT[0], i.fT[1]);
+            } else if (o1 == 3 && o2 <= 2) {
+                intersect(q1, (const _Line&) s2, i);
+            } else {
+                SkASSERT(o1 <= 2 && o2 == 3);
+                intersect(q2, (const _Line&) s1, i);
+                for (int s = 0; s < i.fUsed; ++s) {
+                    SkTSwap(i.fT[0][s], i.fT[1][s]);
+                }
+            }
+            for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
+                double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
+                double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
+                i.insert(to1, to2);
+            }
+            t2Start = t2;
+        }
+        t1Start = t1;
+    }
+    return i.intersected();
+}
+
+int intersect(const Cubic& cubic, const Quadratic& quad, Intersections& i) {
+    SkTDArray<double> ts;
+    double precision = calcPrecision(cubic);
+    cubic_to_quadratics(cubic, precision, ts);
+    double tStart = 0;
+    Cubic part;
+    int tsCount = ts.count();
+    for (int idx = 0; idx <= tsCount; ++idx) {
+        double t = idx < tsCount ? ts[idx] : 1;
+        Quadratic q1;
+        sub_divide(cubic, tStart, t, part);
+        demote_cubic_to_quad(part, q1);
+        Intersections locals;
+        intersect2(q1, quad, locals);
+        for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
+            double globalT = tStart + (t - tStart) * locals.fT[0][tIdx];
+            i.insertOne(globalT, 0);
+            globalT = locals.fT[1][tIdx];
+            i.insertOne(globalT, 1);
+        }
+        tStart = t;
+    }
+    return i.used();
+}
+
+bool intersect(const Cubic& cubic, Intersections& i) {
+    SkTDArray<double> ts;
+    double precision = calcPrecision(cubic);
+    cubic_to_quadratics(cubic, precision, ts);
+    int tsCount = ts.count();
+    if (tsCount == 1) {
+        return false;
+    }
+    double t1Start = 0;
+    Cubic part;
+    for (int idx = 0; idx < tsCount; ++idx) {
+        double t1 = ts[idx];
+        Quadratic q1;
+        sub_divide(cubic, t1Start, t1, part);
+        demote_cubic_to_quad(part, q1);
+        double t2Start = t1;
+        for (int i2 = idx + 1; i2 <= tsCount; ++i2) {
+            const double t2 = i2 < tsCount ? ts[i2] : 1;
+            Quadratic q2;
+            sub_divide(cubic, t2Start, t2, part);
+            demote_cubic_to_quad(part, q2);
+            Intersections locals;
+            intersect2(q1, q2, locals);
+            for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
+            // discard intersections at cusp? (maximum curvature)
+                double t1sect = locals.fT[0][tIdx];
+                double t2sect = locals.fT[1][tIdx];
+                if (idx + 1 == i2 && t1sect == 1 && t2sect == 0) {
+                    continue;
+                }
+                double to1 = t1Start + (t1 - t1Start) * t1sect;
+                double to2 = t2Start + (t2 - t2Start) * t2sect;
+                i.insert(to1, to2);
+            }
+            t2Start = t2;
+        }
+        t1Start = t1;
+    }
+    return i.intersected();
+}
diff --git a/experimental/Intersection/CubicIntersection_Test.cpp b/experimental/Intersection/CubicIntersection_Test.cpp
index 256529c..7d27bf4 100644
--- a/experimental/Intersection/CubicIntersection_Test.cpp
+++ b/experimental/Intersection/CubicIntersection_Test.cpp
@@ -56,3 +56,212 @@ void CubicIntersection_Test() {
         }
     }
 }
+
+static void oneOff(const Cubic& cubic1, const Cubic& cubic2) {
+    SkTDArray<Quadratic> quads1;
+    cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1);
+    for (int index = 0; index < quads1.count(); ++index) {
+        const Quadratic& q = quads1[index];
+        SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, 
+                 q[1].x, q[1].y,  q[2].x, q[2].y);
+    }
+    SkDebugf("\n");
+    SkTDArray<Quadratic> quads2;
+    cubic_to_quadratics(cubic2, calcPrecision(cubic2), quads2);
+    for (int index = 0; index < quads2.count(); ++index) {
+        const Quadratic& q = quads2[index];
+        SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, 
+                 q[1].x, q[1].y,  q[2].x, q[2].y);
+    }
+    SkDebugf("\n");
+    Intersections intersections2;
+    intersect2(cubic1, cubic2, intersections2);
+    for (int pt = 0; pt < intersections2.used(); ++pt) {
+        double tt1 = intersections2.fT[0][pt];
+        double tx1, ty1;
+        xy_at_t(cubic1, tt1, tx1, ty1);
+        int pt2 = intersections2.fFlip ? intersections2.used() - pt - 1 : pt;
+        double tt2 = intersections2.fT[1][pt2];
+        double tx2, ty2;
+        xy_at_t(cubic2, tt2, tx2, ty2);
+        SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__,
+            tt1, tx1, ty1, tx2, ty2, tt2);
+    }
+}
+
+static const Cubic testSet[] = {
+{{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.476863174921306}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.244890038969412}},
+{{61.336508189019057, 82.693132843213675}, {44.639380902349664, 54.074825790745592}, {16.815615499771951, 20.049704667203923}, {41.866884958868326, 56.735503699973002}},
+
+{{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}},
+{{61.3365082, 82.6931328}, {44.6393809, 54.0748258}, {16.8156155, 20.0497047}, {41.866885, 56.7355037}},
+
+{{18.1312339, 31.6473732}, {95.5711034, 63.5350219}, {92.3283165, 62.0158945}, {18.5656052, 32.1268808}},
+{{97.402018, 35.7169972}, {33.1127443, 25.8935163}, {1.13970027, 54.9424981}, {56.4860195, 60.529264}},
+};
+
+const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]);
+
+void CubicIntersection_OneOffTest() {
+    for (size_t outer = 0; outer < testSetCount - 1; ++outer) {
+        SkDebugf("%s quads1[%d]\n", __FUNCTION__, outer);
+        const Cubic& cubic1 = testSet[outer];
+        for (size_t inner = outer + 1; inner < testSetCount; ++inner) {
+        SkDebugf("%s quads2[%d]\n", __FUNCTION__, inner);
+            const Cubic& cubic2 = testSet[inner];
+            oneOff(cubic1, cubic2);
+        }
+    }
+}
+
+#define DEBUG_CRASH 1
+
+class CubicChopper {
+public:
+
+// only finds one intersection
+CubicChopper(const Cubic& c1, const Cubic& c2)
+    : cubic1(c1)
+    , cubic2(c2)
+    , depth(0) {
+}
+
+bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
+    Cubic sub1, sub2;
+    // FIXME: carry last subdivide and reduceOrder result with cubic
+    sub_divide(cubic1, minT1, maxT1, sub1);
+    sub_divide(cubic2, minT2, maxT2, sub2);
+    Intersections i;
+    intersect2(sub1, sub2, i);
+    if (i.used() == 0) {
+        return false;
+    }
+    double x1, y1, x2, y2;
+    t1 = minT1 + i.fT[0][0] * (maxT1 - minT1);
+    t2 = minT2 + i.fT[1][0] * (maxT2 - minT2);
+    xy_at_t(cubic1, t1, x1, y1);
+    xy_at_t(cubic2, t2, x2, y2);
+    if (AlmostEqualUlps(x1, x2) && AlmostEqualUlps(y1, y2)) {
+        return true;
+    }
+    double half1 = (minT1 + maxT1) / 2;
+    double half2 = (minT2 + maxT2) / 2;
+    ++depth;
+    bool result;
+    if (depth & 1) {
+        result = intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2)
+            || intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2);
+    } else {
+        result = intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2)
+            || intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2);
+    }
+    --depth;
+    return result;
+}
+
+const Cubic& cubic1;
+const Cubic& cubic2;
+double t1;
+double t2;
+int depth;
+};
+
+#define TRY_OLD 0 // old way fails on test == 1
+
+void CubicIntersection_RandTest() {
+    srand(0);
+    const int tests = 1000000; // 10000000;
+    double largestFactor = DBL_MAX;
+    for (int test = 0; test < tests; ++test) {
+        Cubic cubic1, cubic2;
+        for (int i = 0; i < 4; ++i) {
+            cubic1[i].x = (double) rand() / RAND_MAX * 100;
+            cubic1[i].y = (double) rand() / RAND_MAX * 100;
+            cubic2[i].x = (double) rand() / RAND_MAX * 100;
+            cubic2[i].y = (double) rand() / RAND_MAX * 100;
+        }
+        if (test == 2513) { // the pair crosses three times, but the quadratic approximation
+            continue; // only sees one -- should be OK to ignore the other two?
+        }
+        if (test == 12932) { // this exposes a weakness when one cubic touches the other but
+            continue; // does not touch the quad approximation. Captured in qc.htm as cubic15
+        }
+    #if DEBUG_CRASH
+        char str[1024];
+        sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n"
+            "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n",
+                cubic1[0].x, cubic1[0].y,  cubic1[1].x, cubic1[1].y, cubic1[2].x, cubic1[2].y,
+                cubic1[3].x, cubic1[3].y,
+                cubic2[0].x, cubic2[0].y,  cubic2[1].x, cubic2[1].y, cubic2[2].x, cubic2[2].y,
+                cubic2[3].x, cubic2[3].y);
+    #endif
+        _Rect rect1, rect2;
+        rect1.setBounds(cubic1);
+        rect2.setBounds(cubic2);
+        bool boundsIntersect = rect1.left <= rect2.right && rect2.left <= rect2.right
+                && rect1.top <= rect2.bottom && rect2.top <= rect1.bottom;
+        Intersections i1, i2;
+    #if TRY_OLD
+        bool oldIntersects = intersect(cubic1, cubic2, i1);
+    #else
+        bool oldIntersects = false;
+    #endif
+        if (test == -1) {
+            SkDebugf("ready...\n");
+        }
+        bool newIntersects = intersect2(cubic1, cubic2, i2);
+        if (!boundsIntersect && (oldIntersects || newIntersects)) {
+            SkDebugf("%s %d unexpected intersection boundsIntersect=%d oldIntersects=%d"
+                    " newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsIntersect,
+                    oldIntersects, newIntersects, __FUNCTION__, str);
+            assert(0);
+        }
+        if (oldIntersects && !newIntersects) {
+            SkDebugf("%s %d missing intersection oldIntersects=%d newIntersects=%d\n%s %s\n",
+                    __FUNCTION__, test, oldIntersects, newIntersects, __FUNCTION__, str);
+            assert(0);
+        }
+        if (!oldIntersects && !newIntersects) {
+            continue;
+        }
+        if (i2.used() > 1) {
+            continue;
+            // just look at single intercepts for simplicity
+        }
+        Intersections self1, self2; // self-intersect checks
+        if (intersect(cubic1, self1)) {
+            continue;
+        }
+        if (intersect(cubic2, self2)) {
+            continue;
+        }
+        // binary search for range necessary to enclose real intersection
+        CubicChopper c(cubic1, cubic2);
+        bool result = c.intersect(0, 1, 0, 1);
+        if (!result) {
+            // FIXME: a failure here probably means that a core routine used by CubicChopper is failing
+            continue;
+        }
+        double delta1 = fabs(c.t1 - i2.fT[0][0]);
+        double delta2 = fabs(c.t2 - i2.fT[1][0]);
+        double calc1 = calcPrecision(cubic1);
+        double calc2 = calcPrecision(cubic2);
+        double factor1 = calc1 / delta1;
+        double factor2 = calc2 / delta2;
+        SkDebugf("%s %d calc1=%1.9g delta1=%1.9g factor1=%1.9g calc2=%1.9g delta2=%1.9g"
+                " factor2=%1.9g\n", __FUNCTION__, test,
+                calc1, delta1, factor1, calc2, delta2, factor2);
+        if (factor1 < largestFactor) {
+            SkDebugf("WE HAVE A WINNER! %1.9g\n", factor1);
+            SkDebugf("%s\n", str);
+            oneOff(cubic1, cubic2);
+            largestFactor = factor1;
+        }
+        if (factor2 < largestFactor) {
+            SkDebugf("WE HAVE A WINNER! %1.9g\n", factor2);
+            SkDebugf("%s\n", str);
+            oneOff(cubic1, cubic2);
+            largestFactor = factor2;
+        }
+    }
+}
diff --git a/experimental/Intersection/CubicIntersection_TestData.cpp b/experimental/Intersection/CubicIntersection_TestData.cpp
index 645d7b0..c138a67 100644
--- a/experimental/Intersection/CubicIntersection_TestData.cpp
+++ b/experimental/Intersection/CubicIntersection_TestData.cpp
@@ -4,7 +4,6 @@
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
-#define IN_TEST 1
 #include "CubicIntersection_TestData.h"
 #include <limits>
 
diff --git a/experimental/Intersection/CubicIntersection_TestData.h b/experimental/Intersection/CubicIntersection_TestData.h
index 27436f8..9893b3c 100644
--- a/experimental/Intersection/CubicIntersection_TestData.h
+++ b/experimental/Intersection/CubicIntersection_TestData.h
@@ -4,11 +4,8 @@
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
-#if !defined(IN_TEST)
-    #define IN_TEST 1
-#endif
-
 #include "DataTypes.h"
+#include "DataTypes_Test.h"
 
 extern const Cubic pointDegenerates[];
 extern const Cubic notPointDegenerates[];
diff --git a/experimental/Intersection/CubicReduceOrder.cpp b/experimental/Intersection/CubicReduceOrder.cpp
index d1775d8..fdc7265 100644
--- a/experimental/Intersection/CubicReduceOrder.cpp
+++ b/experimental/Intersection/CubicReduceOrder.cpp
@@ -149,22 +149,17 @@ static int check_linear(const Cubic& cubic, Cubic& reduction,
 bool isLinear(const Cubic& cubic, int startIndex, int endIndex) {
     LineParameters lineParameters;
     lineParameters.cubicEndPoints(cubic, startIndex, endIndex);
-    double normalSquared = lineParameters.normalSquared();
-    double distance[2]; // distance is not normalized
+    // FIXME: maybe it's possible to avoid this and compare non-normalized
+    lineParameters.normalize();
     int mask = other_two(startIndex, endIndex);
     int inner1 = startIndex ^ mask;
     int inner2 = endIndex ^ mask;
-    lineParameters.controlPtDistance(cubic, inner1, inner2, distance);
-    double limit = normalSquared;
-    int index;
-    for (index = 0; index < 2; ++index) {
-        double distSq = distance[index];
-        distSq *= distSq;
-        if (approximately_greater(distSq, limit)) {
-            return false;
-        }
+    double distance = lineParameters.controlPtDistance(cubic, inner1);
+    if (!approximately_zero(distance)) {
+        return false;
     }
-    return true;
+    distance = lineParameters.controlPtDistance(cubic, inner2);
+    return approximately_zero(distance);
 }
 
 /* food for thought:
diff --git a/experimental/Intersection/CubicToQuadratics.cpp b/experimental/Intersection/CubicToQuadratics.cpp
index 424836c..ff6d7a2 100644
--- a/experimental/Intersection/CubicToQuadratics.cpp
+++ b/experimental/Intersection/CubicToQuadratics.cpp
@@ -40,11 +40,18 @@ Tdiv>=1 - the entire cubic can be approximated by the mid-point approximation
 
 confirmed by (maybe stolen from)
 http://www.caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html
+// maybe in turn derived from  http://www.cccg.ca/proceedings/2004/36.pdf
+// also stored at http://www.cis.usouthal.edu/~hain/general/Publications/Bezier/bezier%20cccg04%20paper.pdf
 
 */
 
 #include "CubicUtilities.h"
 #include "CurveIntersection.h"
+#include "LineIntersection.h"
+
+const bool AVERAGE_END_POINTS = true; // results in better fitting curves
+
+#define USE_CUBIC_END_POINTS 1
 
 static double calcTDiv(const Cubic& cubic, double precision, double start) {
     const double adjust = sqrt(3) / 36;
@@ -62,54 +69,105 @@ static double calcTDiv(const Cubic& cubic, double precision, double start) {
     double dy = c[3].y - 3 * (c[2].y - c[1].y) - c[0].y;
     double dist = sqrt(dx * dx + dy * dy);
     double tDiv3 = precision / (adjust * dist);
-    return cube_root(tDiv3);
+    double t = cube_root(tDiv3);
+    if (start > 0) {
+        t = start + (1 - start) * t;
+    }
+    return t;
 }
 
-static void demote(const Cubic& cubic, Quadratic& quad) {
+void demote_cubic_to_quad(const Cubic& cubic, Quadratic& quad) {
     quad[0] = cubic[0];
-    quad[1].x = (cubic[3].x - 3 * (cubic[2].x - cubic[1].x) - cubic[0].x) / 4;
-    quad[1].y = (cubic[3].y - 3 * (cubic[2].y - cubic[1].y) - cubic[0].y) / 4;
+if (AVERAGE_END_POINTS) {
+    const _Point fromC1 = { (3 * cubic[1].x - cubic[0].x) / 2, (3 * cubic[1].y - cubic[0].y) / 2 };
+    const _Point fromC2 = { (3 * cubic[2].x - cubic[3].x) / 2, (3 * cubic[2].y - cubic[3].y) / 2 };
+    quad[1].x = (fromC1.x + fromC2.x) / 2;
+    quad[1].y = (fromC1.y + fromC2.y) / 2;
+} else {
+    lineIntersect((const _Line&) cubic[0], (const _Line&) cubic[2], quad[1]);
+}
     quad[2] = cubic[3];
 }
 
 int cubic_to_quadratics(const Cubic& cubic, double precision, SkTDArray<Quadratic>& quadratics) {
-    quadratics.setCount(1); // FIXME: every place I have setCount(), I also want setReserve()
+    SkTDArray<double> ts;
+    cubic_to_quadratics(cubic, precision, ts);
+    int tsCount = ts.count();
+    double t1Start = 0;
+    int order = 0;
+    for (int idx = 0; idx <= tsCount; ++idx) {
+        double t1 = idx < tsCount ? ts[idx] : 1;
+        Cubic part;
+        sub_divide(cubic, t1Start, t1, part);
+        Quadratic q1;
+        demote_cubic_to_quad(part, q1);
+        Quadratic s1;
+        int o1 = reduceOrder(q1, s1);
+        if (order < o1) {
+            order = o1;
+        }
+        memcpy(quadratics.append(), o1 < 2 ? s1 : q1, sizeof(Quadratic));
+        t1Start = t1;
+    }
+    return order;
+}
+
+static bool addSimpleTs(const Cubic& cubic, double precision, SkTDArray<double>& ts) {
+    double tDiv = calcTDiv(cubic, precision, 0);
+    if (tDiv >= 1) {
+        return true;
+    }
+    if (tDiv >= 0.5) {
+        *ts.append() = 0.5;
+        return true;
+    }
+    return false;
+}
+
+static void addTs(const Cubic& cubic, double precision, double start, double end,
+        SkTDArray<double>& ts) {
+    double tDiv = calcTDiv(cubic, precision, 0);
+    double parts = ceil(1.0 / tDiv);
+    for (double index = 0; index < parts; ++index) {
+        double newT = start + (index / parts) * (end - start);
+        if (newT > 0 && newT < 1) {
+            *ts.append() = newT;
+        }
+    }
+}
+
+// flavor that returns T values only, deferring computing the quads until they are needed
+void cubic_to_quadratics(const Cubic& cubic, double precision, SkTDArray<double>& ts) {
     Cubic reduced;
     int order = reduceOrder(cubic, reduced, kReduceOrder_QuadraticsAllowed);
     if (order < 3) {
-        memcpy(quadratics[0], reduced, order * sizeof(_Point));
-        return order;
+        return;
     }
-    double tDiv = calcTDiv(cubic, precision, 0);
-    if (approximately_greater_than_one(tDiv)) {
-        demote(cubic, quadratics[0]);
-        return 3;
+    double inflectT[2];
+    int inflections = find_cubic_inflections(cubic, inflectT);
+    SkASSERT(inflections <= 2);
+    if (inflections == 0 && addSimpleTs(cubic, precision, ts)) {
+        return;
     }
-    if (tDiv >= 0.5) {
+    if (inflections == 1) {
         CubicPair pair;
-        chop_at(cubic, pair, 0.5);
-        quadratics.setCount(2);
-        demote(pair.first(), quadratics[0]);
-        demote(pair.second(), quadratics[1]);
-        return 3;
+        chop_at(cubic, pair, inflectT[0]);
+        addTs(pair.first(), precision, 0, inflectT[0], ts);
+        addTs(pair.second(), precision, inflectT[0], 1, ts);
+        return;
     }
-    double start = 0;
-    int index = -1;
-    // if we iterate but make little progress, check to see if the curve is flat
-    // or if the control points are tangent to each other
-    do {
-        Cubic part;
-        sub_divide(cubic, start, tDiv, part);
-        quadratics.append();
-        demote(part, quadratics[++index]);
-        if (tDiv == 1) {
-            break;
+    if (inflections == 2) {
+        if (inflectT[0] > inflectT[1]) {
+            SkTSwap(inflectT[0], inflectT[1]);
         }
-        start = tDiv;
-        tDiv = calcTDiv(cubic, precision, start);
-        if (tDiv > 1) {
-            tDiv = 1;
-        }
-    } while (true);
-    return 3;
+        Cubic part;
+        sub_divide(cubic, 0, inflectT[0], part);
+        addTs(part, precision, 0, inflectT[0], ts);
+        sub_divide(cubic, inflectT[0], inflectT[1], part);
+        addTs(part, precision, inflectT[0], inflectT[1], ts);
+        sub_divide(cubic, inflectT[1], 1, part);
+        addTs(part, precision, inflectT[1], 1, ts);
+        return;
+    }
+    addTs(cubic, precision, 0, 1, ts);
 }
diff --git a/experimental/Intersection/CubicToQuadratics_Test.cpp b/experimental/Intersection/CubicToQuadratics_Test.cpp
index 24c0ffe..843833f 100644
--- a/experimental/Intersection/CubicToQuadratics_Test.cpp
+++ b/experimental/Intersection/CubicToQuadratics_Test.cpp
@@ -3,21 +3,14 @@
 #include "Intersection_Tests.h"
 #include "QuadraticIntersection_TestData.h"
 #include "TestUtilities.h"
+#include "SkGeometry.h"
 
-static double calcPrecision(const Cubic& cubic) {
-    _Rect dRect;
-    dRect.setBounds(cubic);
-    double width = dRect.right - dRect.left;
-    double height = dRect.bottom - dRect.top;
-    return (width > height ? width : height) / 256;
-}
-
-static void test(const Cubic(& cubics)[], const char* name, int firstTest, size_t testCount) {
+static void test(const Cubic* cubics, const char* name, int firstTest, size_t testCount) {
     SkTDArray<Quadratic> quads;
     for (size_t index = firstTest; index < testCount; ++index) {
         const Cubic& cubic = cubics[index];
         double precision = calcPrecision(cubic);
-        cubic_to_quadratics(cubic, precision, quads);
+        (void) cubic_to_quadratics(cubic, precision, quads);
         if (quads.count() != 1) {
             printf("%s [%d] cubic to quadratics failed count=%d\n", name, (int) index,
                     quads.count());
@@ -25,14 +18,14 @@ static void test(const Cubic(& cubics)[], const char* name, int firstTest, size_
     }
 }
 
-static void test(const Quadratic(& quadTests)[], const char* name, int firstTest, size_t testCount) {
+static void test(const Quadratic* quadTests, const char* name, int firstTest, size_t testCount) {
     SkTDArray<Quadratic> quads;
     for (size_t index = firstTest; index < testCount; ++index) {
         const Quadratic& quad = quadTests[index];
         Cubic cubic;
         quad_to_cubic(quad, cubic);
         double precision = calcPrecision(cubic);
-        cubic_to_quadratics(cubic, precision, quads);
+        (void) cubic_to_quadratics(cubic, precision, quads);
         if (quads.count() != 1) {
             printf("%s [%d] cubic to quadratics failed count=%d\n", name, (int) index,
                     quads.count());
@@ -40,7 +33,7 @@ static void test(const Quadratic(& quadTests)[], const char* name, int firstTest
     }
 }
 
-static void testC(const Cubic(& cubics)[], const char* name, int firstTest, size_t testCount) {
+static void testC(const Cubic* cubics, const char* name, int firstTest, size_t testCount) {
     SkTDArray<Quadratic> quads;
     // test if computed line end points are valid
     for (size_t index = firstTest; index < testCount; ++index) {
@@ -63,15 +56,15 @@ static void testC(const Cubic(& cubics)[], const char* name, int firstTest, size
     }
 }
 
-static void testC(const Cubic(& cubics)[][2], const char* name, int firstTest, size_t testCount) {
+static void testC(const Cubic(* cubics)[2], const char* name, int firstTest, size_t testCount) {
     SkTDArray<Quadratic> quads;
     for (size_t index = firstTest; index < testCount; ++index) {
         for (int idx2 = 0; idx2 < 2; ++idx2) {
             const Cubic& cubic = cubics[index][idx2];
             double precision = calcPrecision(cubic);
             int order = cubic_to_quadratics(cubic, precision, quads);
-            assert(order != 4);
-            if (order < 3) {
+        assert(order != 4);
+        if (order < 3) {
                 continue;
             }
             if (!AlmostEqualUlps(cubic[0].x, quads[0][0].x)
@@ -136,6 +129,8 @@ void CubicToQuadratics_Test() {
 }
 
 static Cubic locals[] = {
+ {{14.5975863, 41.632436}, {16.3518929, 26.2639684}, {18.5165519, 7.68775139}, {8.03767257, 89.1628526}},
+ {{69.7292014, 38.6877352}, {24.7648688, 23.1501713}, {84.9283191, 90.2588441}, {80.392774, 61.3533852}},
  {{
     60.776536520932126,
     71.249307306133829
@@ -148,39 +143,113 @@ static Cubic locals[] = {
   }, {
     45.261946574441133,
     17.536076632112298
-  }}
+  }},
 };
 
 static size_t localsCount = sizeof(locals) / sizeof(locals[0]);
 
+#define DEBUG_CRASH 0
+#define TEST_AVERAGE_END_POINTS 0 // must take const off to test
+extern const bool AVERAGE_END_POINTS;
+
 void CubicsToQuadratics_RandTest() {
     for (size_t x = 0; x < localsCount; ++x) {
         const Cubic& cubic = locals[x];
+        const SkPoint skcubic[4] = {{(float) cubic[0].x, (float) cubic[0].y},
+                {(float) cubic[1].x, (float) cubic[1].y}, {(float) cubic[2].x, (float) cubic[2].y},
+                {(float) cubic[3].x, (float) cubic[3].y}};
+        SkScalar skinflect[2];
+        int skin = SkFindCubicInflections(skcubic, skinflect);
+        SkDebugf("%s %d %1.9g\n", __FUNCTION__, skin, skinflect[0]);
         SkTDArray<Quadratic> quads;
         double precision = calcPrecision(cubic);
-        cubic_to_quadratics(cubic, precision, quads);
+        (void) cubic_to_quadratics(cubic, precision, quads);
+        SkDebugf("%s quads=%d\n", __FUNCTION__, quads.count());
     }
     srand(0);
-    const int arrayMax = 1000;
-    const int tests = 1000000;
+    const int arrayMax = 8;
+    const int sampleMax = 10;
+    const int tests = 1000000; // 10000000;
     int quadDist[arrayMax];
     bzero(quadDist, sizeof(quadDist));
+    Cubic samples[arrayMax][sampleMax];
+    int sampleCount[arrayMax];
+    bzero(sampleCount, sizeof(sampleCount));
     for (int x = 0; x < tests; ++x) {
         Cubic cubic;
         for (int i = 0; i < 4; ++i) {
             cubic[i].x = (double) rand() / RAND_MAX * 100;
             cubic[i].y = (double) rand() / RAND_MAX * 100;
         }
+    #if DEBUG_CRASH
+        char str[1024];
+        sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n",
+                cubic[0].x, cubic[0].y,  cubic[1].x, cubic[1].y, cubic[2].x, cubic[2].y,
+                cubic[3].x, cubic[3].y);
+    #endif
         SkTDArray<Quadratic> quads;
         double precision = calcPrecision(cubic);
-        cubic_to_quadratics(cubic, precision, quads);
-        assert(quads.count() < arrayMax);
-        quadDist[quads.count()]++;
+        (void) cubic_to_quadratics(cubic, precision, quads);
+        int count = quads.count();
+        assert(count > 0);
+        assert(--count < arrayMax);
+        quadDist[count]++;
+        int sCount = sampleCount[count];
+        if (sCount < sampleMax) {
+            memcpy(samples[count][sCount], cubic, sizeof(Cubic));
+            sampleCount[count]++;
+        }
     }
     for (int x = 0; x < arrayMax; ++x) {
         if (!quadDist[x]) {
             continue;
         }
-        printf("%d 1.9%g%%\n", x, (double) quadDist[x] / tests * 100);
+        SkDebugf("%d %1.9g%%\n", x + 1, (double) quadDist[x] / tests * 100);
+    }
+    SkDebugf("\n");
+    for (int x = 0; x < arrayMax; ++x) {
+        for (int y = 0; y < sampleCount[x]; ++y) {
+#if TEST_AVERAGE_END_POINTS
+            for (int w = 0; w < 2; ++w) {
+                AVERAGE_END_POINTS = w;
+#else
+                int w = 0;
+#endif
+                SkDebugf("<div id=\"cubic%dx%d%s\">\n", x + 1, y, w ? "x" : "");
+                const Cubic& cubic = samples[x][y];
+                SkDebugf("{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n",
+                    cubic[0].x, cubic[0].y,  cubic[1].x, cubic[1].y, cubic[2].x, cubic[2].y,
+                    cubic[3].x, cubic[3].y);
+                SkTDArray<Quadratic> quads;
+                double precision = calcPrecision(cubic);
+                (void) cubic_to_quadratics(cubic, precision, quads);
+                for (int z = 0; z < quads.count(); ++z) {
+                    const Quadratic& quad = quads[z];
+                    SkDebugf("{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n",
+                        quad[0].x, quad[0].y,  quad[1].x, quad[1].y, quad[2].x, quad[2].y);
+                }
+                SkDebugf("</div>\n\n");
+#if TEST_AVERAGE_END_POINTS
+            }
+#endif
+        }
+    }
+    SkDebugf("</div>\n\n");
+    SkDebugf("<script type=\"text/javascript\">\n\n");
+    SkDebugf("var testDivs = [\n");
+    for (int x = 0; x < arrayMax; ++x) {
+        for (int y = 0; y < sampleCount[x]; ++y) {
+#if TEST_AVERAGE_END_POINTS
+            for (int w = 0; w < 2; ++w) {
+#else
+            int w = 0;
+#endif
+                SkDebugf("    cubic%dx%d%s,\n", x + 1, y, w ? "x" : "");
+#if TEST_AVERAGE_END_POINTS
+            }
+#endif
+        }
     }
+    SkDebugf("\n\n\n");
+    SkDebugf("%s end\n", __FUNCTION__);
 }
diff --git a/experimental/Intersection/CubicUtilities.cpp b/experimental/Intersection/CubicUtilities.cpp
index 958cabb..36aa9e8 100644
--- a/experimental/Intersection/CubicUtilities.cpp
+++ b/experimental/Intersection/CubicUtilities.cpp
@@ -7,6 +7,14 @@
 #include "CubicUtilities.h"
 #include "QuadraticUtilities.h"
 
+double calcPrecision(const Cubic& cubic) {
+    _Rect dRect;
+    dRect.setBounds(cubic);
+    double width = dRect.right - dRect.left;
+    double height = dRect.bottom - dRect.top;
+    return (width > height ? width : height) / 256;
+}
+
 void coefficients(const double* cubic, double& A, double& B, double& C, double& D) {
     A = cubic[6]; // d
     B = cubic[4] * 3; // 3*c
@@ -93,15 +101,6 @@ double derivativeAtT(const double* cubic, double t) {
     return (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
 }
 
-// same as derivativeAtT
-// which is more accurate? which is faster?
-double derivativeAtT_2(const double* cubic, double t) {
-    double a = cubic[2] - cubic[0];
-    double b = cubic[4] - 2 * cubic[2] + cubic[0];
-    double c = cubic[6] + 3 * (cubic[2] - cubic[4]) - cubic[0];
-    return c * c * t * t + 2 * b * t + a;
-}
-
 void dxdy_at_t(const Cubic& cubic, double t, double& dx, double& dy) {
     if (&dx) {
         dx = derivativeAtT(&cubic[0].x, t);
@@ -111,6 +110,17 @@ void dxdy_at_t(const Cubic& cubic, double t, double& dx, double& dy) {
     }
 }
 
+int find_cubic_inflections(const Cubic& src, double tValues[])
+{
+    double Ax = src[1].x - src[0].x;
+    double Ay = src[1].y - src[0].y;
+    double Bx = src[2].x - 2 * src[1].x + src[0].x;
+    double By = src[2].y - 2 * src[1].y + src[0].y;
+    double Cx = src[3].x + 3 * (src[1].x - src[2].x) - src[0].x;
+    double Cy = src[3].y + 3 * (src[1].y - src[2].y) - src[0].y;
+    return quadraticRoots(Bx * Cy - By * Cx, (Ax * Cy - Ay * Cx) / 2, Ax * By - Ay * Bx, tValues);
+}
+
 bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath) {
     double dy = cubic[index].y - cubic[zero].y;
     double dx = cubic[index].x - cubic[zero].x;
diff --git a/experimental/Intersection/CubicUtilities.h b/experimental/Intersection/CubicUtilities.h
index 890ff00..6159472 100644
--- a/experimental/Intersection/CubicUtilities.h
+++ b/experimental/Intersection/CubicUtilities.h
@@ -10,15 +10,18 @@
 #include "DataTypes.h"
 #include "SkTDArray.h"
 
+double calcPrecision(const Cubic& cubic);
 double cube_root(double x);
 int cubic_to_quadratics(const Cubic& cubic, double precision,
         SkTDArray<Quadratic>& quadratics);
+void cubic_to_quadratics(const Cubic& cubic, double precision, SkTDArray<double>& ts);
 void coefficients(const double* cubic, double& A, double& B, double& C, double& D);
 int cubicRoots(double A, double B, double C, double D, double t[3]);
+int cubicRootsX(double A, double B, double C, double D, double s[3]);
+void demote_cubic_to_quad(const Cubic& cubic, Quadratic& quad);
 double derivativeAtT(const double* cubic, double t);
-// competing version that should produce same results
-double derivativeAtT_2(const double* cubic, double t);
 void dxdy_at_t(const Cubic& , double t, double& x, double& y);
+int find_cubic_inflections(const Cubic& src, double tValues[]);
 bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath);
 double secondDerivativeAtT(const double* cubic, double t);
 void xy_at_t(const Cubic& , double t, double& x, double& y);
diff --git a/experimental/Intersection/CurveIntersection.h b/experimental/Intersection/CurveIntersection.h
index 664145b..4b34b31 100644
--- a/experimental/Intersection/CurveIntersection.h
+++ b/experimental/Intersection/CurveIntersection.h
@@ -50,7 +50,11 @@ int horizontalIntersect(const Quadratic& quad, double left, double right,
 int horizontalIntersect(const Quadratic& quad, double left, double right,
         double y, bool flipped, Intersections& );
 bool intersect(const Cubic& cubic1, const Cubic& cubic2, Intersections& );
-int intersect(const Cubic& cubic, const _Line& line, double cRange[3], double lRange[3]);
+// the following flavor uses quadratic approximation instead of convex hulls
+bool intersect2(const Cubic& cubic1, const Cubic& cubic2, Intersections& );
+bool intersect(const Cubic& cubic, Intersections& i); // return true if cubic self-intersects
+int intersect(const Cubic& cubic, const Quadratic& quad, Intersections& );
+int intersect(const Cubic& cubic, const _Line& line, Intersections& );
 bool intersect(const Quadratic& q1, const Quadratic& q2, Intersections& );
 int intersect(const Quadratic& quad, const _Line& line, Intersections& );
 // the following flavor uses the implicit form instead of convex hulls
diff --git a/experimental/Intersection/DataTypes.cpp b/experimental/Intersection/DataTypes.cpp
index 2832ab2..2be8938 100644
--- a/experimental/Intersection/DataTypes.cpp
+++ b/experimental/Intersection/DataTypes.cpp
@@ -74,11 +74,4 @@ int UlpsDiff(float A, float B)
 
     return abs(uA.i - uB.i);
 }
-
-int FloatAsInt(float A)
-{
-    Float_t uA(A);
-    return uA.i;
-}
 #endif
-
diff --git a/experimental/Intersection/DataTypes.h b/experimental/Intersection/DataTypes.h
index 265e3b7..56931d4 100644
--- a/experimental/Intersection/DataTypes.h
+++ b/experimental/Intersection/DataTypes.h
@@ -23,13 +23,9 @@ inline bool AlmostEqualUlps(double A, double B) { return AlmostEqualUlps((float)
 
 // FIXME: delete
 int UlpsDiff(float A, float B);
-int FloatAsInt(float A);
 
-#if defined(IN_TEST)
-// FIXME: move to test-only header
-const double PointEpsilon = 0.000001;
-const double SquaredEpsilon = PointEpsilon * PointEpsilon;
-#endif
+const double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON;
+const double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON);
 
 inline bool approximately_zero(double x) {
 
@@ -47,7 +43,11 @@ inline bool approximately_zero(float x) {
 }
 
 inline bool approximately_zero_squared(double x) {
-    return fabs(x) < FLT_EPSILON * FLT_EPSILON;
+    return fabs(x) < FLT_EPSILON_SQUARED;
+}
+
+inline bool approximately_zero_sqrt(double x) {
+    return fabs(x) < FLT_EPSILON_SQRT;
 }
 
 inline bool approximately_equal(double x, double y) {
@@ -107,7 +107,7 @@ inline bool approximately_positive(double x) {
 }
 
 inline bool approximately_positive_squared(double x) {
-    return x > -(FLT_EPSILON * FLT_EPSILON);
+    return x > -(FLT_EPSILON_SQUARED);
 }
 
 inline bool approximately_zero_or_more(double x) {
@@ -130,6 +130,11 @@ struct _Point {
     double x;
     double y;
 
+    friend _Point operator-(const _Point& a, const _Point& b) {
+        _Point v = {a.x - b.x, a.y - b.y};
+        return v;
+    }
+
     void operator-=(const _Point& v) {
         x -= v.x;
         y -= v.y;
@@ -150,7 +155,10 @@ struct _Point {
         return AlmostEqualUlps((float) x, (float) a.x)
                 && AlmostEqualUlps((float) y, (float) a.y);
     }
-
+    
+    double dot(const _Point& a) {
+        return x * a.x + y * a.y;
+    }
 };
 
 typedef _Point _Line[2];
diff --git a/experimental/Intersection/DataTypes_Test.h b/experimental/Intersection/DataTypes_Test.h
new file mode 100644
index 0000000..a8f14fa
--- /dev/null
+++ b/experimental/Intersection/DataTypes_Test.h
@@ -0,0 +1,7 @@
+#ifndef __DataTypes_Test_h__
+#define __DataTypes_Test_h__
+
+const double PointEpsilon = 0.000001;
+const double SquaredEpsilon = PointEpsilon * PointEpsilon;
+
+#endif
diff --git a/experimental/Intersection/EdgeWalker.cpp b/experimental/Intersection/EdgeWalker.cpp
index 12fe30d..79334b4 100644
--- a/experimental/Intersection/EdgeWalker.cpp
+++ b/experimental/Intersection/EdgeWalker.cpp
@@ -80,7 +80,7 @@ static int CubicLineIntersect(const SkPoint a[2], const SkPoint b[3],
     const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
             {a[3].fX, a[3].fY}};
     const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
-    return intersect(aCubic, bLine, intersections.fT[0], intersections.fT[1]);
+    return intersect(aCubic, bLine, intersections);
 }
 
 static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
diff --git a/experimental/Intersection/Intersection_Tests.cpp b/experimental/Intersection/Intersection_Tests.cpp
index 6bad957..8e6e63e 100644
--- a/experimental/Intersection/Intersection_Tests.cpp
+++ b/experimental/Intersection/Intersection_Tests.cpp
@@ -15,9 +15,12 @@ void cubecode_test(int test);
 void Intersection_Tests() {
     int testsRun = 0;
 
+    QuadraticIntersection_Test();
+    CubicIntersection_OneOffTest();
+    CubicIntersection_RandTest();
+    SimplifyNew_Test();
     CubicsToQuadratics_RandTest();
     CubicToQuadratics_Test();
-    SimplifyNew_Test();
     Simplify4x4RectsThreaded_Test(testsRun);
     Simplify4x4QuadraticsThreaded_Test(testsRun);
     QuadLineIntersectThreaded_Test(testsRun);
@@ -26,7 +29,6 @@ void Intersection_Tests() {
     Simplify4x4QuadralateralsThreaded_Test(testsRun);
     ShapeOps4x4RectsThreaded_Test(testsRun);
     SkDebugf("%s total testsRun=%d\n", __FUNCTION__, testsRun);
-    QuadraticIntersection_Test();
     LineQuadraticIntersection_Test();
     MiniSimplify_Test();
     SimplifyAngle_Test();
diff --git a/experimental/Intersection/Intersection_Tests.h b/experimental/Intersection/Intersection_Tests.h
index 7da4e09..2ca1e05 100644
--- a/experimental/Intersection/Intersection_Tests.h
+++ b/experimental/Intersection/Intersection_Tests.h
@@ -4,16 +4,16 @@
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
-#if !defined(IN_TEST)
-    #define IN_TEST 1
-#endif
+#include "DataTypes_Test.h"
 
 void ActiveEdge_Test();
 void ConvexHull_Test();
 void ConvexHull_X_Test();
 void CubicBezierClip_Test();
 void CubicCoincidence_Test();
+void CubicIntersection_OneOffTest();
 void CubicIntersection_Test();
+void CubicIntersection_RandTest();
 void CubicParameterization_Test();
 void CubicReduceOrder_Test();
 void CubicsToQuadratics_RandTest();
diff --git a/experimental/Intersection/Intersections.cpp b/experimental/Intersection/Intersections.cpp
index 3f4e8cf..d1e0f9b 100644
--- a/experimental/Intersection/Intersections.cpp
+++ b/experimental/Intersection/Intersections.cpp
@@ -8,9 +8,108 @@
 #include "DataTypes.h"
 #include "Intersections.h"
 
+void Intersections::addCoincident(double s1, double e1, double s2, double e2) {
+    assert((fCoincidentUsed & 1) != 1);
+    for (int index = 0; index < fCoincidentUsed; index += 2) {
+        double cs1 = fCoincidentT[fSwap][index];
+        double ce1 = fCoincidentT[fSwap][index + 1];
+        bool s1in = approximately_between(cs1, s1, ce1);
+        bool e1in = approximately_between(cs1, e1, ce1);
+        double cs2 = fCoincidentT[fSwap ^ 1][index];
+        double ce2 = fCoincidentT[fSwap ^ 1][index + 1];
+        bool s2in = approximately_between(cs2, s2, ce2);
+        bool e2in = approximately_between(cs2, e2, ce2);
+        if ((s1in | e1in) & (s2in | e2in)) {
+            double lesser1 = std::min(cs1, ce1);
+            index += cs1 > ce1;
+            if (s1in < lesser1) {
+                fCoincidentT[fSwap][index] = s1in;
+            } else if (e1in < lesser1) {
+                fCoincidentT[fSwap][index] = e1in;
+            }
+            index ^= 1;
+            double greater1 = fCoincidentT[fSwap][index];
+            if (s1in > greater1) {
+                fCoincidentT[fSwap][index] = s1in;
+            } else if (e1in > greater1) {
+                fCoincidentT[fSwap][index] = e1in;
+            }
+            index &= ~1;
+            double lesser2 = std::min(cs2, ce2);
+            index += cs2 > ce2;
+            if (s2in < lesser2) {
+                fCoincidentT[fSwap ^ 1][index] = s2in;
+            } else if (e2in < lesser2) {
+                fCoincidentT[fSwap ^ 1][index] = e2in;
+            }
+            index ^= 1;
+            double greater2 = fCoincidentT[fSwap ^ 1][index];
+            if (s2in > greater2) {
+                fCoincidentT[fSwap ^ 1][index] = s2in;
+            } else if (e2in > greater2) {
+                fCoincidentT[fSwap ^ 1][index] = e2in;
+            }
+            return;
+        }
+    }
+    assert(fCoincidentUsed < 9);
+    fCoincidentT[fSwap][fCoincidentUsed] = s1;
+    fCoincidentT[fSwap ^ 1][fCoincidentUsed] = s2;
+    ++fCoincidentUsed;
+    fCoincidentT[fSwap][fCoincidentUsed] = e1;
+    fCoincidentT[fSwap ^ 1][fCoincidentUsed] = e2;
+    ++fCoincidentUsed;
+}
+
 void Intersections::cleanUp() {
     assert(fCoincidentUsed);
     assert(fUsed);
     // find any entries in fT that could be part of the coincident range
 
 }
+
+void Intersections::insert(double one, double two) {
+    assert(fUsed <= 1 || fT[0][0] < fT[0][1]);
+    int index;
+    for (index = 0; index < fUsed; ++index) {
+        if (approximately_equal(fT[0][index], one)
+                && approximately_equal(fT[1][index], two)) {
+            return;
+        }
+        if (fT[0][index] > one) {
+            break;
+        }
+    }
+    assert(fUsed < 9);
+    int remaining = fUsed - index;
+    if (remaining > 0) {
+        memmove(&fT[0][index + 1], &fT[0][index], sizeof(fT[0][0]) * remaining);
+        memmove(&fT[1][index + 1], &fT[1][index], sizeof(fT[1][0]) * remaining);
+    }
+    fT[0][index] = one;
+    fT[1][index] = two;
+    ++fUsed;
+}
+
+// FIXME: all callers should be moved to regular insert. Failures are likely
+// if two separate callers differ on whether ts are equal or not
+void Intersections::insertOne(double t, int side) {
+    int used = side ? fUsed2 : fUsed;
+    assert(used <= 1 || fT[side][0] < fT[side][1]);
+    int index;
+    for (index = 0; index < used; ++index) {
+        if (approximately_equal(fT[side][index], t)) {
+            return;
+        }
+        if (fT[side][index] > t) {
+            break;
+        }
+    }
+    assert(used < 9);
+    int remaining = used - index;
+    if (remaining > 0) {
+        memmove(&fT[side][index + 1], &fT[side][index], sizeof(fT[side][0]) * remaining);
+    }
+    fT[side][index] = t;
+    side ? ++fUsed2 : ++fUsed;
+}
diff --git a/experimental/Intersection/Intersections.h b/experimental/Intersection/Intersections.h
index fe12b25..618c2c1 100644
--- a/experimental/Intersection/Intersections.h
+++ b/experimental/Intersection/Intersections.h
@@ -7,7 +7,8 @@
 #ifndef Intersections_DEFINE
 #define Intersections_DEFINE
 
-#include <algorithm> // for std::min
+#include <algorithm> // for std::min -- Skia doesn't have a SkMinDouble
+#include "SkTypes.h"
 
 class Intersections {
 public:
@@ -15,8 +16,9 @@ public:
         : fUsed(0)
         , fUsed2(0)
         , fCoincidentUsed(0)
+        , fFlip(false)
+        , fUnsortable(false)
         , fSwap(0)
-        , fFlip(0)
     {
         // OPTIMIZE: don't need to be initialized in release
         bzero(fT, sizeof(fT));
@@ -50,64 +52,13 @@ public:
         ++fCoincidentUsed;
     }
 
-    void addCoincident(double s1, double e1, double s2, double e2) {
-        assert((fCoincidentUsed & 1) != 1);
-        for (int index = 0; index < fCoincidentUsed; index += 2) {
-            double cs1 = fCoincidentT[fSwap][index];
-            double ce1 = fCoincidentT[fSwap][index + 1];
-            bool s1in = approximately_between(cs1, s1, ce1);
-            bool e1in = approximately_between(cs1, e1, ce1);
-            double cs2 = fCoincidentT[fSwap ^ 1][index];
-            double ce2 = fCoincidentT[fSwap ^ 1][index + 1];
-            bool s2in = approximately_between(cs2, s2, ce2);
-            bool e2in = approximately_between(cs2, e2, ce2);
-            if ((s1in | e1in) & (s2in | e2in)) {
-                double lesser1 = std::min(cs1, ce1);
-                index += cs1 > ce1;
-                if (s1in < lesser1) {
-                    fCoincidentT[fSwap][index] = s1in;
-                } else if (e1in < lesser1) {
-                    fCoincidentT[fSwap][index] = e1in;
-                }
-                index ^= 1;
-                double greater1 = fCoincidentT[fSwap][index];
-                if (s1in > greater1) {
-                    fCoincidentT[fSwap][index] = s1in;
-                } else if (e1in > greater1) {
-                    fCoincidentT[fSwap][index] = e1in;
-                }
-                index &= ~1;
-                double lesser2 = std::min(cs2, ce2);
-                index += cs2 > ce2;
-                if (s2in < lesser2) {
-                    fCoincidentT[fSwap ^ 1][index] = s2in;
-                } else if (e2in < lesser2) {
-                    fCoincidentT[fSwap ^ 1][index] = e2in;
-                }
-                index ^= 1;
-                double greater2 = fCoincidentT[fSwap ^ 1][index];
-                if (s2in > greater2) {
-                    fCoincidentT[fSwap ^ 1][index] = s2in;
-                } else if (e2in > greater2) {
-                    fCoincidentT[fSwap ^ 1][index] = e2in;
-                }
-                return;
-            }
-        }
-        assert(fCoincidentUsed < 9);
-        fCoincidentT[fSwap][fCoincidentUsed] = s1;
-        fCoincidentT[fSwap ^ 1][fCoincidentUsed] = s2;
-        ++fCoincidentUsed;
-        fCoincidentT[fSwap][fCoincidentUsed] = e1;
-        fCoincidentT[fSwap ^ 1][fCoincidentUsed] = e2;
-        ++fCoincidentUsed;
-    }
+    void addCoincident(double s1, double e1, double s2, double e2);
 
     // FIXME: this is necessary because curve/curve intersections are noisy
     // remove once curve/curve intersections are improved
     void cleanUp();
 
-    int coincidentUsed() {
+    int coincidentUsed() const{
         return fCoincidentUsed;
     }
 
@@ -120,51 +71,8 @@ public:
         }
     }
 
-    void insert(double one, double two) {
-        assert(fUsed <= 1 || fT[0][0] < fT[0][1]);
-        int index;
-        for (index = 0; index < fUsed; ++index) {
-            if (approximately_equal(fT[0][index], one)
-                    && approximately_equal(fT[1][index], two)) {
-                return;
-            }
-            if (fT[0][index] > one) {
-                break;
-            }
-        }
-        assert(fUsed < 9);
-        int remaining = fUsed - index;
-        if (remaining > 0) {
-            memmove(&fT[0][index + 1], &fT[0][index], sizeof(fT[0][0]) * remaining);
-            memmove(&fT[1][index + 1], &fT[1][index], sizeof(fT[1][0]) * remaining);
-        }
-        fT[0][index] = one;
-        fT[1][index] = two;
-        ++fUsed;
-    }
-
-    // FIXME: all callers should be moved to regular insert. Failures are likely
-    // if two separate callers differ on whether ts are equal or not
-    void insertOne(double t, int side) {
-        int used = side ? fUsed2 : fUsed;
-        assert(used <= 1 || fT[side][0] < fT[side][1]);
-        int index;
-        for (index = 0; index < used; ++index) {
-            if (approximately_equal(fT[side][index], t)) {
-                return;
-            }
-            if (fT[side][index] > t) {
-                break;
-            }
-        }
-        assert(used < 9);
-        int remaining = used - index;
-        if (remaining > 0) {
-            memmove(&fT[side][index + 1], &fT[side][index], sizeof(fT[side][0]) * remaining);
-        }
-        fT[side][index] = t;
-        side ? ++fUsed2 : ++fUsed;
-    }
+    void insert(double one, double two);
+    void insertOne(double t, int side);
 
     bool intersected() const {
         return fUsed > 0;
@@ -175,14 +83,25 @@ public:
     }
 
     void swap() {
-        fSwap ^= 1;
+        fSwap ^= true;
+    }
+    
+    void swapPts() {
+        int index;
+        for (index = 0; index < fUsed; ++index) {
+            SkTSwap(fT[0][index], fT[1][index]);
+        }
     }
 
-    bool swapped() {
+    bool swapped() const {
         return fSwap;
     }
 
-    int used() {
+    bool unsortable() const {
+        return fUnsortable;
+    }
+
+    int used() const {
         return fUsed;
     }
 
@@ -191,10 +110,10 @@ public:
     int fUsed;
     int fUsed2;
     int fCoincidentUsed;
-    int fFlip;
+    bool fFlip;
+    bool fUnsortable;
 private:
     int fSwap;
 };
 
 #endif
-
diff --git a/experimental/Intersection/LineCubicIntersection.cpp b/experimental/Intersection/LineCubicIntersection.cpp
index 91a0b7d..333e30f 100644
--- a/experimental/Intersection/LineCubicIntersection.cpp
+++ b/experimental/Intersection/LineCubicIntersection.cpp
@@ -77,160 +77,213 @@ So the cubic coefficients are:
 
  */
 
-class LineCubicIntersections : public Intersections {
+class LineCubicIntersections {
 public:
 
-LineCubicIntersections(const Cubic& c, const _Line& l, double r[3])
+LineCubicIntersections(const Cubic& c, const _Line& l, Intersections& i)
     : cubic(c)
     , line(l)
-    , range(r) {
+    , intersections(i) {
 }
 
-int intersect() {
-    double slope;
-    double axisIntercept;
-    moreHorizontal = implicitLine(line, slope, axisIntercept);
+// see parallel routine in line quadratic intersections
+int intersectRay(double roots[3]) {
+    double adj = line[1].x - line[0].x;
+    double opp = line[1].y - line[0].y;
+    Cubic r;
+    for (int n = 0; n < 4; ++n) {
+        r[n].x = (cubic[n].y - line[0].y) * adj - (cubic[n].x - line[0].x) * opp;
+    }
     double A, B, C, D;
-    coefficients(&cubic[0].x, A, B, C, D);
-    double E, F, G, H;
-    coefficients(&cubic[0].y, E, F, G, H);
-    if (moreHorizontal) {
-        A = A * slope - E;
-        B = B * slope - F;
-        C = C * slope - G;
-        D = D * slope - H + axisIntercept;
-    } else {
-        A = A - E * slope;
-        B = B - F * slope;
-        C = C - G * slope;
-        D = D - H * slope - axisIntercept;
-    }
-    return cubicRoots(A, B, C, D, range);
-}
-
-int horizontalIntersect(double axisIntercept) {
+    coefficients(&r[0].x, A, B, C, D);
+    return cubicRoots(A, B, C, D, roots);
+}
+
+int intersect() {
+    addEndPoints();
+    double rootVals[3];
+    int roots = intersectRay(rootVals);
+    for (int index = 0; index < roots; ++index) {
+        double cubicT = rootVals[index];
+        double lineT = findLineT(cubicT);
+        if (pinTs(cubicT, lineT)) {
+            intersections.insert(cubicT, lineT);
+        }
+    }
+    return intersections.fUsed;
+}
+
+int horizontalIntersect(double axisIntercept, double roots[3]) {
     double A, B, C, D;
     coefficients(&cubic[0].y, A, B, C, D);
     D -= axisIntercept;
-    return cubicRoots(A, B, C, D, range);
+    return cubicRoots(A, B, C, D, roots);
 }
 
-int verticalIntersect(double axisIntercept) {
+int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) {
+    addHorizontalEndPoints(left, right, axisIntercept);
+    double rootVals[3];
+    int roots = horizontalIntersect(axisIntercept, rootVals);
+    for (int index = 0; index < roots; ++index) {
+        double x;
+        double cubicT = rootVals[index];
+        xy_at_t(cubic, cubicT, x, *(double*) NULL);
+        double lineT = (x - left) / (right - left);
+        if (pinTs(cubicT, lineT)) {
+            intersections.insert(cubicT, lineT);
+        }
+    }
+    if (flipped) {
+        flip();
+    }
+    return intersections.fUsed;
+}
+
+int verticalIntersect(double axisIntercept, double roots[3]) {
     double A, B, C, D;
     coefficients(&cubic[0].x, A, B, C, D);
     D -= axisIntercept;
-    return cubicRoots(A, B, C, D, range);
+    return cubicRoots(A, B, C, D, roots);
+}
+
+int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) {
+    addVerticalEndPoints(top, bottom, axisIntercept);
+    double rootVals[3];
+    int roots = verticalIntersect(axisIntercept, rootVals);
+    for (int index = 0; index < roots; ++index) {
+        double y;
+        double cubicT = rootVals[index];
+        xy_at_t(cubic, cubicT, *(double*) NULL, y);
+        double lineT = (y - top) / (bottom - top);
+        if (pinTs(cubicT, lineT)) {
+            intersections.insert(cubicT, lineT);
+        }
+    }
+    if (flipped) {
+        flip();
+    }
+    return intersections.fUsed;
+}
+
+protected:
+
+void addEndPoints()
+{
+    for (int cIndex = 0; cIndex < 4; cIndex += 3) {
+        for (int lIndex = 0; lIndex < 2; lIndex++) {
+            if (cubic[cIndex] == line[lIndex]) {
+                intersections.insert(cIndex >> 1, lIndex);
+            }
+        }
+    }
+}
+
+void addHorizontalEndPoints(double left, double right, double y)
+{
+    for (int cIndex = 0; cIndex < 4; cIndex += 3) {
+        if (cubic[cIndex].y != y) {
+            continue;
+        }
+        if (cubic[cIndex].x == left) {
+            intersections.insert(cIndex >> 1, 0);
+        }
+        if (cubic[cIndex].x == right) {
+            intersections.insert(cIndex >> 1, 1);
+        }
+    }
+}
+
+void addVerticalEndPoints(double top, double bottom, double x)
+{
+    for (int cIndex = 0; cIndex < 4; cIndex += 3) {
+        if (cubic[cIndex].x != x) {
+            continue;
+        }
+        if (cubic[cIndex].y == top) {
+            intersections.insert(cIndex >> 1, 0);
+        }
+        if (cubic[cIndex].y == bottom) {
+            intersections.insert(cIndex >> 1, 1);
+        }
+    }
 }
 
 double findLineT(double t) {
-    const double* cPtr;
-    const double* lPtr;
-    if (moreHorizontal) {
-        cPtr = &cubic[0].x;
-        lPtr = &line[0].x;
-    } else {
-        cPtr = &cubic[0].y;
-        lPtr = &line[0].y;
-    }
-    // FIXME: should fold the following in with TestUtilities.cpp xy_at_t()
-    double s = 1 - t;
-    double cubicVal = cPtr[0] * s * s * s + 3 * cPtr[2] * s * s * t
-                + 3 * cPtr[4] * s * t * t + cPtr[6] * t * t * t;
-    return (cubicVal - lPtr[0]) / (lPtr[2] - lPtr[0]);
+    double x, y;
+    xy_at_t(cubic, t, x, y);
+    double dx = line[1].x - line[0].x;
+    double dy = line[1].y - line[0].y;
+    if (fabs(dx) > fabs(dy)) {
+        return (x - line[0].x) / dx;
+    }
+    return (y - line[0].y) / dy;
+}
+
+void flip() {
+    // OPTIMIZATION: instead of swapping, pass original line, use [1].y - [0].y
+    int roots = intersections.fUsed;
+    for (int index = 0; index < roots; ++index) {
+        intersections.fT[1][index] = 1 - intersections.fT[1][index];
+    }
+}
+
+bool pinTs(double& cubicT, double& lineT) {
+    if (!approximately_one_or_less(lineT)) {
+        return false;
+    }
+    if (!approximately_zero_or_more(lineT)) {
+        return false;
+    }
+    if (cubicT < 0) {
+        cubicT = 0;
+    } else if (cubicT > 1) {
+        cubicT = 1;
+    }
+    if (lineT < 0) {
+        lineT = 0;
+    } else if (lineT > 1) {
+        lineT = 1;
+    }
+    return true;
 }
 
 private:
 
 const Cubic& cubic;
 const _Line& line;
-double* range;
-bool moreHorizontal;
-
+Intersections& intersections;
 };
 
-int horizontalIntersect(const Cubic& cubic, double y, double tRange[3]) {
-    LineCubicIntersections c(cubic, *((_Line*) 0), tRange);
-    return c.horizontalIntersect(y);
-}
-
 int horizontalIntersect(const Cubic& cubic, double left, double right, double y,
         double tRange[3]) {
-    LineCubicIntersections c(cubic, *((_Line*) 0), tRange);
-    int result = c.horizontalIntersect(y);
-    for (int index = 0; index < result; ) {
+    LineCubicIntersections c(cubic, *((_Line*) 0), *((Intersections*) 0));
+    double rootVals[3];
+    int result = c.horizontalIntersect(y, rootVals);
+    int tCount = 0;
+    for (int index = 0; index < result; ++index) {
         double x, y;
-        xy_at_t(cubic, tRange[index], x, y);
+        xy_at_t(cubic, rootVals[index], x, y);
         if (x < left || x > right) {
-            if (--result > index) {
-                tRange[index] = tRange[result];
-            }
             continue;
         }
-        ++index;
+        tRange[tCount++] = rootVals[index];
     }
     return result;
 }
 
 int horizontalIntersect(const Cubic& cubic, double left, double right, double y,
         bool flipped, Intersections& intersections) {
-    LineCubicIntersections c(cubic, *((_Line*) 0), intersections.fT[0]);
-    int result = c.horizontalIntersect(y);
-    for (int index = 0; index < result; ) {
-        double x, y;
-        xy_at_t(cubic, intersections.fT[0][index], x, y);
-        if (x < left || x > right) {
-            if (--result > index) {
-                intersections.fT[0][index] = intersections.fT[0][result];
-            }
-            continue;
-        }
-        intersections.fT[1][index] = (x - left) / (right - left);
-        ++index;
-    }
-    if (flipped) {
-        // OPTIMIZATION: instead of swapping, pass original line, use [1].x - [0].x
-        for (int index = 0; index < result; ++index) {
-            intersections.fT[1][index] = 1 - intersections.fT[1][index];
-        }
-    }
-    return result;
+    LineCubicIntersections c(cubic, *((_Line*) 0), intersections);
+    return c.horizontalIntersect(y, left, right, flipped);
 }
 
 int verticalIntersect(const Cubic& cubic, double top, double bottom, double x,
         bool flipped, Intersections& intersections) {
-    LineCubicIntersections c(cubic, *((_Line*) 0), intersections.fT[0]);
-    int result = c.verticalIntersect(x);
-    for (int index = 0; index < result; ) {
-        double x, y;
-        xy_at_t(cubic, intersections.fT[0][index], x, y);
-        if (y < top || y > bottom) {
-            if (--result > index) {
-                intersections.fT[1][index] = intersections.fT[0][result];
-            }
-            continue;
-        }
-        intersections.fT[0][index] = (y - top) / (bottom - top);
-        ++index;
-    }
-    if (flipped) {
-        // OPTIMIZATION: instead of swapping, pass original line, use [1].x - [0].x
-        for (int index = 0; index < result; ++index) {
-            intersections.fT[1][index] = 1 - intersections.fT[1][index];
-        }
-    }
-    return result;
+    LineCubicIntersections c(cubic, *((_Line*) 0), intersections);
+    return c.verticalIntersect(x, top, bottom, flipped);
 }
 
-int intersect(const Cubic& cubic, const _Line& line, double cRange[3], double lRange[3]) {
-    LineCubicIntersections c(cubic, line, cRange);
-    int roots;
-    if (AlmostEqualUlps(line[0].y, line[1].y)) {
-        roots = c.horizontalIntersect(line[0].y);
-    } else {
-        roots = c.intersect();
-    }
-    for (int index = 0; index < roots; ++index) {
-        lRange[index] = c.findLineT(cRange[index]);
-    }
-    return roots;
+int intersect(const Cubic& cubic, const _Line& line, Intersections& i) {
+    LineCubicIntersections c(cubic, line, i);
+    return c.intersect();
 }
diff --git a/experimental/Intersection/LineCubicIntersection_Test.cpp b/experimental/Intersection/LineCubicIntersection_Test.cpp
index 48754dd..b81a87e 100644
--- a/experimental/Intersection/LineCubicIntersection_Test.cpp
+++ b/experimental/Intersection/LineCubicIntersection_Test.cpp
@@ -36,8 +36,10 @@ void LineCubicIntersection_Test() {
             printf("[%d] line order=%d\n", (int) index, order2);
         }
         if (order1 == 4 && order2 == 2) {
-            double range1[2], range2[2];
-            int roots = intersect(reduce1, reduce2, range1, range2);
+            Intersections i;
+            double* range1 = i.fT[0];
+            double* range2 = i.fT[1];
+            int roots = intersect(reduce1, reduce2, i);
             for (int pt = 0; pt < roots; ++pt) {
                 double tt1 = range1[pt];
                 double tx1, ty1;
diff --git a/experimental/Intersection/LineIntersection.cpp b/experimental/Intersection/LineIntersection.cpp
index ab23c44..5308a26 100644
--- a/experimental/Intersection/LineIntersection.cpp
+++ b/experimental/Intersection/LineIntersection.cpp
@@ -9,12 +9,28 @@
 #include "LineIntersection.h"
 #include <algorithm> // used for std::swap
 
+/* Determine the intersection point of two lines. This assumes the lines are not parallel,
+   and that that the lines are infinite.
+   From http://en.wikipedia.org/wiki/Line-line_intersection
+ */
+void lineIntersect(const _Line& a, const _Line& b, _Point& p) {
+    double axLen = a[1].x - a[0].x;
+    double ayLen = a[1].y - a[0].y;
+    double bxLen = b[1].x - b[0].x;
+    double byLen = b[1].y - b[0].y;
+    double denom = byLen * axLen - ayLen * bxLen;
+    assert(denom);
+    double term1 = a[1].x * a[0].y - a[1].y * a[0].x;
+    double term2 = b[1].x * b[0].y - b[1].y * b[0].x;
+    p.x = (term1 * bxLen - axLen * term2) / denom;
+    p.y = (term1 * byLen - ayLen * term2) / denom;
+}
 
 /*
    Determine the intersection point of two line segments
    Return FALSE if the lines don't intersect
    from: http://paulbourke.net/geometry/lineline2d/
-*/
+ */
 
 int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]) {
     double axLen = a[1].x - a[0].x;
@@ -27,7 +43,7 @@ int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]
              byLen  * axLen         ==  ayLen          * bxLen
              byLen  * axLen         -   ayLen          * bxLen == 0 ( == denom )
      */
-    double denom  = byLen * axLen - ayLen * bxLen;
+    double denom = byLen * axLen - ayLen * bxLen;
     if (approximately_zero(denom)) {
        /* See if the axis intercepts match:
                   ay - ax * ayLen / axLen  ==          by - bx * ayLen / axLen
diff --git a/experimental/Intersection/LineIntersection.h b/experimental/Intersection/LineIntersection.h
index 33076b6..adb5789 100644
--- a/experimental/Intersection/LineIntersection.h
+++ b/experimental/Intersection/LineIntersection.h
@@ -12,9 +12,10 @@
 int horizontalIntersect(const _Line& line, double y, double tRange[2]);
 int horizontalLineIntersect(const _Line& line, double left, double right,
         double y, double tRange[2]);
-int verticalLineIntersect(const _Line& line, double top, double bottom,
-        double x, double tRange[2]);
+void lineIntersect(const _Line& a, const _Line& b, _Point& p);
 int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]);
 bool testIntersect(const _Line& a, const _Line& b);
+int verticalLineIntersect(const _Line& line, double top, double bottom,
+        double x, double tRange[2]);
 
 #endif
diff --git a/experimental/Intersection/LineParameters.h b/experimental/Intersection/LineParameters.h
index fc1bcc8..8155ad8 100644
--- a/experimental/Intersection/LineParameters.h
+++ b/experimental/Intersection/LineParameters.h
@@ -80,15 +80,9 @@ public:
         }
     }
 
-    void controlPtDistance(const Cubic& pts, double distance[2]) const {
-        for (int index = 0; index < 2; ++index) {
-            distance[index] = a * pts[index + 1].x + b * pts[index + 1].y + c;
-        }
-    }
-
-    void controlPtDistance(const Cubic& pts, int i, int j, double distance[2]) const {
-        distance[0] = a * pts[i].x + b * pts[i].y + c;
-        distance[1] = a * pts[j].x + b * pts[j].y + c;
+    double controlPtDistance(const Cubic& pts, int index) const {
+        assert(index == 1 || index == 2);
+        return a * pts[index].x + b * pts[index].y + c;
     }
 
     double controlPtDistance(const Quadratic& pts) const {
diff --git a/experimental/Intersection/LineParameteters_Test.cpp b/experimental/Intersection/LineParameteters_Test.cpp
index 6d85325..326477e 100644
--- a/experimental/Intersection/LineParameteters_Test.cpp
+++ b/experimental/Intersection/LineParameteters_Test.cpp
@@ -45,7 +45,8 @@ void LineParameter_Test() {
         const Cubic& cubic = tests[index];
         lineParameters.cubicEndPoints(cubic);
         double denormalizedDistance[2];
-        lineParameters.controlPtDistance(cubic, denormalizedDistance);
+        denormalizedDistance[0] = lineParameters.controlPtDistance(cubic, 1);
+        denormalizedDistance[1] = lineParameters.controlPtDistance(cubic, 2);
         double normalSquared = lineParameters.normalSquared();
         size_t inner;
         for (inner = 0; inner < 2; ++inner) {
@@ -64,7 +65,8 @@ void LineParameter_Test() {
         }
         lineParameters.normalize();
         double normalizedDistance[2];
-        lineParameters.controlPtDistance(cubic, normalizedDistance);
+        normalizedDistance[0] = lineParameters.controlPtDistance(cubic, 1);
+        normalizedDistance[1] = lineParameters.controlPtDistance(cubic, 2);
         for (inner = 0; inner < 2; ++inner) {
             if (AlmostEqualUlps(fabs(normalizedDistance[inner]), answers[index][inner])) {
                 continue;
diff --git a/experimental/Intersection/QuadraticImplicit.cpp b/experimental/Intersection/QuadraticImplicit.cpp
index d892ae9..72a4186 100644
--- a/experimental/Intersection/QuadraticImplicit.cpp
+++ b/experimental/Intersection/QuadraticImplicit.cpp
@@ -5,11 +5,15 @@
 // http://planetmath.org/encyclopedia/GaloisTheoreticDerivationOfTheQuarticFormula.html#step
 
 
+#include "CubicUtilities.h"
 #include "CurveIntersection.h"
 #include "Intersections.h"
 #include "QuadraticParameterization.h"
 #include "QuarticRoot.h"
 #include "QuadraticUtilities.h"
+#include "TSearch.h"
+
+#include <algorithm> // for std::min, max
 
 /* given the implicit form 0 = Ax^2 + Bxy + Cy^2 + Dx + Ey + F
  * and given x = at^2 + bt + c  (the parameterized form)
@@ -17,8 +21,15 @@
  * then
  * 0 = A(at^2+bt+c)(at^2+bt+c)+B(at^2+bt+c)(dt^2+et+f)+C(dt^2+et+f)(dt^2+et+f)+D(at^2+bt+c)+E(dt^2+et+f)+F
  */
+ 
+#if SK_DEBUG
+#define QUARTIC_DEBUG 1
+#else
+#define QUARTIC_DEBUG 0
+#endif
 
-static int findRoots(const QuadImplicitForm& i, const Quadratic& q2, double roots[4]) {
+static int findRoots(const QuadImplicitForm& i, const Quadratic& q2, double roots[4],
+        bool useCubic, bool& disregardCount) {
     double a, b, c;
     set_abc(&q2[0].x, a, b, c);
     double d, e, f;
@@ -45,6 +56,42 @@ static int findRoots(const QuadImplicitForm& i, const Quadratic& q2, double root
                     +     i.x()  *  c
                     +     i.y()  *  f
                     +     i.c();
+#if QUARTIC_DEBUG
+    // create a string mathematica understands
+    char str[1024];
+    bzero(str, sizeof(str));
+    sprintf(str, "Solve[%1.19g x^4 + %1.19g x^3 + %1.19g x^2 + %1.19g x + %1.19g == 0, x]",
+        t4, t3, t2, t1, t0);
+#endif
+    if (approximately_zero(t4)) {
+        disregardCount = true;
+        if (approximately_zero(t3)) {
+            return quadraticRootsX(t2, t1, t0, roots);
+        }
+        return cubicRootsX(t3, t2, t1, t0, roots);
+    }
+    if (approximately_zero(t0)) { // 0 is one root
+        disregardCount = true;
+        int num = cubicRootsX(t4, t3, t2, t1, roots);
+        for (int i = 0; i < num; ++i) {
+            if (approximately_zero(roots[i])) {
+                return num;
+            }
+        }
+        roots[num++] = 0;
+        return num;
+    }
+    if (useCubic) {
+        assert(approximately_zero(t4 + t3 + t2 + t1 + t0)); // 1 is one root
+        int num = cubicRootsX(t4, t4 + t3, -(t1 + t0), -t0, roots); // note that -C==A+B+D+E
+        for (int i = 0; i < num; ++i) {
+            if (approximately_equal(roots[i], 1)) {
+                return num;
+            }
+        }
+        roots[num++] = 1;
+        return num;
+    }
     return quarticRoots(t4, t3, t2, t1, t0, roots);
 }
 
@@ -83,7 +130,9 @@ static bool onlyEndPtsInCommon(const Quadratic& q1, const Quadratic& q2, Interse
         double adj = endPt[1]->x - origX;
         double opp = endPt[1]->y - origY;
         double sign = (q1[oddMan].y - origY) * adj - (q1[oddMan].x - origX) * opp;
-        assert(!approximately_zero(sign));
+        if (approximately_zero(sign)) {
+            goto tryNextHalfPlane;
+        }
         for (int n = 0; n < 3; ++n) {
             double test = (q2[n].y - origY) * adj - (q2[n].x - origX) * opp;
             if (test * sign > 0) {
@@ -105,12 +154,227 @@ tryNextHalfPlane:
     return false;
 }
 
+// http://www.blackpawn.com/texts/pointinpoly/default.html
+static bool pointInTriangle(const _Point& pt, const _Line* testLines[]) {
+    const _Point& A = (*testLines[0])[0];
+    const _Point& B = (*testLines[1])[0];
+    const _Point& C = (*testLines[2])[0];
+
+// Compute vectors        
+    _Point v0 = C - A;
+    _Point v1 = B - A;
+    _Point v2 = pt - A;
+
+// Compute dot products
+    double dot00 = v0.dot(v0);
+    double dot01 = v0.dot(v1);
+    double dot02 = v0.dot(v2);
+    double dot11 = v1.dot(v1);
+    double dot12 = v1.dot(v2);
+
+// Compute barycentric coordinates
+    double invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
+    double u = (dot11 * dot02 - dot01 * dot12) * invDenom;
+    double v = (dot00 * dot12 - dot01 * dot02) * invDenom;
+
+// Check if point is in triangle
+    return (u >= 0) && (v >= 0) && (u + v < 1);
+}
+
+static bool addIntercept(const Quadratic& q1, const Quadratic& q2, double tMin, double tMax,
+        Intersections& i) {
+    double tMid = (tMin + tMax) / 2;
+    _Point mid;
+    xy_at_t(q2, tMid, mid.x, mid.y);
+    _Line line;
+    line[0] = line[1] = mid;
+    double dx, dy;
+    dxdy_at_t(q2, tMid, dx, dy);
+    line[0].x -= dx;
+    line[0].y -= dy;
+    line[1].x += dx;
+    line[1].y += dy;
+    Intersections rootTs;
+    int roots = intersect(q1, line, rootTs);
+    assert(roots == 1);
+    _Point pt2;
+    xy_at_t(q1, rootTs.fT[0][0], pt2.x, pt2.y);
+    if (!pt2.approximatelyEqual(mid)) {
+        return false;
+    }
+    i.add(rootTs.fT[0][0], tMid);
+    return true;
+}
+
+static bool isLinearInner(const Quadratic& q1, double t1s, double t1e, const Quadratic& q2,
+        double t2s, double t2e, Intersections& i) {
+    Quadratic hull;
+    sub_divide(q1, t1s, t1e, hull);
+    _Line line = {hull[2], hull[0]};
+    const _Line* testLines[] = { &line, (const _Line*) &hull[0], (const _Line*) &hull[1] };
+    size_t testCount = sizeof(testLines) / sizeof(testLines[0]);
+    SkTDArray<double> tsFound;
+    for (size_t index = 0; index < testCount; ++index) {
+        Intersections rootTs;
+        int roots = intersect(q2, *testLines[index], rootTs);
+        for (int idx2 = 0; idx2 < roots; ++idx2) {
+            double t = rootTs.fT[0][idx2];
+            if (approximately_negative(t - t2s) || approximately_positive(t - t2e)) {
+                continue;
+            }
+            *tsFound.append() = rootTs.fT[0][idx2];
+        }
+    }
+    int tCount = tsFound.count();
+    if (!tCount) {
+        return true;
+    }
+    double tMin, tMax;
+    _Point dxy1, dxy2;
+    if (tCount == 1) {
+        tMin = tMax = tsFound[0];
+    } else if (tCount > 1) {
+        QSort<double>(tsFound.begin(), tsFound.end() - 1);
+        tMin = tsFound[0];
+        tMax = tsFound[1];
+    }
+    _Point end;
+    xy_at_t(q2, t2s, end.x, end.y);
+    bool startInTriangle = pointInTriangle(end, testLines);
+    if (startInTriangle) {
+        tMin = t2s;
+    } 
+    xy_at_t(q2, t2e, end.x, end.y);
+    bool endInTriangle = pointInTriangle(end, testLines);
+    if (endInTriangle) {
+        tMax = t2e;
+    }
+    int split = 0;
+    if (tMin != tMax || tCount > 2) {
+        dxdy_at_t(q2, tMin, dxy2.x, dxy2.y);
+        for (int index = 1; index < tCount; ++index) {
+            dxy1 = dxy2;
+            dxdy_at_t(q2, tsFound[index], dxy2.x, dxy2.y);
+            double dot = dxy1.dot(dxy2);
+            if (dot < 0) {
+                split = index - 1;
+                break;
+            }
+        }
+        
+    }
+    if (split == 0) { // there's one point
+        if (addIntercept(q1, q2, tMin, tMax, i)) {
+            return true;
+        }
+        i.swap();
+        return isLinearInner(q2, tMin, tMax, q1, t1s, t1e, i);
+    }
+    // At this point, we have two ranges of t values -- treat each separately at the split
+    bool result;
+    if (addIntercept(q1, q2, tMin, tsFound[split - 1], i)) {
+        result = true;
+    } else {
+        i.swap();
+        result = isLinearInner(q2, tMin, tsFound[split - 1], q1, t1s, t1e, i);
+    }
+    if (addIntercept(q1, q2, tsFound[split], tMax, i)) {
+        result = true;
+    } else {
+        i.swap();
+        result |= isLinearInner(q2, tsFound[split], tMax, q1, t1s, t1e, i);
+    }
+    return result;
+}
+
+static double flatMeasure(const Quadratic& q) {
+    _Point mid;
+    xy_at_t(q, 0.5, mid.x, mid.y);
+    double dx = q[2].x - q[0].x;
+    double dy = q[2].y - q[0].y;
+    double length = sqrt(dx * dx + dy * dy); // OPTIMIZE: get rid of sqrt
+    return ((mid.x - q[0].x) * dy - (mid.y - q[0].y) * dx) / length;
+}
+
+// FIXME ? should this measure both and then use the quad that is the flattest as the line?
+static bool isLinear(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
+    double measure = flatMeasure(q1);
+    // OPTIMIZE: (get rid of sqrt) use approximately_zero
+    if (!approximately_zero_sqrt(measure)) {
+        return false;
+    }
+    return isLinearInner(q1, 0, 1, q2, 0, 1, i);
+}
+
+static bool relaxedIsLinear(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
+    double m1 = flatMeasure(q1);
+    double m2 = flatMeasure(q2);
+    if (fabs(m1) < fabs(m2)) {
+        isLinearInner(q1, 0, 1, q2, 0, 1, i);
+        return false;
+    } else {
+        isLinearInner(q2, 0, 1, q1, 0, 1, i);
+        return true;
+    }
+}
+
+#if 0
+static void unsortableExpanse(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
+    const Quadratic* qs[2] = { &q1, &q2 };
+    // need t values for start and end of unsortable expanse on both curves
+    // try projecting lines parallel to the end points
+    i.fT[0][0] = 0;
+    i.fT[0][1] = 1;
+    int flip = -1; // undecided
+    for (int qIdx = 0; qIdx < 2; qIdx++) {
+        for (int t = 0; t < 2; t++) {
+            _Point dxdy;
+            dxdy_at_t(*qs[qIdx], t, dxdy.x, dxdy.y);
+            _Line perp;
+            perp[0] = perp[1] = (*qs[qIdx])[t == 0 ? 0 : 2];
+            perp[0].x += dxdy.y;
+            perp[0].y -= dxdy.x;
+            perp[1].x -= dxdy.y;
+            perp[1].y += dxdy.x;
+            Intersections hitData;
+            int hits = intersectRay(*qs[qIdx ^ 1], perp, hitData);
+            assert(hits <= 1);
+            if (hits) {
+                if (flip < 0) {
+                    _Point dxdy2;
+                    dxdy_at_t(*qs[qIdx ^ 1], hitData.fT[0][0], dxdy2.x, dxdy2.y);
+                    double dot = dxdy.dot(dxdy2);
+                    flip = dot < 0;
+                    i.fT[1][0] = flip;
+                    i.fT[1][1] = !flip;
+                }
+                i.fT[qIdx ^ 1][t ^ flip] = hitData.fT[0][0];
+            }
+        }
+    }
+    i.fUnsortable = true; // failed, probably coincident or near-coincident
+    i.fUsed = 2;
+}
+#endif
+
 bool intersect2(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
     // if the quads share an end point, check to see if they overlap
 
     if (onlyEndPtsInCommon(q1, q2, i)) {
         return i.intersected();
     }
+    if (onlyEndPtsInCommon(q2, q1, i)) {
+        i.swapPts();
+        return i.intersected();
+    }
+    // see if either quad is really a line
+    if (isLinear(q1, q2, i)) {
+        return i.intersected();
+    }
+    if (isLinear(q2, q1, i)) {
+        i.swapPts();
+        return i.intersected();
+    }
     QuadImplicitForm i1(q1);
     QuadImplicitForm i2(q2);
     if (i1.implicit_match(i2)) {
@@ -135,15 +399,20 @@ bool intersect2(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
         return i.fCoincidentUsed > 0;
     }
     double roots1[4], roots2[4];
-    int rootCount = findRoots(i2, q1, roots1);
+    bool disregardCount1 = false;
+    bool disregardCount2 = false;
+    bool useCubic = q1[0] == q2[0] || q1[0] == q2[2] || q1[2] == q2[0];
+    int rootCount = findRoots(i2, q1, roots1, useCubic, disregardCount1);
     // OPTIMIZATION: could short circuit here if all roots are < 0 or > 1
-#ifndef NDEBUG
-    int rootCount2 =
-#endif
-        findRoots(i1, q2, roots2);
-    assert(rootCount == rootCount2);
+    int rootCount2 = findRoots(i1, q2, roots2, useCubic, disregardCount2);
+ #if 0
+    if (rootCount != rootCount2 && !disregardCount1 && !disregardCount2) {
+        unsortableExpanse(q1, q2, i);
+        return false;
+    }
+ #endif
     addValidRoots(roots1, rootCount, 0, i);
-    addValidRoots(roots2, rootCount, 1, i);
+    addValidRoots(roots2, rootCount2, 1, i);
     if (i.insertBalanced() && i.fUsed <= 1) {
         if (i.fUsed == 1) {
             _Point xy1, xy2;
@@ -157,16 +426,13 @@ bool intersect2(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
         return i.intersected();
     }
     _Point pts[4];
-    bool matches[4];
-    int flipCheck[4];
     int closest[4];
     double dist[4];
     int index, ndex2;
-    int flipIndex = 0;
     for (ndex2 = 0; ndex2 < i.fUsed2; ++ndex2) {
         xy_at_t(q2, i.fT[1][ndex2], pts[ndex2].x, pts[ndex2].y);
-        matches[ndex2] = false;
     }
+    bool foundSomething = false;
     for (index = 0; index < i.fUsed; ++index) {
         _Point xy;
         xy_at_t(q1, i.fT[0][index], xy.x, xy.y);
@@ -193,38 +459,41 @@ bool intersect2(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
             }
             dist[index] = distance;
             closest[index] = ndex2;
+            foundSomething = true;
         next:
             ;
         }
     }
-    for (index = 0; index < i.fUsed; ) {
-        for (ndex2 = 0; ndex2 < i.fUsed2; ++ndex2) {
-             if (closest[index] == ndex2) {
-                assert(flipIndex < 4);
-                flipCheck[flipIndex++] = ndex2;
-                matches[ndex2] = true;
-                goto next2;
-             }
-        }
-        if (--i.fUsed > index) {
-            memmove(&i.fT[0][index], &i.fT[0][index + 1], (i.fUsed - index) * sizeof(i.fT[0][0]));
-            memmove(&closest[index], &closest[index + 1], (i.fUsed - index) * sizeof(closest[0]));
-            continue;
+    if (i.fUsed && i.fUsed2 && !foundSomething) {
+        if (relaxedIsLinear(q1, q2, i)) {
+            i.swapPts();
         }
-    next2:
-        ++index;
+        return i.intersected();
     }
-    for (ndex2 = 0; ndex2 < i.fUsed2; ) {
-        if (!matches[ndex2]) {
-             if (--i.fUsed2 > ndex2) {
-                memmove(&i.fT[1][ndex2], &i.fT[1][ndex2 + 1], (i.fUsed2 - ndex2) * sizeof(i.fT[1][0]));
-                memmove(&matches[ndex2], &matches[ndex2 + 1], (i.fUsed2 - ndex2) * sizeof(matches[0]));
+    double roots1Copy[4], roots2Copy[4];
+    memcpy(roots1Copy, i.fT[0], i.fUsed * sizeof(double));
+    memcpy(roots2Copy, i.fT[1], i.fUsed2 * sizeof(double));
+    int used = 0;
+    do {
+        double lowest = DBL_MAX;
+        int lowestIndex = -1;
+        for (index = 0; index < i.fUsed; ++index) {
+            if (closest[index] < 0) {
                 continue;
-             }
+            }
+            if (roots1Copy[index] < lowest) {
+                lowestIndex = index;
+                lowest = roots1Copy[index];
+            }
         }
-        ++ndex2;
-    }
-    i.fFlip = i.fUsed >= 2 && flipCheck[0] > flipCheck[1];
-    assert(i.insertBalanced());
+        if (lowestIndex < 0) {
+            break;
+        }
+        i.fT[0][used] = roots1Copy[lowestIndex];
+        i.fT[1][used] = roots2Copy[closest[lowestIndex]];
+        closest[lowestIndex] = -1;
+    } while (++used < i.fUsed);
+    i.fUsed = i.fUsed2 = used;
+    i.fFlip = false;
     return i.intersected();
 }
diff --git a/experimental/Intersection/QuadraticIntersection_Test.cpp b/experimental/Intersection/QuadraticIntersection_Test.cpp
index bab6c73..829dffe 100644
--- a/experimental/Intersection/QuadraticIntersection_Test.cpp
+++ b/experimental/Intersection/QuadraticIntersection_Test.cpp
@@ -59,9 +59,41 @@ static void standardTestCases() {
 }
 
 static const Quadratic testSet[] = {
+{{53.774852327053594, 53.318060789841951}, {45.787877803416805, 51.393492026284981}, {46.703936967162392, 53.06860709822206}},
+{{46.703936967162392, 53.06860709822206}, {47.619996130907957, 54.74372217015916}, {53.020051653535361, 48.633140968832024}},
+
+{{67.4265481,37.9937726}, {51.1295132,57.5422812}, {44.5947482,65.6442674}},
+{{61.3365082,82.6931328}, {54.8250789,71.6639328}, {47.7274442,61.4049645}},
+
+{{50.934805397717923, 51.52391952648901}, {56.803308902971423, 44.246234610627596}, {69.776888596721406, 40.166645096692555}},
+{{50.230212796400401, 38.386469101526998}, {49.855620812184917, 38.818990392153609}, {56.356567496227363, 47.229909093319407}},
+
+{{36.148792695174222, 70.336952793070424}, {36.141613037691357, 70.711654739870085}, {36.154708826402597, 71.088492662905836}},
+{{35.216235592661825, 70.580199617313212}, {36.244476835123969, 71.010897787304074}, {37.230244263238326, 71.423156953613102}},
+
+// this pair is nearly coincident, and causes the quartic code to produce bad
+// data. Mathematica doesn't think they touch. Graphically, I can't tell.
+// it may not be so bad to pretend that they don't touch, if I can detect that
+{{369.848602,145.680267}, {382.360413,121.298294}, {406.207703,121.298294}},
+{{369.850525,145.675964}, {382.362915,121.29287}, {406.211273,121.29287}},
+
+{{33.567436351153468, 62.336347586395924}, {35.200980274619084, 65.038561460144479}, {36.479571811084995, 67.632178905412445}},
+{{41.349524945572696, 67.886658677862641}, {39.125562529359087, 67.429772735149214}, {35.600314083992416, 66.705372160552685}},
+
+{{67.25299631583178, 21.109080184767524}, {43.617595267398613, 33.658034168577529}, {33.38371819435676, 44.214192553988745}},
+{{40.476838859398541, 39.543209911285999}, {36.701186108431131, 34.8817994016458}, {30.102144288878023, 26.739063172945315}},
+
+{{25.367434474345036, 50.4712103169743}, {17.865013304933097, 37.356741010559439}, {16.818988838905465, 37.682915484123129}},
+{{16.818988838905465, 37.682915484123129}, {15.772964372877833, 38.009089957686811}, {20.624104547604965, 41.825131596683121}},
+
+{{26.440225044088567, 79.695009812848298}, {26.085525979582247, 83.717928354134784}, {27.075079976297072, 84.820633667838905}},
+{{27.075079976297072, 84.820633667838905}, {28.276546859574015, 85.988574184029034}, {25.649263209500006, 87.166762066617025}},
+
+{{34.879150914024962, 83.862726601601125}, {35.095810134304429, 83.693473210169543}, {35.359284111931586, 83.488069234177502}},
+{{54.503204203015471, 76.094098492518242}, {51.366889541918894, 71.609856061299155}, {46.53086955445437, 69.949863036494207}},
+
 {{0, 0}, {1, 0}, {0, 3}},
 {{1, 0}, {0, 1}, {1, 1}},
-{{369.848602,145.680267}, {382.360413,121.298294}, {406.207703,121.298294}},
 {{369.961151,137.980698}, {383.970093,121.298294}, {406.213287,121.298294}},
 {{353.2948,194.351074}, {353.2948,173.767563}, {364.167572,160.819855}},
 {{360.416077,166.795715}, {370.126831,147.872162}, {388.635406,147.872162}},
@@ -71,7 +103,6 @@ static const Quadratic testSet[] = {
 {{369.8543701171875, 145.66734313964844}, {382.36788940429688, 121.28203582763672}, {406.21844482421875, 121.28203582763672}},
 {{369.96469116210938, 137.96672058105469}, {383.97555541992188, 121.28203582763672}, {406.2218017578125, 121.28203582763672}},
 
-    {{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}},
     {{369.962311, 137.976044}, {383.971893, 121.29287}, {406.216125, 121.29287}},
 
     {{400.121704, 149.468719}, {391.949493, 161.037186}, {391.949493, 181.202423}},
@@ -90,25 +121,27 @@ static void oneOffTest() {
         for (size_t inner = outer + 1; inner < testSetCount; ++inner) {
             const Quadratic& quad1 = testSet[outer];
             const Quadratic& quad2 = testSet[inner];
-            double tt1, tt2;
             Intersections intersections2;
             intersect2(quad1, quad2, intersections2);
+            if (intersections2.fUnsortable) {
+                continue;
+            }
             for (int pt = 0; pt < intersections2.used(); ++pt) {
-                tt1 = intersections2.fT[0][pt];
+                double tt1 = intersections2.fT[0][pt];
                 double tx1, ty1;
                 xy_at_t(quad1, tt1, tx1, ty1);
                 int pt2 = intersections2.fFlip ? intersections2.used() - pt - 1 : pt;
-                tt2 = intersections2.fT[1][pt2];
+                double tt2 = intersections2.fT[1][pt2];
                 double tx2, ty2;
                 xy_at_t(quad2, tt2, tx2, ty2);
-                if (!approximately_equal(tx1, tx2)) {
+                if (!AlmostEqualUlps(tx1, tx2)) {
                     SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
-                        __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
+                        __FUNCTION__, (int)outer, (int)inner, tt1, tx1, ty1, tt2, tx2, ty2);
                     SkASSERT(0);
                 }
-                if (!approximately_equal(ty1, ty2)) {
+                if (!AlmostEqualUlps(ty1, ty2)) {
                     SkDebugf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
-                        __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
+                        __FUNCTION__, (int)outer, (int)inner, tt1, tx1, ty1, tt2, tx2, ty2);
                     SkASSERT(0);
                 }
                 SkDebugf("%s [%d][%d] t1=%1.9g (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__,
diff --git a/experimental/Intersection/QuadraticIntersection_TestData.h b/experimental/Intersection/QuadraticIntersection_TestData.h
index 4c95d5e..2dbf34a 100644
--- a/experimental/Intersection/QuadraticIntersection_TestData.h
+++ b/experimental/Intersection/QuadraticIntersection_TestData.h
@@ -4,11 +4,8 @@
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
-#if !defined(IN_TEST)
-    #define IN_TEST 1
-#endif
-
 #include "DataTypes.h"
+#include "DataTypes_Test.h"
 
 extern const Quadratic quadraticLines[];
 extern const Quadratic quadraticModEpsilonLines[];
diff --git a/experimental/Intersection/QuadraticUtilities.h b/experimental/Intersection/QuadraticUtilities.h
index 5bc15ea..3230e9b 100644
--- a/experimental/Intersection/QuadraticUtilities.h
+++ b/experimental/Intersection/QuadraticUtilities.h
@@ -4,6 +4,10 @@
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
+ 
+#if !defined QUADRATIC_UTILITIES_H
+#define QUADRATIC_UTILITIES_H
+
 #include "DataTypes.h"
 
 void dxdy_at_t(const Quadratic& , double t, double& x, double& y);
@@ -24,5 +28,7 @@ inline void set_abc(const double* quad, double& a, double& b, double& c) {
 }
 
 int quadraticRoots(double A, double B, double C, double t[2]);
-
+int quadraticRootsX(const double A, const double B, const double C, double s[2]);
 void xy_at_t(const Quadratic& , double t, double& x, double& y);
+
+#endif
diff --git a/experimental/Intersection/QuarticRoot.cpp b/experimental/Intersection/QuarticRoot.cpp
index 66ce3bf..86ea7a6 100644
--- a/experimental/Intersection/QuarticRoot.cpp
+++ b/experimental/Intersection/QuarticRoot.cpp
@@ -27,13 +27,20 @@
 
 #include    <math.h>
 #include "CubicUtilities.h"
+#include "QuadraticUtilities.h"
 #include "QuarticRoot.h"
 
+#if SK_DEBUG
+#define QUARTIC_DEBUG 1
+#else
+#define QUARTIC_DEBUG 0
+#endif
+
 const double PI = 4 * atan(1);
 
 // unlike quadraticRoots in QuadraticUtilities.cpp, this does not discard
 // real roots <= 0 or >= 1
-static int quadraticRootsX(const double A, const double B, const double C,
+int quadraticRootsX(const double A, const double B, const double C,
         double s[2]) {
     if (approximately_zero(A)) {
         if (approximately_zero(B)) {
@@ -68,7 +75,7 @@ static int quadraticRootsX(const double A, const double B, const double C,
 #if USE_GEMS
 // unlike cubicRoots in CubicUtilities.cpp, this does not discard
 // real roots <= 0 or >= 1
-static int cubicRootsX(const double A, const double B, const double C,
+int cubicRootsX(const double A, const double B, const double C,
         const double D, double s[3]) {
     int num;
     /* normal form: x^3 + Ax^2 + Bx + C = 0 */
@@ -119,7 +126,13 @@ static int cubicRootsX(const double A, const double B, const double C,
 }
 #else
 
-static int cubicRootsX(double A, double B, double C, double D, double s[3]) {
+int cubicRootsX(double A, double B, double C, double D, double s[3]) {
+#if QUARTIC_DEBUG
+    // create a string mathematica understands
+    char str[1024];
+    bzero(str, sizeof(str));
+    sprintf(str, "Solve[%1.19g x^3 + %1.19g x^2 + %1.19g x + %1.19g == 0, x]", A, B, C, D);
+#endif
     if (approximately_zero(A)) {  // we're just a quadratic
         return quadraticRootsX(B, C, D, s);
     }
@@ -202,34 +215,6 @@ static int cubicRootsX(double A, double B, double C, double D, double s[3]) {
 
 int quarticRoots(const double A, const double B, const double C, const double D,
         const double E, double s[4]) {
-    if (approximately_zero(A)) {
-        if (approximately_zero(B)) {
-            return quadraticRootsX(C, D, E, s);
-        }
-        return cubicRootsX(B, C, D, E, s);
-    }
-    int num;
-    int i;
-    if (approximately_zero(E)) { // 0 is one root
-        num = cubicRootsX(A, B, C, D, s);
-        for (i = 0; i < num; ++i) {
-            if (approximately_zero(s[i])) {
-                return num;
-            }
-        }
-        s[num++] = 0;
-        return num;
-    }
-    if (approximately_zero_squared(A + B + C + D + E)) { // 1 is one root
-        num = cubicRootsX(A, A + B, -(D + E), -E, s); // note that -C==A+B+D+E
-        for (i = 0; i < num; ++i) {
-            if (approximately_equal(s[i], 1)) {
-                return num;
-            }
-        }
-        s[num++] = 1;
-        return num;
-    }
     double  u, v;
     /* normal form: x^4 + Ax^3 + Bx^2 + Cx + D = 0 */
     const double invA = 1 / A;
@@ -243,6 +228,7 @@ int quarticRoots(const double A, const double B, const double C, const double D,
     const double p = -3 * a2 / 8 + b;
     const double q = a2 * a / 8 - a * b / 2 + c;
     const double r = -3 * a2 * a2 / 256 + a2 * b / 16 - a * c / 4 + d;
+    int num;
     if (approximately_zero(r)) {
     /* no absolute term: y(y^3 + py + q) = 0 */
         num = cubicRootsX(1, 0, p, q, s);
@@ -250,19 +236,19 @@ int quarticRoots(const double A, const double B, const double C, const double D,
     } else {
         /* solve the resolvent cubic ... */
         (void) cubicRootsX(1, -p / 2, -r, r * p / 2 - q * q / 8, s);
-        /* ... and take the one real solution ... */
+        /* ... and take one real solution ... */
         const double z = s[0];
         /* ... to build two quadric equations */
         u = z * z - r;
         v = 2 * z - p;
-        if (approximately_zero(u)) {
+        if (approximately_zero_squared(u)) {
             u = 0;
         } else if (u > 0) {
             u = sqrt(u);
         } else {
             return 0;
         }
-        if (approximately_zero(v)) {
+        if (approximately_zero_squared(v)) {
             v = 0;
         } else if (v > 0) {
             v = sqrt(v);
@@ -273,7 +259,7 @@ int quarticRoots(const double A, const double B, const double C, const double D,
         num += quadraticRootsX(1, q < 0 ? v : -v, z + u, s + num);
     }
     // eliminate duplicates
-    for (i = 0; i < num - 1; ++i) {
+    for (int i = 0; i < num - 1; ++i) {
         for (int j = i + 1; j < num; ) {
             if (approximately_equal(s[i], s[j])) {
                 if (j < --num) {
@@ -286,10 +272,8 @@ int quarticRoots(const double A, const double B, const double C, const double D,
     }
     /* resubstitute */
     const double sub = a / 4;
-    for (i = 0; i < num; ++i) {
+    for (int i = 0; i < num; ++i) {
         s[i] -= sub;
     }
     return num;
 }
-
-
diff --git a/experimental/Intersection/QuarticRoot_Test.cpp b/experimental/Intersection/QuarticRoot_Test.cpp
index 2fe3e72..0f310bb 100644
--- a/experimental/Intersection/QuarticRoot_Test.cpp
+++ b/experimental/Intersection/QuarticRoot_Test.cpp
@@ -2,12 +2,8 @@
 #include <math.h>
 #include "CubicUtilities.h"
 #include "Intersection_Tests.h"
-
-namespace QuarticRootTest {
-
-#include "QuarticRoot.cpp"
-
-}
+#include "QuadraticUtilities.h"
+#include "QuarticRoot.h"
 
 double mulA[] = {-3, -1, 1, 3};
 size_t mulACount = sizeof(mulA) / sizeof(mulA[0]);
@@ -20,6 +16,7 @@ size_t rootDCount = sizeof(rootD) / sizeof(rootD[0]);
 double rootE[] = {-5, -1, 0, 1, 7};
 size_t rootECount = sizeof(rootE) / sizeof(rootE[0]);
 
+
 static void quadraticTest() {
     // (x - a)(x - b) == x^2 - (a + b)x + ab
     for (size_t aIndex = 0; aIndex < mulACount; ++aIndex) {
@@ -31,7 +28,7 @@ static void quadraticTest() {
                 const double b = A * (B + C);
                 const double c = A * B * C;
                 double roots[2];
-                const int rootCount = QuarticRootTest::quadraticRootsX(A, b, c, roots);
+                const int rootCount = quadraticRootsX(A, b, c, roots);
                 const int expected = 1 + (B != C);
                 assert(rootCount == expected);
                 assert(approximately_equal(roots[0], -B)
@@ -60,7 +57,7 @@ static void cubicTest() {
                     const double c = A * (B * C + C * D + B * D);
                     const double d = A * B * C * D;
                     double roots[3];
-                    const int rootCount = QuarticRootTest::cubicRootsX(A, b, c, d, roots);
+                    const int rootCount = cubicRootsX(A, b, c, d, roots);
                     const int expected = 1 + (B != C) + (B != D && C != D);
                     assert(rootCount == expected);
                     assert(approximately_equal(roots[0], -B)
@@ -103,7 +100,7 @@ static void quarticTest() {
                         const double d = A * (B * C * D + B * C * E + B * D * E + C * D * E);
                         const double e = A * B * C * D * E;
                         double roots[4];
-                        const int rootCount = QuarticRootTest::quarticRoots(A, b, c, d, e, roots);
+                        const int rootCount = quarticRoots(A, b, c, d, e, roots);
                         const int expected = 1 + (B != C) + (B != D && C != D) + (B != E && C != E && D != E);
                         assert(rootCount == expected);
                         assert(approximately_equal(roots[0], -B)
diff --git a/experimental/Intersection/Simplify.cpp b/experimental/Intersection/Simplify.cpp
index e29b0df..5fd0fd5 100644
--- a/experimental/Intersection/Simplify.cpp
+++ b/experimental/Intersection/Simplify.cpp
@@ -28,9 +28,10 @@ int gDebugMaxWindValue = SK_MaxS32;
 #define PIN_ADD_T 0
 #define TRY_ROTATE 1
 #define ONE_PASS_COINCIDENCE_CHECK 0
+#define APPROXIMATE_CUBICS 1
 
 #define DEBUG_UNUSED 0 // set to expose unused functions
-#define FORCE_RELEASE 1  // set force release to 1 for multiple thread -- no debugging
+#define FORCE_RELEASE 0  // set force release to 1 for multiple thread -- no debugging
 
 #if FORCE_RELEASE || defined SK_RELEASE
 
@@ -118,7 +119,7 @@ static int CubicLineIntersect(const SkPoint a[4], const SkPoint b[2],
         Intersections& intersections) {
     MAKE_CONST_CUBIC(aCubic, a);
     MAKE_CONST_LINE(bLine, b);
-    return intersect(aCubic, bLine, intersections.fT[0], intersections.fT[1]);
+    return intersect(aCubic, bLine, intersections);
 }
 
 static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
@@ -134,11 +135,23 @@ static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
     return intersections.fUsed ? intersections.fUsed : intersections.fCoincidentUsed;
 }
 
-static int CubicIntersect(const SkPoint a[4], const SkPoint b[4],
+#if APPROXIMATE_CUBICS
+static int CubicQuadIntersect(const SkPoint a[4], const SkPoint b[3],
         Intersections& intersections) {
     MAKE_CONST_CUBIC(aCubic, a);
+    MAKE_CONST_QUAD(bQuad, b);
+    return intersect(aCubic, bQuad, intersections);
+}
+#endif
+
+static int CubicIntersect(const SkPoint a[4], const SkPoint b[4], Intersections& intersections) {
+    MAKE_CONST_CUBIC(aCubic, a);
     MAKE_CONST_CUBIC(bCubic, b);
+#if APPROXIMATE_CUBICS
+    intersect2(aCubic, bCubic, intersections);
+#else
     intersect(aCubic, bCubic, intersections);
+#endif
     return intersections.fUsed;
 }
 
@@ -1665,6 +1678,23 @@ public:
             other.addCancelOutsides(tStart, oStart, *this, endT);
         }
     }
+    
+    int addUnsortableT(double newT, Segment* other, bool start) {
+        int result = addT(newT, other);
+        Span* span = &fTs[result];
+        if (start) {
+            if (result > 0) {
+                span[result - 1].fUnsortableEnd = true;
+            }
+            span[result].fUnsortableStart = true;
+        } else {
+            span[result].fUnsortableEnd = true;
+            if (result + 1 < fTs.count()) {
+                span[result + 1].fUnsortableStart = true;
+            }
+        }
+        return result;
+    }
 
     int bumpCoincidentThis(const Span* oTest, bool opp, int index,
             SkTDArray<double>& outsideTs) {
@@ -2722,6 +2752,8 @@ public:
         int local = spanSign(start, end);
         int oppLocal = oppSign(start, end);
         (void) markAndChaseWinding(start, end, local, oppLocal);
+        // OPTIMIZATION: the reverse mark and chase could skip the first marking
+        (void) markAndChaseWinding(end, start, local, oppLocal);
     }
 
     void initWinding(int start, int end, int winding, int oppWinding) {
@@ -4138,6 +4170,10 @@ public:
         return fSegments[segIndex].addT(newT, &other->fSegments[otherIndex]);
     }
 
+    int addUnsortableT(int segIndex, double newT, Contour* other, int otherIndex, bool start) {
+        return fSegments[segIndex].addUnsortableT(newT, &other->fSegments[otherIndex], start);
+    }
+
     const Bounds& bounds() const {
         return fBounds;
     }
@@ -4820,6 +4856,10 @@ public:
         return fContour->addT(fIndex, newT, other.fContour, other.fIndex);
     }
 
+    int addUnsortableT(double newT, const Work& other, bool start) {
+        return fContour->addUnsortableT(fIndex, newT, other.fContour, other.fIndex, start);
+    }
+
     bool advance() {
         return ++fIndex < fLast;
     }
@@ -4832,9 +4872,11 @@ public:
         return fContour->segments()[fIndex].bounds();
     }
 
+#if !APPROXIMATE_CUBICS
     const SkPoint* cubic() const {
         return fCubic;
     }
+#endif
 
     void init(Contour* contour) {
         fContour = contour;
@@ -4855,6 +4897,7 @@ public:
         return bounds().fLeft;
     }
 
+#if !APPROXIMATE_CUBICS
     void promoteToCubic() {
         fCubic[0] = pts()[0];
         fCubic[2] = pts()[1];
@@ -4864,6 +4907,7 @@ public:
         fCubic[2].fX = (fCubic[3].fX + fCubic[2].fX * 2) / 3;
         fCubic[2].fY = (fCubic[3].fY + fCubic[2].fY * 2) / 3;
     }
+#endif
 
     const SkPoint* pts() const {
         return fContour->segments()[fIndex].pts();
@@ -4923,7 +4967,9 @@ public:
 
 protected:
     Contour* fContour;
+#if !APPROXIMATE_CUBICS
     SkPoint fCubic[4];
+#endif
     int fIndex;
     int fLast;
 };
@@ -4990,6 +5036,7 @@ static void debugShowQuadLineIntersection(int pts, const Work& wt,
     SkDebugf("\n");
 }
 
+// FIXME: show more than two intersection points
 static void debugShowQuadIntersection(int pts, const Work& wt,
         const Work& wn, const double wtTs[2], const double wnTs[2]) {
     if (!pts) {
@@ -5021,6 +5068,106 @@ static void debugShowQuadIntersection(int pts, const Work& wt,
     }
     SkDebugf("\n");
 }
+
+static void debugShowCubicLineIntersection(int pts, const Work& wt,
+        const Work& wn, const double wtTs[2], const double wnTs[2]) {
+    if (!pts) {
+        SkDebugf("%s no intersect (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
+                " (%1.9g,%1.9g %1.9g,%1.9g)\n",
+                __FUNCTION__, wt.pts()[0].fX, wt.pts()[0].fY, wt.pts()[1].fX, wt.pts()[1].fY,
+                wt.pts()[2].fX, wt.pts()[2].fY, wt.pts()[3].fX, wt.pts()[3].fY,
+                wn.pts()[0].fX, wn.pts()[0].fY, wn.pts()[1].fX, wn.pts()[1].fY);
+        return;
+    }
+    SkPoint wtOutPt, wnOutPt;
+    CubicXYAtT(wt.pts(), wtTs[0], &wtOutPt);
+    LineXYAtT(wn.pts(), wnTs[0], &wnOutPt);
+    SkDebugf("%s wtTs[0]=%1.9g (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g)",
+            __FUNCTION__,
+            wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY, wt.pts()[1].fX, wt.pts()[1].fY,
+            wt.pts()[2].fX, wt.pts()[2].fY, wt.pts()[3].fX, wt.pts()[3].fY,
+            wtOutPt.fX, wtOutPt.fY);
+    if (pts == 2) {
+        CubicXYAtT(wt.pts(), wtTs[1], &wtOutPt);
+        SkDebugf(" wtTs[1]=%1.9g (%1.9g,%1.9g)", wtTs[1], wtOutPt.fX, wtOutPt.fY);
+    }
+    SkDebugf(" wnTs[0]=%g (%1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g)",
+            wtTs[0], wn.pts()[0].fX, wn.pts()[0].fY, wn.pts()[1].fX, wn.pts()[1].fY,
+            wnOutPt.fX, wnOutPt.fY);
+    if (pts == 2) {
+        LineXYAtT(wn.pts(), wnTs[1], &wnOutPt);
+        SkDebugf(" wnTs[1]=%1.9g (%1.9g,%1.9g)", wnTs[1], wnOutPt.fX, wnOutPt.fY);
+    }
+    SkDebugf("\n");
+}
+
+#if APPROXIMATE_CUBICS
+// FIXME: show more than two intersection points
+static void debugShowCubicQuadIntersection(int pts, const Work& wt,
+        const Work& wn, const double wtTs[2], const double wnTs[2]) {
+    if (!pts) {
+        SkDebugf("%s no intersect (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
+                " (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)\n",
+                __FUNCTION__, wt.pts()[0].fX, wt.pts()[0].fY, wt.pts()[1].fX, wt.pts()[1].fY,
+                wt.pts()[2].fX, wt.pts()[2].fY, wt.pts()[3].fX, wt.pts()[3].fY,
+                wn.pts()[0].fX, wn.pts()[0].fY, wn.pts()[1].fX, wn.pts()[1].fY,
+                wn.pts()[2].fX, wn.pts()[2].fY );
+        return;
+    }
+    SkPoint wtOutPt, wnOutPt;
+    CubicXYAtT(wt.pts(), wtTs[0], &wtOutPt);
+    CubicXYAtT(wn.pts(), wnTs[0], &wnOutPt);
+    SkDebugf("%s wtTs[0]=%1.9g (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g)",
+            __FUNCTION__,
+            wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY, wt.pts()[1].fX, wt.pts()[1].fY,
+            wt.pts()[2].fX, wt.pts()[2].fY, wt.pts()[3].fX, wt.pts()[3].fY,
+            wtOutPt.fX, wtOutPt.fY);
+    if (pts == 2) {
+        SkDebugf(" wtTs[1]=%1.9g", wtTs[1]);
+    }
+    SkDebugf(" wnTs[0]=%g (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g)",
+            wnTs[0], wn.pts()[0].fX, wn.pts()[0].fY, wn.pts()[1].fX, wn.pts()[1].fY,
+            wn.pts()[2].fX, wn.pts()[2].fY,
+            wnOutPt.fX, wnOutPt.fY);
+    if (pts == 2) {
+        SkDebugf(" wnTs[1]=%1.9g", wnTs[1]);
+    }
+    SkDebugf("\n");
+}
+
+// FIXME: show more than two intersection points
+static void debugShowCubicIntersection(int pts, const Work& wt,
+        const Work& wn, const double wtTs[2], const double wnTs[2]) {
+    if (!pts) {
+        SkDebugf("%s no intersect (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
+                " (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)\n",
+                __FUNCTION__, wt.pts()[0].fX, wt.pts()[0].fY, wt.pts()[1].fX, wt.pts()[1].fY,
+                wt.pts()[2].fX, wt.pts()[2].fY, wt.pts()[3].fX, wt.pts()[3].fY,
+                wn.pts()[0].fX, wn.pts()[0].fY, wn.pts()[1].fX, wn.pts()[1].fY,
+                wn.pts()[2].fX, wn.pts()[2].fY, wn.pts()[3].fX, wn.pts()[3].fY );
+        return;
+    }
+    SkPoint wtOutPt, wnOutPt;
+    CubicXYAtT(wt.pts(), wtTs[0], &wtOutPt);
+    CubicXYAtT(wn.pts(), wnTs[0], &wnOutPt);
+    SkDebugf("%s wtTs[0]=%1.9g (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g)",
+            __FUNCTION__,
+            wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY, wt.pts()[1].fX, wt.pts()[1].fY,
+            wt.pts()[2].fX, wt.pts()[2].fY, wt.pts()[3].fX, wt.pts()[3].fY,
+            wtOutPt.fX, wtOutPt.fY);
+    if (pts == 2) {
+        SkDebugf(" wtTs[1]=%1.9g", wtTs[1]);
+    }
+    SkDebugf(" wnTs[0]=%g (%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g)",
+            wnTs[0], wn.pts()[0].fX, wn.pts()[0].fY, wn.pts()[1].fX, wn.pts()[1].fY,
+            wn.pts()[2].fX, wn.pts()[2].fY, wn.pts()[3].fX, wn.pts()[3].fY,
+            wnOutPt.fX, wnOutPt.fY);
+    if (pts == 2) {
+        SkDebugf(" wnTs[1]=%1.9g", wnTs[1]);
+    }
+    SkDebugf("\n");
+}
+#endif
 #else
 static void debugShowLineIntersection(int , const Work& ,
         const Work& , const double [2], const double [2]) {
@@ -5033,6 +5180,20 @@ static void debugShowQuadLineIntersection(int , const Work& ,
 static void debugShowQuadIntersection(int , const Work& ,
         const Work& , const double [2], const double [2]) {
 }
+
+static void debugShowCubicLineIntersection(int , const Work& ,
+        const Work& , const double [2], const double [2]) {
+}
+
+#if APPROXIMATE_CUBICS
+static void debugShowCubicQuadIntersection(int , const Work& ,
+        const Work& , const double [2], const double [2]) {
+}
+
+static void debugShowCubicIntersection(int , const Work& ,
+        const Work& , const double [2], const double [2]) {
+}
+#endif
 #endif
 
 static bool addIntersectTs(Contour* test, Contour* next) {
@@ -5082,6 +5243,7 @@ static bool addIntersectTs(Contour* test, Contour* next) {
                         case Work::kCubic_Segment: {
                             pts = HCubicIntersect(wn.pts(), wt.left(),
                                     wt.right(), wt.y(), wt.xFlipped(), ts);
+                            debugShowCubicLineIntersection(pts, wn, wt, ts.fT[0], ts.fT[1]);
                             break;
                         }
                         default:
@@ -5108,6 +5270,7 @@ static bool addIntersectTs(Contour* test, Contour* next) {
                         case Work::kCubic_Segment: {
                             pts = VCubicIntersect(wn.pts(), wt.top(),
                                     wt.bottom(), wt.x(), wt.yFlipped(), ts);
+                            debugShowCubicLineIntersection(pts, wn, wt, ts.fT[0], ts.fT[1]);
                             break;
                         }
                         default:
@@ -5144,6 +5307,7 @@ static bool addIntersectTs(Contour* test, Contour* next) {
                         case Work::kCubic_Segment: {
                             swap = true;
                             pts = CubicLineIntersect(wn.pts(), wt.pts(), ts);
+                            debugShowCubicLineIntersection(pts, wn, wt, ts.fT[0], ts.fT[1]);
                             break;
                         }
                         default:
@@ -5173,8 +5337,14 @@ static bool addIntersectTs(Contour* test, Contour* next) {
                             break;
                         }
                         case Work::kCubic_Segment: {
+                    #if APPROXIMATE_CUBICS
+                            swap = true;
+                            pts = CubicQuadIntersect(wn.pts(), wt.pts(), ts);
+                            debugShowCubicQuadIntersection(pts, wn, wt, ts.fT[0], ts.fT[1]);
+                    #else
                             wt.promoteToCubic();
                             pts = CubicIntersect(wt.cubic(), wn.pts(), ts);
+                    #endif
                             break;
                         }
                         default:
@@ -5190,18 +5360,30 @@ static bool addIntersectTs(Contour* test, Contour* next) {
                         case Work::kVerticalLine_Segment:
                             pts = VCubicIntersect(wt.pts(), wn.top(),
                                     wn.bottom(), wn.x(), wn.yFlipped(), ts);
+                            debugShowCubicLineIntersection(pts, wt, wn, ts.fT[0], ts.fT[1]);
                             break;
                         case Work::kLine_Segment: {
                             pts = CubicLineIntersect(wt.pts(), wn.pts(), ts);
+                            debugShowCubicLineIntersection(pts, wt, wn, ts.fT[0], ts.fT[1]);
                             break;
                         }
                         case Work::kQuad_Segment: {
+                    #if APPROXIMATE_CUBICS
+                            pts = CubicQuadIntersect(wt.pts(), wn.pts(), ts);
+                            debugShowCubicQuadIntersection(pts, wt, wn, ts.fT[0], ts.fT[1]);
+                    #else
                             wn.promoteToCubic();
                             pts = CubicIntersect(wt.pts(), wn.cubic(), ts);
+                    #endif
                             break;
                         }
                         case Work::kCubic_Segment: {
+                    #if APPROXIMATE_CUBICS
+                            pts = CubicIntersect(wt.pts(), wn.pts(), ts);
+                            debugShowCubicIntersection(pts, wt, wn, ts.fT[0], ts.fT[1]);
+                    #else
                             pts = CubicIntersect(wt.pts(), wn.pts(), ts);
+                    #endif
                             break;
                         }
                         default:
@@ -5217,6 +5399,19 @@ static bool addIntersectTs(Contour* test, Contour* next) {
                 foundCommonContour = true;
             }
             // in addition to recording T values, record matching segment
+            if (ts.unsortable()) {
+                bool start = true;
+                for (int pt = 0; pt < ts.used(); ++pt) {
+                    // FIXME: if unsortable, the other points to the original. This logic is
+                    // untested downstream.
+                    int testTAt = wt.addUnsortableT(ts.fT[swap][pt], wt, start);
+                    wt.addOtherT(testTAt, ts.fT[swap][pt], testTAt);
+                    testTAt = wn.addUnsortableT(ts.fT[!swap][pt], wn, start ^ ts.fFlip);
+                    wn.addOtherT(testTAt, ts.fT[!swap][pt], testTAt);
+                    start ^= true;
+                }
+                continue;
+            }
             if (pts == 2) {
                 if (wn.segmentType() <= Work::kLine_Segment
                         && wt.segmentType() <= Work::kLine_Segment) {
@@ -6047,4 +6242,3 @@ void simplifyx(const SkPath& path, SkPath& result) {
         result = *assembled.nativePath();
     }
 }
-
diff --git a/experimental/Intersection/SimplifyNew_Test.cpp b/experimental/Intersection/SimplifyNew_Test.cpp
index 2559e80..b6cc26e 100644
--- a/experimental/Intersection/SimplifyNew_Test.cpp
+++ b/experimental/Intersection/SimplifyNew_Test.cpp
@@ -3510,12 +3510,40 @@ static void testLine85() {
     testSimplifyx(path);
 }
 
-static void (*firstTest)() = testLine85;
+static void testQuadralateral1() {
+    SkPath path;
+    path.moveTo(0, 0);
+    path.lineTo(0, 0);
+    path.lineTo(0, 0);
+    path.lineTo(3, 2);
+    path.close();
+    path.moveTo(0, 0);
+    path.lineTo(2, 1);
+    path.lineTo(2, 2);
+    path.lineTo(2, 3);
+    path.close();
+    testSimplifyx(path);
+}
+
+static void testCubic1() {
+    SkPath path;
+    path.moveTo(0, 0);
+    path.cubicTo(0, 1, 1, 1, 1, 0);
+    path.close();
+    path.moveTo(1, 0);
+    path.cubicTo(0, 0, 0, 1, 1, 1);
+    path.close();
+    testSimplifyx(path);
+}
+
+static void (*firstTest)() = 0;
 
 static struct {
     void (*fun)();
     const char* str;
 } tests[] = {
+    TEST(testCubic1),
+    TEST(testQuadralateral1),
     TEST(testLine85),
     TEST(testLine84),
     TEST(testLine84x),
@@ -3997,12 +4025,22 @@ static void testOp2u() {
     testShapeOp(path, pathB, kUnion_Op);
 }
 
+static void testOp8d() {
+    SkPath path, pathB;
+    path.addRect(0, 0, 640, 480);
+    pathB.moveTo(577330, 1971.72f);
+    pathB.cubicTo(10.7082f, -116.596f, 262.057f, 45.6468f, 294.694f, 1.96237f);
+    pathB.close();
+    testShapeOp(path, pathB, kDifference_Op);
+}    
+
 static const size_t testCount = sizeof(tests) / sizeof(tests[0]);
 
 static struct {
     void (*fun)();
     const char* str;
 } subTests[] = {
+    TEST(testOp8d),
     TEST(testDiff1),
     TEST(testIntersect1),
     TEST(testUnion1),
@@ -4024,10 +4062,10 @@ static struct {
 
 static const size_t subTestCount = sizeof(subTests) / sizeof(subTests[0]);
 
-static void (*firstBinaryTest)() = 0;
+static void (*firstBinaryTest)() = testOp8d;
 
 static bool skipAll = false;
-static bool runBinaryTestsFirst = false;
+static bool runBinaryTestsFirst = true;
 static bool runReverse = false;
 static void (*stopTest)() = 0;
 
diff --git a/experimental/Intersection/TSearch.h b/experimental/Intersection/TSearch.h
index 010e69f..6952425 100644
--- a/experimental/Intersection/TSearch.h
+++ b/experimental/Intersection/TSearch.h
@@ -12,6 +12,35 @@
 // FIXME: Move this templated version into SKTSearch.h
 
 template <typename T>
+static T* QSort_Partition(T* left, T* right, T* pivot)
+{
+    T pivotValue = *pivot;
+    SkTSwap(*pivot, *right);
+    T* newPivot = left;
+    while (left < right) {
+        if (*left < pivotValue) {
+            SkTSwap(*left, *newPivot);
+            newPivot += 1;
+        }
+        left += 1;
+    }
+    SkTSwap(*newPivot, *right);
+    return newPivot;
+}
+
+template <typename T>
+void QSort(T* left, T* right)
+{
+    if (left >= right) {
+        return;
+    }
+    T* pivot = left + (right - left >> 1);
+    pivot = QSort_Partition(left, right, pivot);
+    QSort(left, pivot - 1);
+    QSort(pivot + 1, right);
+}
+
+template <typename T>
 static T** QSort_Partition(T** left, T** right, T** pivot)
 {
     T* pivotValue = *pivot;
diff --git a/experimental/Intersection/op.htm b/experimental/Intersection/op.htm
index 50c26e9..8c8a991 100644
--- a/experimental/Intersection/op.htm
+++ b/experimental/Intersection/op.htm
@@ -3295,11 +3295,35 @@ path.addRect(4, 13, 13, 16, SkPath::kCCW_Direction);
     path.addRect(32, 0, 36, 41, SkPath::kCCW_Direction);
 </div>
 
+<div id="testQuadralateral1">
+    path.moveTo(0, 0);
+    path.lineTo(0, 0);
+    path.lineTo(0, 0);
+    path.lineTo(3, 2);
+    path.close();
+    path.moveTo(0, 0);
+    path.lineTo(2, 1);
+    path.lineTo(2, 2);
+    path.lineTo(2, 3);
+    path.close();
+</div>
+
+<div id="testCubic1">
+    path.moveTo(0, 0);
+    path.cubicTo(0, 1, 1, 1, 1, 0);
+    path.close();
+    path.moveTo(1, 0);
+    path.cubicTo(0, 0, 0, 1, 1, 1);
+    path.close();
+</div>
+
 </div>
 
 <script type="text/javascript">
 
 var testDivs = [
+    testCubic1,
+    testQuadralateral1,
     testLine85,
     testLine84x,
     testLine83,
@@ -3763,9 +3787,8 @@ function draw(test, title, _at_x, _at_y, scale) {
         }
         ctx.closePath();
     }
-    if (hasXor) {
-        ctx.fillType=xor; // how is this done?
-    }
+  // uncomment if ever part of the standard
+  //  ctx.fillRule=hasXor ? evenodd : nonzero;
     ctx.stroke();
     ctx.fillStyle="rgba(192,192,255, 0.3)";
     ctx.fill();
diff --git a/experimental/Intersection/qc.htm b/experimental/Intersection/qc.htm
new file mode 100644
index 0000000..29fedab
--- /dev/null
+++ b/experimental/Intersection/qc.htm
@@ -0,0 +1,2079 @@
+<html>
+<head>
+<div style="height:0">
+
+<div id="cubic1">
+$1 = (Cubic &) @0x297c40: {{x = 60.776536520932126, y = 71.249307306133829}, {x = 87.107894191103014, y = 22.377669868235323}, {x = 1.4974754310666936, y = 68.069569937917208}, {x = 45.261946574441133, y = 17.536076632112298}}
+$3 = {{{x = 60.776536520932126, y = 71.249307306133829}, {x = 66.996745328074098, y = 59.419614231505768}, {x = 65.760655441289899, y = 53.975522936482086}}, {{x = 65.760655441289899, y = 53.975522936482086}, {x = 64.524565554505699, y = 48.531431641458411}, {x = 59.040356119613065, y = 46.936502854722001}}, {{x = 59.040356119613065, y = 46.936502854722001}, {x = 53.556146684720431, y = 45.341574067985597}, {x = 47.031996847537108, y = 45.059368518219323}}, {{x = 47.031996847537108, y = 45.059368518219323}, {x = 40.29980253329046, y = 44.781843489000011}, {x = 35.915024002796116, y = 43.168182836391942}}, {{x = 35.915024002796116, y = 43.168182836391942}, {x = 31.530245472301775, y = 41.554522183783902}, {x = 32.992157437282373, y = 35.838141687728616}}, {{x = 32.992157437282373, y = 35.838141687728616}, {x = 34.454069402262967, y = 30.121761191673329}, {x = 45.261946574441133, y = 17.536076632112298}}}
+</div>
+
+<div id="cubic2">
+$1 = {{x = 73.565270739405079, y = 11.505317181118446}, {x = 69.865863057722279, y = 35.56041113825534}, {x = 63.830000657509075, y = 90.821050755130614}, {x = 29.400041480269302, y = 26.497158886164968}}
+</div>
+
+<div id="cubic3">
+$3 = {{x = 69.729201388419241, y = 38.687735162064307}, {x = 24.764868814854356, y = 23.150171257159752}, {x = 84.928319083959011, y = 90.258844099128083}, {x = 80.39277404565027, y = 61.35338524419506}}
+</div>
+
+<div id="cubic1x0">
+{{14.5975863, 41.632436}, {16.3518929, 26.2639684}, {18.5165519, 7.68775139}, {8.03767257, 89.1628526}},
+{{14.5975863, 41.632436}, {8.03767257, 89.1628526}, {8.03767257, 89.1628526}},
+</div>
+
+<div id="cubic1x0x">
+{{14.5975863, 41.632436}, {16.3518929, 26.2639684}, {18.5165519, 7.68775139}, {8.03767257, 89.1628526}},
+{{14.5975863, 41.632436}, {8.03767257, 89.1628526}, {8.03767257, 89.1628526}},
+</div>
+
+<div id="cubic1x1">
+{{32.0437334, 59.0267425}, {62.4615541, 91.340573}, {61.0102145, 98.6747985}, {27.3387826, 82.9194526}},
+{{32.0437334, 59.0267425}, {75.9425223, 105.66184}, {27.3387826, 82.9194526}},
+</div>
+
+<div id="cubic1x1x">
+{{32.0437334, 59.0267425}, {62.4615541, 91.340573}, {61.0102145, 98.6747985}, {27.3387826, 82.9194526}},
+{{32.0437334, 59.0267425}, {77.7581975, 107.02498}, {27.3387826, 82.9194526}},
+</div>
+
+<div id="cubic1x2">
+{{57.8949944, 41.1707465}, {56.7368674, 76.5309905}, {56.356649, 86.19953}, {55.5002867, 93.318629}},
+{{57.8949944, 41.1707465}, {55.5002867, 93.318629}, {55.5002867, 93.318629}},
+</div>
+
+<div id="cubic1x2x">
+{{57.8949944, 41.1707465}, {56.7368674, 76.5309905}, {56.356649, 86.19953}, {55.5002867, 93.318629}},
+{{57.8949944, 41.1707465}, {55.5002867, 93.318629}, {55.5002867, 93.318629}},
+</div>
+
+<div id="cubic1x3">
+{{41.1844187, 86.52533}, {31.2211043, 33.1005529}, {20.992908, 27.8044979}, {10.1965708, 73.7658388}},
+{{41.1844187, 86.52533}, {26.1439273, 5.87597256}, {10.1965708, 73.7658388}},
+</div>
+
+<div id="cubic1x3x">
+{{41.1844187, 86.52533}, {31.2211043, 33.1005529}, {20.992908, 27.8044979}, {10.1965708, 73.7658388}},
+{{41.1844187, 86.52533}, {26.3152619, 5.60599593}, {10.1965708, 73.7658388}},
+</div>
+
+<div id="cubic1x4">
+{{51.1608132, 59.7881237}, {58.9955693, 38.5338731}, {38.8048957, 93.8817224}, {70.1083283, 10.6741861}},
+{{51.1608132, 59.7881237}, {70.1083283, 10.6741861}, {70.1083283, 10.6741861}},
+</div>
+
+<div id="cubic1x4x">
+{{51.1608132, 59.7881237}, {58.9955693, 38.5338731}, {38.8048957, 93.8817224}, {70.1083283, 10.6741861}},
+{{51.1608132, 59.7881237}, {70.1083283, 10.6741861}, {70.1083283, 10.6741861}},
+</div>
+
+<div id="cubic1x5">
+{{9.45225228, 64.0040808}, {16.5855418, 53.2003115}, {37.6356814, 42.8968969}, {68.1461999, 33.1817941}},
+{{9.45225228, 64.0040808}, {19.5957859, 48.641127}, {68.1461999, 33.1817941}},
+</div>
+
+<div id="cubic1x5x">
+{{9.45225228, 64.0040808}, {16.5855418, 53.2003115}, {37.6356814, 42.8968969}, {68.1461999, 33.1817941}},
+{{9.45225228, 64.0040808}, {21.2663043, 47.7764376}, {68.1461999, 33.1817941}},
+</div>
+
+<div id="cubic1x6">
+{{96.2293269, 26.2973682}, {79.8675829, 34.4649929}, {53.1353046, 45.0651411}, {9.82676512, 58.4413866}},
+{{96.2293269, 26.2973682}, {67.554114, 40.6117577}, {9.82676512, 58.4413866}},
+</div>
+
+<div id="cubic1x6x">
+{{96.2293269, 26.2973682}, {79.8675829, 34.4649929}, {53.1353046, 45.0651411}, {9.82676512, 58.4413866}},
+{{96.2293269, 26.2973682}, {73.2381426, 38.4629118}, {9.82676512, 58.4413866}},
+</div>
+
+<div id="cubic1x7">
+{{77.9926032, 21.6823036}, {14.4765247, 6.95017395}, {11.5735665, 16.9314125}, {66.2493838, 53.3932579}},
+{{77.9926032, 21.6823036}, {-12.9236155, 0.594894684}, {66.2493838, 53.3932579}},
+</div>
+
+<div id="cubic1x7x">
+{{77.9926032, 21.6823036}, {14.4765247, 6.95017395}, {11.5735665, 16.9314125}, {66.2493838, 53.3932579}},
+{{77.9926032, 21.6823036}, {-16.5229284, -0.857700571}, {66.2493838, 53.3932579}},
+</div>
+
+<div id="cubic1x8">
+{{56.479229, 46.4012343}, {65.5444116, 4.92526628}, {78.9504195, 19.6997536}, {93.7579262, 89.4649302}},
+{{56.479229, 46.4012343}, {70.7547833, -18.9137695}, {93.7579262, 89.4649302}},
+</div>
+
+<div id="cubic1x8x">
+{{56.479229, 46.4012343}, {65.5444116, 4.92526628}, {78.9504195, 19.6997536}, {93.7579262, 89.4649302}},
+{{56.479229, 46.4012343}, {70.8118345, -15.4977762}, {93.7579262, 89.4649302}},
+</div>
+
+<div id="cubic1x9">
+{{14.1826743, 68.2075081}, {63.5890486, 41.1398453}, {37.3805687, 55.2173676}, {38.296851, 55.1751163}},
+{{14.1826743, 68.2075081}, {38.296851, 55.1751163}, {38.296851, 55.1751163}},
+</div>
+
+<div id="cubic1x9x">
+{{14.1826743, 68.2075081}, {63.5890486, 41.1398453}, {37.3805687, 55.2173676}, {38.296851, 55.1751163}},
+{{14.1826743, 68.2075081}, {38.296851, 55.1751163}, {38.296851, 55.1751163}},
+</div>
+
+<div id="cubic2x0">
+{{27.9052884, 4.18132628}, {75.550717, 80.9000193}, {86.6244633, 97.3541595}, {31.358766, 46.7795742}},
+{{27.9052884, 4.18132628}, {66.5480157, 66.4038653}, {68.2236994, 73.2154296}},
+{{68.2236994, 73.2154296}, {70.5412458, 82.636132}, {31.358766, 46.7795742}},
+</div>
+
+<div id="cubic2x0x">
+{{27.9052884, 4.18132628}, {75.550717, 80.9000193}, {86.6244633, 97.3541595}, {31.358766, 46.7795742}},
+{{27.9052884, 4.18132628}, {64.5696024, 61.9317264}, {68.2236994, 73.2154296}},
+{{68.2236994, 73.2154296}, {71.8777964, 84.4991328}, {31.358766, 46.7795742}},
+</div>
+
+<div id="cubic2x1">
+{{55.6607299, 89.8878963}, {45.872586, 80.5522712}, {42.0218181, 60.6961261}, {19.7918636, 41.8513322}},
+{{55.6607299, 89.8878963}, {52.7119153, 87.0754092}, {42.3919757, 69.4355526}},
+{{42.3919757, 69.4355526}, {32.6126647, 52.7197915}, {19.7918636, 41.8513322}},
+</div>
+
+<div id="cubic2x1x">
+{{55.6607299, 89.8878963}, {45.872586, 80.5522712}, {42.0218181, 60.6961261}, {19.7918636, 41.8513322}},
+{{55.6607299, 89.8878963}, {49.0795145, 82.5258065}, {42.3919757, 69.4355526}},
+{{42.3919757, 69.4355526}, {35.7044369, 56.3452986}, {19.7918636, 41.8513322}},
+</div>
+
+<div id="cubic2x2">
+{{80.5982112, 14.1354079}, {73.8005055, 65.0951435}, {54.0762929, 60.254824}, {2.82780649, 26.9437232}},
+{{80.5982112, 14.1354079}, {75.7174786, 50.7243473}, {58.3820516, 52.1411292}},
+{{58.3820516, 52.1411292}, {43.4686812, 53.3599624}, {2.82780649, 26.9437232}},
+</div>
+
+<div id="cubic2x2x">
+{{80.5982112, 14.1354079}, {73.8005055, 65.0951435}, {54.0762929, 60.254824}, {2.82780649, 26.9437232}},
+{{80.5982112, 14.1354079}, {76.0811121, 51.5011698}, {58.3820516, 52.1411292}},
+{{58.3820516, 52.1411292}, {40.6829911, 52.7810886}, {2.82780649, 26.9437232}},
+</div>
+
+<div id="cubic2x3">
+{{1.6014867, 16.1869736}, {54.4660745, 11.3148647}, {68.9317074, 35.2054791}, {98.4868263, 68.0902175}},
+{{1.6014867, 16.1869736}, {36.7068582, 12.9515906}, {58.7852073, 27.9797778}},
+{{58.7852073, 27.9797778}, {68.1927213, 34.3832403}, {98.4868263, 68.0902175}},
+</div>
+
+<div id="cubic2x3x">
+{{1.6014867, 16.1869736}, {54.4660745, 11.3148647}, {68.9317074, 35.2054791}, {98.4868263, 68.0902175}},
+{{1.6014867, 16.1869736}, {39.5784138, 13.1506607}, {58.7852073, 27.9797778}},
+{{58.7852073, 27.9797778}, {77.9920009, 42.808895}, {98.4868263, 68.0902175}},
+</div>
+
+<div id="cubic2x4">
+{{23.0453529, 23.2462522}, {99.7603064, 71.4695575}, {88.8529841, 52.1034408}, {2.52897437, 4.4722111}},
+{{23.0453529, 23.2462522}, {83.1995453, 61.0594014}, {73.9267748, 49.8046823}},
+{{73.9267748, 49.8046823}, {64.9578598, 38.9187642}, {2.52897437, 4.4722111}},
+</div>
+
+<div id="cubic2x4x">
+{{23.0453529, 23.2462522}, {99.7603064, 71.4695575}, {88.8529841, 52.1034408}, {2.52897437, 4.4722111}},
+{{23.0453529, 23.2462522}, {80.2001434, 58.1848465}, {73.9267748, 49.8046823}},
+{{73.9267748, 49.8046823}, {67.6534063, 41.424518}, {2.52897437, 4.4722111}},
+</div>
+
+<div id="cubic2x5">
+{{64.4519328, 43.6345262}, {65.4821636, 58.7228333}, {54.6599207, 69.286817}, {3.532848, 76.5762786}},
+{{64.4519328, 43.6345262}, {65.2901892, 55.9112614}, {53.5513792, 63.0299695}},
+{{53.5513792, 63.0299695}, {39.721686, 71.4166414}, {3.532848, 76.5762786}},
+</div>
+
+<div id="cubic2x5x">
+{{64.4519328, 43.6345262}, {65.4821636, 58.7228333}, {54.6599207, 69.286817}, {3.532848, 76.5762786}},
+{{64.4519328, 43.6345262}, {66.113742, 54.9117003}, {53.5513792, 63.0299695}},
+{{53.5513792, 63.0299695}, {40.9890164, 71.1482387}, {3.532848, 76.5762786}},
+</div>
+
+<div id="cubic2x6">
+{{82.5366784, 93.9543251}, {90.3418213, 74.9907304}, {69.20575, 41.039441}, {49.884656, 11.4126389}},
+{{82.5366784, 93.9543251}, {87.7472455, 81.2945847}, {76.383006, 56.6821848}},
+{{76.383006, 56.6821848}, {69.0501277, 40.8008111}, {49.884656, 11.4126389}},
+</div>
+
+<div id="cubic2x6x">
+{{82.5366784, 93.9543251}, {90.3418213, 74.9907304}, {69.20575, 41.039441}, {49.884656, 11.4126389}},
+{{82.5366784, 93.9543251}, {87.4294046, 79.1281234}, {76.383006, 56.6821848}},
+{{76.383006, 56.6821848}, {65.3366074, 34.2362462}, {49.884656, 11.4126389}},
+</div>
+
+<div id="cubic2x7">
+{{81.6027334, 97.1400425}, {32.694003, 88.1076582}, {25.4108981, 80.9641684}, {64.7788314, 37.8185316}},
+{{81.6027334, 97.1400425}, {43.6639346, 90.1335672}, {40.0870335, 80.2717567}},
+{{40.0870335, 80.2717567}, {36.0922592, 69.2578356}, {64.7788314, 37.8185316}},
+</div>
+
+<div id="cubic2x7x">
+{{81.6027334, 97.1400425}, {32.694003, 88.1076582}, {25.4108981, 80.9641684}, {64.7788314, 37.8185316}},
+{{81.6027334, 97.1400425}, {44.7641414, 91.5498493}, {40.0870335, 80.2717567}},
+{{40.0870335, 80.2717567}, {35.4099255, 68.9936642}, {64.7788314, 37.8185316}},
+</div>
+
+<div id="cubic2x8">
+{{43.6332675, 44.3267048}, {98.9277035, 77.9134953}, {92.1152147, 80.4133992}, {7.99971512, 51.2120151}},
+{{43.6332675, 44.3267048}, {85.4039037, 69.6989069}, {78.0952172, 71.3149254}},
+{{78.0952172, 71.3149254}, {70.649222, 72.9613041}, {7.99971512, 51.2120151}},
+</div>
+
+<div id="cubic2x8x">
+{{43.6332675, 44.3267048}, {98.9277035, 77.9134953}, {92.1152147, 80.4133992}, {7.99971512, 51.2120151}},
+{{43.6332675, 44.3267048}, {85.5789722, 69.5359977}, {78.0952172, 71.3149254}},
+{{78.0952172, 71.3149254}, {70.6114621, 73.0938531}, {7.99971512, 51.2120151}},
+</div>
+
+<div id="cubic2x9">
+{{3.42763756, 8.30440876}, {72.1979502, 30.9497829}, {73.001545, 36.9676506}, {15.3033876, 4.03527813}},
+{{3.42763756, 8.30440876}, {62.7221525, 27.8294978}, {56.7911889, 27.0114984}},
+{{56.7911889, 27.0114984}, {55.1652933, 26.7872547}, {15.3033876, 4.03527813}},
+</div>
+
+<div id="cubic2x9x">
+{{3.42763756, 8.30440876}, {72.1979502, 30.9497829}, {73.001545, 36.9676506}, {15.3033876, 4.03527813}},
+{{3.42763756, 8.30440876}, {54.7095919, 25.9860248}, {56.7911889, 27.0114984}},
+{{56.7911889, 27.0114984}, {58.8727859, 28.036972}, {15.3033876, 4.03527813}},
+</div>
+
+<div id="cubic3x0">
+{{37.7493998, 54.1620116}, {0.928181503, 99.9465276}, {1.29019157, 84.2497321}, {85.2470221, 46.7010984}},
+{{37.7493998, 54.1620116}, {30.0262679, 63.7651662}, {19.9157535, 75.222785}},
+{{19.9157535, 75.222785}, {12.0739437, 84.1094218}, {23.0870945, 77.9306985}},
+{{23.0870945, 77.9306985}, {53.2236264, 61.0231583}, {85.2470221, 46.7010984}},
+</div>
+
+<div id="cubic3x0x">
+{{37.7493998, 54.1620116}, {0.928181503, 99.9465276}, {1.29019157, 84.2497321}, {85.2470221, 46.7010984}},
+{{37.7493998, 54.1620116}, {26.0576358, 68.4753229}, {19.9157535, 75.222785}},
+{{19.9157535, 75.222785}, {7.36020346, 87.8757618}, {23.0870945, 77.9306985}},
+{{23.0870945, 77.9306985}, {37.855802, 68.7339725}, {85.2470221, 46.7010984}},
+</div>
+
+<div id="cubic3x1">
+{{77.853445, 82.8493315}, {48.7140421, 36.904878}, {60.2845497, 2.42643608}, {81.1111786, 35.5792593}},
+{{77.853445, 82.8493315}, {64.326138, 61.5206609}, {61.1190571, 42.8070764}},
+{{61.1190571, 42.8070764}, {58.2548088, 26.0939491}, {64.5348786, 22.8899965}},
+{{64.5348786, 22.8899965}, {71.0512995, 19.5654629}, {81.1111786, 35.5792593}},
+</div>
+
+<div id="cubic3x1x">
+{{77.853445, 82.8493315}, {48.7140421, 36.904878}, {60.2845497, 2.42643608}, {81.1111786, 35.5792593}},
+{{77.853445, 82.8493315}, {63.5749823, 59.3570561}, {61.1190571, 42.8070764}},
+{{61.1190571, 42.8070764}, {58.6631319, 26.2570968}, {64.5348786, 22.8899965}},
+{{64.5348786, 22.8899965}, {70.4066254, 19.5228963}, {81.1111786, 35.5792593}},
+</div>
+
+<div id="cubic3x2">
+{{38.2012882, 49.0499648}, {82.7576585, 7.96646616}, {92.3967278, 11.8042378}, {93.8251679, 19.597347}},
+{{38.2012882, 49.0499648}, {58.8845939, 29.9787846}, {72.1076941, 21.4229661}},
+{{72.1076941, 21.4229661}, {83.1166319, 14.2997899}, {88.6707154, 14.6399404}},
+{{88.6707154, 14.6399404}, {92.9647013, 14.9029184}, {93.8251679, 19.597347}},
+</div>
+
+<div id="cubic3x2x">
+{{38.2012882, 49.0499648}, {82.7576585, 7.96646616}, {92.3967278, 11.8042378}, {93.8251679, 19.597347}},
+{{38.2012882, 49.0499648}, {60.2321893, 28.8875296}, {72.1076941, 21.4229661}},
+{{72.1076941, 21.4229661}, {83.983199, 13.9584026}, {88.6707154, 14.6399404}},
+{{88.6707154, 14.6399404}, {93.3582319, 15.3214782}, {93.8251679, 19.597347}},
+</div>
+
+<div id="cubic3x3">
+{{52.7120295, 31.0801866}, {64.6964272, 52.8517052}, {78.6098203, 95.2490945}, {51.5310243, 81.9254304}},
+{{52.7120295, 31.0801866}, {59.5211432, 43.4499986}, {63.7497522, 56.8993316}},
+{{63.7497522, 56.8993316}, {68.6258107, 72.4079153}, {66.5354307, 79.5030739}},
+{{66.5354307, 79.5030739}, {64.0124137, 88.0666872}, {51.5310243, 81.9254304}},
+</div>
+
+<div id="cubic3x3x">
+{{52.7120295, 31.0801866}, {64.6964272, 52.8517052}, {78.6098203, 95.2490945}, {51.5310243, 81.9254304}},
+{{52.7120295, 31.0801866}, {59.1016467, 42.6728619}, {63.7497522, 56.8993316}},
+{{63.7497522, 56.8993316}, {68.3978576, 71.1258013}, {66.5354307, 79.5030739}},
+{{66.5354307, 79.5030739}, {64.6730039, 87.8803465}, {51.5310243, 81.9254304}},
+</div>
+
+<div id="cubic3x4">
+{{20.7082833, 44.1170772}, {75.7169666, 75.0570675}, {84.1330966, 24.9551825}, {21.7528516, 0.176163297}},
+{{20.7082833, 44.1170772}, {46.6273271, 58.6954113}, {59.2896776, 51.9825439}},
+{{59.2896776, 51.9825439}, {71.1540672, 45.6927106}, {61.4307428, 29.4567029}},
+{{61.4307428, 29.4567029}, {50.807026, 11.71722}, {21.7528516, 0.176163297}},
+</div>
+
+<div id="cubic3x4x">
+{{20.7082833, 44.1170772}, {75.7169666, 75.0570675}, {84.1330966, 24.9551825}, {21.7528516, 0.176163297}},
+{{20.7082833, 44.1170772}, {48.4367344, 58.6022136}, {59.2896776, 51.9825439}},
+{{59.2896776, 51.9825439}, {70.1426209, 45.3628742}, {61.4307428, 29.4567029}},
+{{61.4307428, 29.4567029}, {52.7188646, 13.5505316}, {21.7528516, 0.176163297}},
+</div>
+
+<div id="cubic3x5">
+{{20.8291142, 74.9221559}, {16.6750469, 57.513008}, {21.1249099, 46.360262}, {76.9233116, 50.0985771}},
+{{20.8291142, 74.9221559}, {18.4755741, 65.0587801}, {21.1261573, 59.9182775}},
+{{21.1261573, 59.9182775}, {24.474036, 53.4254499}, {36.6579558, 51.0041468}},
+{{36.6579558, 51.0041468}, {50.2178533, 48.3093965}, {76.9233116, 50.0985771}},
+</div>
+
+<div id="cubic3x5x">
+{{20.8291142, 74.9221559}, {16.6750469, 57.513008}, {21.1249099, 46.360262}, {76.9233116, 50.0985771}},
+{{20.8291142, 74.9221559}, {18.3562971, 66.1376314}, {21.1261573, 59.9182775}},
+{{21.1261573, 59.9182775}, {23.8960175, 53.6989236}, {36.6579558, 51.0041468}},
+{{36.6579558, 51.0041468}, {49.4198942, 48.3093701}, {76.9233116, 50.0985771}},
+</div>
+
+<div id="cubic3x6">
+{{39.306348, 21.7912016}, {44.72463, 86.8568551}, {3.16400146, 77.3725818}, {0.981986477, 4.24671164}},
+{{39.306348, 21.7912016}, {41.8751537, 52.6388057}, {32.26342, 62.4108917}},
+{{32.26342, 62.4108917}, {23.2193358, 71.6058581}, {13.0917792, 55.754704}},
+{{13.0917792, 55.754704}, {2.00097021, 38.3959145}, {0.981986477, 4.24671164}},
+</div>
+
+<div id="cubic3x6x">
+{{39.306348, 21.7912016}, {44.72463, 86.8568551}, {3.16400146, 77.3725818}, {0.981986477, 4.24671164}},
+{{39.306348, 21.7912016}, {41.2158823, 54.2230253}, {32.26342, 62.4108917}},
+{{32.26342, 62.4108917}, {23.3109577, 70.5987581}, {13.0917792, 55.754704}},
+{{13.0917792, 55.754704}, {2.87260067, 40.9106498}, {0.981986477, 4.24671164}},
+</div>
+
+<div id="cubic3x7">
+{{85.4907277, 42.6604079}, {93.4752654, 38.7852218}, {63.2230996, 90.6357313}, {14.7351715, 54.0271501}},
+{{85.4907277, 42.6604079}, {92.9820656, 39.0245896}, {81.4704732, 52.0202764}},
+{{81.4704732, 52.0202764}, {71.0697229, 63.7619094}, {56.4037366, 66.489545}},
+{{56.4037366, 66.489545}, {36.2148038, 70.2443591}, {14.7351715, 54.0271501}},
+</div>
+
+<div id="cubic3x7x">
+{{85.4907277, 42.6604079}, {93.4752654, 38.7852218}, {63.2230996, 90.6357313}, {14.7351715, 54.0271501}},
+{{85.4907277, 42.6604079}, {89.2978026, 42.0578592}, {81.4704732, 52.0202764}},
+{{81.4704732, 52.0202764}, {73.6431437, 61.9826936}, {56.4037366, 66.489545}},
+{{56.4037366, 66.489545}, {39.1643295, 70.9963964}, {14.7351715, 54.0271501}},
+</div>
+
+<div id="cubic3x8">
+{{95.2957887, 36.3209844}, {46.7852652, 19.9519225}, {31.9607143, 63.7251956}, {29.3620354, 87.7284659}},
+{{95.2957887, 36.3209844}, {73.0036621, 28.7988805}, {57.2191042, 37.0396513}},
+{{57.2191042, 37.0396513}, {44.4309585, 43.7160611}, {36.8308235, 60.0949108}},
+{{36.8308235, 60.0949108}, {30.9912846, 72.6795466}, {29.3620354, 87.7284659}},
+</div>
+
+<div id="cubic3x8x">
+{{95.2957887, 36.3209844}, {46.7852652, 19.9519225}, {31.9607143, 63.7251956}, {29.3620354, 87.7284659}},
+{{95.2957887, 36.3209844}, {71.2392316, 28.8763825}, {57.2191042, 37.0396513}},
+{{57.2191042, 37.0396513}, {43.1989768, 45.20292}, {36.8308235, 60.0949108}},
+{{36.8308235, 60.0949108}, {30.4626702, 74.9869017}, {29.3620354, 87.7284659}},
+</div>
+
+<div id="cubic3x9">
+{{11.6274826, 23.1005334}, {50.665531, 35.5788199}, {73.2259434, 8.43082047}, {96.7997166, 12.8374226}},
+{{11.6274826, 23.1005334}, {26.8690196, 27.9724026}, {42.2684837, 25.6341105}},
+{{42.2684837, 25.6341105}, {51.3514943, 24.254924}, {67.0182186, 18.4582098}},
+{{67.0182186, 18.4582098}, {87.1065443, 11.0254957}, {96.7997166, 12.8374226}},
+</div>
+
+<div id="cubic3x9x">
+{{11.6274826, 23.1005334}, {50.665531, 35.5788199}, {73.2259434, 8.43082047}, {96.7997166, 12.8374226}},
+{{11.6274826, 23.1005334}, {28.7555518, 28.1569895}, {42.2684837, 25.6341105}},
+{{42.2684837, 25.6341105}, {55.7814156, 23.1112314}, {67.0182186, 18.4582098}},
+{{67.0182186, 18.4582098}, {82.5639521, 11.3566582}, {96.7997166, 12.8374226}},
+</div>
+
+<div id="cubic4x0">
+{{24.2578299, 1.34695745}, {38.313885, 41.465269}, {6.77689729, 99.312693}, {48.4308047, 76.5337766}},
+{{24.2578299, 1.34695745}, {27.9750096, 11.9564045}, {28.1705087, 26.7539994}},
+{{28.1705087, 26.7539994}, {28.2848367, 35.4076429}, {26.8433323, 51.6959666}},
+{{26.8433323, 51.6959666}, {24.9672902, 72.8943612}, {27.4957684, 77.9195086}},
+{{27.4957684, 77.9195086}, {31.4664535, 85.8109263}, {48.4308047, 76.5337766}},
+</div>
+
+<div id="cubic4x0x">
+{{24.2578299, 1.34695745}, {38.313885, 41.465269}, {6.77689729, 99.312693}, {48.4308047, 76.5337766}},
+{{24.2578299, 1.34695745}, {28.2364584, 13.5769276}, {28.1705087, 26.7539994}},
+{{28.1705087, 26.7539994}, {28.104559, 39.9310711}, {26.8433323, 51.6959666}},
+{{26.8433323, 51.6959666}, {24.5051265, 69.7176532}, {27.4957684, 77.9195086}},
+{{27.4957684, 77.9195086}, {30.4864104, 86.121364}, {48.4308047, 76.5337766}},
+</div>
+
+<div id="cubic4x1">
+{{3.18338154, 3.09354817}, {93.264044, 88.7879534}, {59.132973, 47.8778685}, {83.3354337, 18.6335197}},
+{{3.18338154, 3.09354817}, {35.8260971, 34.1468066}, {48.9325859, 44.6922254}},
+{{48.9325859, 44.6922254}, {62.4915199, 55.6016796}, {67.1257676, 54.3074276}},
+{{67.1257676, 54.3074276}, {70.2512267, 53.4345498}, {72.6465479, 43.2128608}},
+{{72.6465479, 43.2128608}, {76.4594277, 26.9419442}, {83.3354337, 18.6335197}},
+</div>
+
+<div id="cubic4x1x">
+{{3.18338154, 3.09354817}, {93.264044, 88.7879534}, {59.132973, 47.8778685}, {83.3354337, 18.6335197}},
+{{3.18338154, 3.09354817}, {34.807442, 33.2979688}, {48.9325859, 44.6922254}},
+{{48.9325859, 44.6922254}, {63.0577297, 56.086482}, {67.1257676, 54.3074276}},
+{{67.1257676, 54.3074276}, {71.1938054, 52.5283732}, {72.6465479, 43.2128608}},
+{{72.6465479, 43.2128608}, {74.0679283, 31.8888383}, {83.3354337, 18.6335197}},
+</div>
+
+<div id="cubic4x2">
+{{5.3607232, 97.6747591}, {19.6754743, 85.6972941}, {14.421376, 80.0662188}, {72.9397619, 98.5790647}},
+{{5.3607232, 97.6747591}, {7.15867444, 96.170374}, {9.99357731, 93.4972246}},
+{{9.99357731, 93.4972246}, {15.4658237, 88.3372129}, {19.1058065, 87.2914549}},
+{{19.1058065, 87.2914549}, {24.5745003, 85.7203128}, {35.9606711, 88.1040392}},
+{{35.9606711, 88.1040392}, {47.3960315, 90.4980635}, {72.9397619, 98.5790647}},
+</div>
+
+<div id="cubic4x2x">
+{{5.3607232, 97.6747591}, {19.6754743, 85.6972941}, {14.421376, 80.0662188}, {72.9397619, 98.5790647}},
+{{5.3607232, 97.6747591}, {8.01636596, 95.4093652}, {9.99357731, 93.4972246}},
+{{9.99357731, 93.4972246}, {14.161732, 88.9702622}, {19.1058065, 87.2914549}},
+{{19.1058065, 87.2914549}, {24.0498811, 85.6126476}, {35.9606711, 88.1040392}},
+{{35.9606711, 88.1040392}, {47.871461, 90.5954307}, {72.9397619, 98.5790647}},
+</div>
+
+<div id="cubic4x3">
+{{18.340571, 49.9760211}, {46.9862021, 97.0991299}, {45.0770262, 9.57918773}, {97.4081647, 39.0235061}},
+{{18.340571, 49.9760211}, {27.6759966, 65.333137}, {34.9254897, 64.1054159}},
+{{34.9254897, 64.1054159}, {39.46946, 63.3358824}, {47.9840785, 52.4199142}},
+{{47.9840785, 52.4199142}, {58.4594697, 38.9901831}, {66.2068641, 35.3036404}},
+{{66.2068641, 35.3036404}, {79.5296469, 28.9640886}, {97.4081647, 39.0235061}},
+</div>
+
+<div id="cubic4x3x">
+{{18.340571, 49.9760211}, {46.9862021, 97.0991299}, {45.0770262, 9.57918773}, {97.4081647, 39.0235061}},
+{{18.340571, 49.9760211}, {28.406995, 66.1423531}, {34.9254897, 64.1054159}},
+{{34.9254897, 64.1054159}, {41.4439844, 62.0684788}, {47.9840785, 52.4199142}},
+{{47.9840785, 52.4199142}, {54.9532374, 41.9238105}, {66.2068641, 35.3036404}},
+{{66.2068641, 35.3036404}, {77.4604907, 28.6834703}, {97.4081647, 39.0235061}},
+</div>
+
+<div id="cubic4x4">
+{{68.0670356, 2.66693188}, {23.1241074, 46.8739094}, {9.79601006, 41.5410025}, {79.6294187, 31.6402602}},
+{{68.0670356, 2.66693188}, {56.7853646, 13.7638629}, {41.0137122, 27.3042275}},
+{{41.0137122, 27.3042275}, {29.788878, 36.941033}, {31.0433353, 38.0354879}},
+{{31.0433353, 38.0354879}, {32.2977925, 39.1299429}, {51.0493703, 36.059867}},
+{{51.0493703, 36.059867}, {67.7999464, 33.3174024}, {79.6294187, 31.6402602}},
+</div>
+
+<div id="cubic4x4x">
+{{68.0670356, 2.66693188}, {23.1241074, 46.8739094}, {9.79601006, 41.5410025}, {79.6294187, 31.6402602}},
+{{68.0670356, 2.66693188}, {50.940695, 19.1344928}, {41.0137122, 27.3042275}},
+{{41.0137122, 27.3042275}, {29.4752637, 36.6674193}, {31.0433353, 38.0354879}},
+{{31.0433353, 38.0354879}, {32.6114068, 39.4035566}, {51.0493703, 36.059867}},
+{{51.0493703, 36.059867}, {61.9478496, 34.2106234}, {79.6294187, 31.6402602}},
+</div>
+
+<div id="cubic4x5">
+{{80.6109054, 27.4877124}, {85.9817399, 95.1019056}, {77.7276185, 68.083746}, {83.5185407, 96.1129614}},
+{{80.6109054, 27.4877124}, {82.5499811, 51.8990092}, {82.5259477, 65.0368853}},
+{{82.5259477, 65.0368853}, {82.5124299, 72.4264589}, {81.7002161, 78.1564815}},
+{{81.7002161, 78.1564815}, {81.2315331, 81.462956}, {81.4316783, 83.8990214}},
+{{81.4316783, 83.8990214}, {81.7199102, 87.4072321}, {83.5185407, 96.1129614}},
+</div>
+
+<div id="cubic4x5x">
+{{80.6109054, 27.4877124}, {85.9817399, 95.1019056}, {77.7276185, 68.083746}, {83.5185407, 96.1129614}},
+{{80.6109054, 27.4877124}, {82.6925268, 54.7439407}, {82.5259477, 65.0368853}},
+{{82.5259477, 65.0368853}, {82.3593687, 75.3298298}, {81.7002161, 78.1564815}},
+{{81.7002161, 78.1564815}, {81.2086421, 80.6624342}, {81.4316783, 83.8990214}},
+{{81.4316783, 83.8990214}, {81.6547145, 87.1356086}, {83.5185407, 96.1129614}},
+</div>
+
+<div id="cubic4x6">
+{{70.5424749, 7.37512261}, {53.6857094, 95.7185581}, {41.8065019, 41.8776796}, {38.1617001, 83.6927474}},
+{{70.5424749, 7.37512261}, {64.0240124, 41.5372735}, {57.0495799, 54.4661558}},
+{{57.0495799, 54.4661558}, {53.0372544, 61.9040203}, {46.633996, 64.0865108}},
+{{46.633996, 64.0865108}, {42.8562175, 65.3741311}, {41.4346736, 67.9484678}},
+{{41.4346736, 67.9484678}, {39.1777978, 72.0355437}, {38.1617001, 83.6927474}},
+</div>
+
+<div id="cubic4x6x">
+{{70.5424749, 7.37512261}, {53.6857094, 95.7185581}, {41.8065019, 41.8776796}, {38.1617001, 83.6927474}},
+{{70.5424749, 7.37512261}, {63.0887524, 44.8198844}, {57.0495799, 54.4661558}},
+{{57.0495799, 54.4661558}, {51.0104074, 64.1124273}, {46.633996, 64.0865108}},
+{{46.633996, 64.0865108}, {43.5741104, 64.6069899}, {41.4346736, 67.9484678}},
+{{41.4346736, 67.9484678}, {39.2952367, 71.2899457}, {38.1617001, 83.6927474}},
+</div>
+
+<div id="cubic4x7">
+{{24.0062249, 72.6211198}, {43.1612821, 11.6690897}, {22.3913226, 30.9587957}, {24.4801394, 37.7033828}},
+{{24.0062249, 72.6211198}, {30.5430063, 51.8208637}, {31.8675739, 40.5026282}},
+{{31.8675739, 40.5026282}, {32.9179067, 31.5276894}, {30.6430223, 29.7760199}},
+{{30.6430223, 29.7760199}, {28.7741669, 28.3369942}, {26.2185506, 31.7425273}},
+{{26.2185506, 31.7425273}, {23.6812077, 35.1237098}, {24.4801394, 37.7033828}},
+</div>
+
+<div id="cubic4x7x">
+{{24.0062249, 72.6211198}, {43.1612821, 11.6690897}, {22.3913226, 30.9587957}, {24.4801394, 37.7033828}},
+{{24.0062249, 72.6211198}, {30.9441221, 50.1265572}, {31.8675739, 40.5026282}},
+{{31.8675739, 40.5026282}, {32.7910257, 30.8786991}, {30.6430223, 29.7760199}},
+{{30.6430223, 29.7760199}, {28.4950189, 28.6733406}, {26.2185506, 31.7425273}},
+{{26.2185506, 31.7425273}, {23.9420823, 34.811714}, {24.4801394, 37.7033828}},
+</div>
+
+<div id="cubic4x8">
+{{83.4128604, 19.944285}, {3.59808416, 73.0005231}, {19.791118, 29.3197498}, {77.0346567, 21.4750355}},
+{{83.4128604, 19.944285}, {56.4409479, 37.8736494}, {40.6945347, 43.6697281}},
+{{40.6945347, 43.6697281}, {27.6832174, 48.4590486}, {28.8268904, 43.5475174}},
+{{28.8268904, 43.5475174}, {29.9619906, 38.6728026}, {42.6576802, 32.0063781}},
+{{42.6576802, 32.0063781}, {57.6563877, 24.1306537}, {77.0346567, 21.4750355}},
+</div>
+
+<div id="cubic4x8x">
+{{83.4128604, 19.944285}, {3.59808416, 73.0005231}, {19.791118, 29.3197498}, {77.0346567, 21.4750355}},
+{{83.4128604, 19.944285}, {53.6969963, 39.3225107}, {40.6945347, 43.6697281}},
+{{40.6945347, 43.6697281}, {27.6920731, 48.0169456}, {28.8268904, 43.5475174}},
+{{28.8268904, 43.5475174}, {29.9617077, 39.0780892}, {42.6576802, 32.0063781}},
+{{42.6576802, 32.0063781}, {55.3536527, 24.9346669}, {77.0346567, 21.4750355}},
+</div>
+
+<div id="cubic4x9">
+{{13.6133623, 99.7800201}, {2.79733483, 14.8064674}, {52.2975031, 64.1339272}, {98.9146078, 57.8132952}},
+{{13.6133623, 99.7800201}, {10.1036384, 72.2067072}, {14.9007617, 60.2808941}},
+{{14.9007617, 60.2808941}, {19.0431228, 49.9828423}, {30.5807774, 49.2954321}},
+{{30.5807774, 49.2954321}, {37.7022355, 48.8711377}, {56.117561, 53.190874}},
+{{56.117561, 53.190874}, {84.2814202, 59.7973522}, {98.9146078, 57.8132952}},
+</div>
+
+<div id="cubic4x9x">
+{{13.6133623, 99.7800201}, {2.79733483, 14.8064674}, {52.2975031, 64.1339272}, {98.9146078, 57.8132952}},
+{{13.6133623, 99.7800201}, {10.0919269, 71.197946}, {14.9007617, 60.2808941}},
+{{14.9007617, 60.2808941}, {19.7095965, 49.3638421}, {30.5807774, 49.2954321}},
+{{30.5807774, 49.2954321}, {41.4519583, 49.2270222}, {56.117561, 53.190874}},
+{{56.117561, 53.190874}, {76.476137, 59.3205959}, {98.9146078, 57.8132952}},
+</div>
+
+<div id="cubic5x0">
+{{73.5652707, 11.5053172}, {69.8658631, 35.5604111}, {63.8300007, 90.8210508}, {29.4000415, 26.4971589}},
+{{73.5652707, 11.5053172}, {73.3885843, 12.654206}, {73.0163837, 15.1491032}},
+{{73.0163837, 15.1491032}, {70.9175181, 29.2180034}, {69.2121151, 36.2586021}},
+{{69.2121151, 36.2586021}, {66.2435432, 48.5140774}, {62.0808557, 53.3239452}},
+{{62.0808557, 53.3239452}, {56.8541433, 59.3632637}, {49.5132747, 54.1388813}},
+{{49.5132747, 54.1388813}, {40.9233022, 48.0255311}, {29.4000415, 26.4971589}},
+</div>
+
+<div id="cubic5x0x">
+{{73.5652707, 11.5053172}, {69.8658631, 35.5604111}, {63.8300007, 90.8210508}, {29.4000415, 26.4971589}},
+{{73.5652707, 11.5053172}, {73.3009509, 13.2327574}, {73.0163837, 15.1491032}},
+{{73.0163837, 15.1491032}, {71.6823308, 25.1891102}, {69.2121151, 36.2586021}},
+{{69.2121151, 36.2586021}, {66.7418995, 47.328094}, {62.0808557, 53.3239452}},
+{{62.0808557, 53.3239452}, {57.4198119, 59.3197964}, {49.5132747, 54.1388813}},
+{{49.5132747, 54.1388813}, {41.6067374, 48.9579661}, {29.4000415, 26.4971589}},
+</div>
+
+<div id="cubic5x1">
+{{80.7539402, 31.4736433}, {77.5229567, 28.3334108}, {99.6348716, 63.2867312}, {60.0910899, 50.9480224}},
+{{80.7539402, 31.4736433}, {80.1293736, 30.8666193}, {81.0927918, 33.3061348}},
+{{81.0927918, 33.3061348}, {82.7770389, 37.5708941}, {83.4256875, 40.319949}},
+{{83.4256875, 40.319949}, {84.5951485, 45.2762733}, {83.5574674, 48.3997103}},
+{{83.5574674, 48.3997103}, {82.2131806, 52.4460356}, {77.2064841, 53.3431558}},
+{{77.2064841, 53.3431558}, {71.2104332, 54.4175525}, {60.0910899, 50.9480224}},
+</div>
+
+<div id="cubic5x1x">
+{{80.7539402, 31.4736433}, {77.5229567, 28.3334108}, {99.6348716, 63.2867312}, {60.0910899, 50.9480224}},
+{{80.7539402, 31.4736433}, {79.9741932, 30.7172975}, {81.0927918, 33.3061348}},
+{{81.0927918, 33.3061348}, {82.2743126, 36.0212723}, {83.4256875, 40.319949}},
+{{83.4256875, 40.319949}, {84.5770623, 44.6186258}, {83.5574674, 48.3997103}},
+{{83.5574674, 48.3997103}, {82.5378725, 52.1807949}, {77.2064841, 53.3431558}},
+{{77.2064841, 53.3431558}, {71.8750956, 54.5055166}, {60.0910899, 50.9480224}},
+</div>
+
+<div id="cubic5x2">
+{{30.9220007, 6.06626757}, {55.7590106, 41.691652}, {11.5944877, 68.5545306}, {95.99508, 89.3088364}},
+{{30.9220007, 6.06626757}, {36.6680413, 14.3081978}, {38.6632502, 23.8943374}},
+{{38.6632502, 23.8943374}, {39.8467707, 29.5806556}, {40.109652, 40.2122054}},
+{{40.109652, 40.2122054}, {40.4211241, 52.8088852}, {42.588681, 58.5795625}},
+{{42.588681, 58.5795625}, {46.141784, 68.0389732}, {57.1660752, 74.8906876}},
+{{57.1660752, 74.8906876}, {70.1317224, 82.9489754}, {95.99508, 89.3088364}},
+</div>
+
+<div id="cubic5x2x">
+{{30.9220007, 6.06626757}, {55.7590106, 41.691652}, {11.5944877, 68.5545306}, {95.99508, 89.3088364}},
+{{30.9220007, 6.06626757}, {37.1487855, 15.3683637}, {38.6632502, 23.8943374}},
+{{38.6632502, 23.8943374}, {40.1777149, 32.4203112}, {40.109652, 40.2122054}},
+{{40.109652, 40.2122054}, {39.8437309, 49.9303489}, {42.588681, 58.5795625}},
+{{42.588681, 58.5795625}, {45.3336311, 67.2287761}, {57.1660752, 74.8906876}},
+{{57.1660752, 74.8906876}, {68.9985192, 82.5525991}, {95.99508, 89.3088364}},
+</div>
+
+<div id="cubic5x3">
+{{74.7743754, 32.9274563}, {11.7577089, 11.8127863}, {37.4985242, 37.696964}, {72.8744837, 1.44809908}},
+{{74.7743754, 32.9274563}, {60.7273344, 28.2207866}, {49.5992486, 25.6169692}},
+{{49.5992486, 25.6169692}, {43.5981152, 24.2127874}, {37.944249, 23.3667683}},
+{{37.944249, 23.3667683}, {35.9715145, 23.0715771}, {37.4878767, 22.7373028}},
+{{37.4878767, 22.7373028}, {44.1459136, 21.2695724}, {50.3950023, 18.2059418}},
+{{50.3950023, 18.2059418}, {62.1391178, 12.4483612}, {72.8744837, 1.44809908}},
+</div>
+
+<div id="cubic5x3x">
+{{74.7743754, 32.9274563}, {11.7577089, 11.8127863}, {37.4985242, 37.696964}, {72.8744837, 1.44809908}},
+{{74.7743754, 32.9274563}, {58.4980331, 27.5812922}, {49.5992486, 25.6169692}},
+{{49.5992486, 25.6169692}, {40.7004642, 23.6526461}, {37.944249, 23.3667683}},
+{{37.944249, 23.3667683}, {35.0992403, 23.0813479}, {37.4878767, 22.7373028}},
+{{37.4878767, 22.7373028}, {40.7578786, 22.4379602}, {50.3950023, 18.2059418}},
+{{50.3950023, 18.2059418}, {60.0321261, 13.9739234}, {72.8744837, 1.44809908}},
+</div>
+
+<div id="cubic5x4">
+{{72.6117562, 85.7863012}, {10.3637705, 83.8910282}, {56.5110395, 81.0400843}, {40.6969416, 93.4977145}},
+{{72.6117562, 85.7863012}, {59.583082, 85.3896153}, {50.1257271, 84.8566602}},
+{{50.1257271, 84.8566602}, {45.0042708, 84.5680481}, {40.4221343, 84.1941021}},
+{{40.4221343, 84.1941021}, {38.6138335, 84.0465275}, {39.3498335, 84.2964765}},
+{{39.3498335, 84.2964765}, {42.6031074, 85.4013033}, {43.6650027, 86.8548971}},
+{{43.6650027, 86.8548971}, {45.661047, 89.587217}, {40.6969416, 93.4977145}},
+</div>
+
+<div id="cubic5x4x">
+{{72.6117562, 85.7863012}, {10.3637705, 83.8910282}, {56.5110395, 81.0400843}, {40.6969416, 93.4977145}},
+{{72.6117562, 85.7863012}, {57.6253009, 85.3070124}, {50.1257271, 84.8566602}},
+{{50.1257271, 84.8566602}, {42.6261532, 84.4063079}, {40.4221343, 84.1941021}},
+{{40.4221343, 84.1941021}, {37.9777583, 83.9471466}, {39.3498335, 84.2964765}},
+{{39.3498335, 84.2964765}, {41.4441267, 84.7344658}, {43.6650027, 86.8548971}},
+{{43.6650027, 86.8548971}, {45.8858786, 88.9753284}, {40.6969416, 93.4977145}},
+</div>
+
+<div id="cubic5x5">
+{{49.5466436, 30.4382438}, {75.5627334, 82.8610433}, {45.5550553, 43.8144668}, {89.743077, 11.8944428}},
+{{49.5466436, 30.4382438}, {54.1919031, 39.7985093}, {58.8653675, 50.331813}},
+{{58.8653675, 50.331813}, {61.2282341, 55.6573679}, {61.7133948, 56.0247083}},
+{{61.7133948, 56.0247083}, {62.1985554, 56.3920486}, {62.7466525, 53.2705356}},
+{{62.7466525, 53.2705356}, {64.4490529, 43.5750541}, {68.2227928, 36.1296005}},
+{{68.2227928, 36.1296005}, {75.1711506, 22.4207397}, {89.743077, 11.8944428}},
+</div>
+
+<div id="cubic5x5x">
+{{49.5466436, 30.4382438}, {75.5627334, 82.8610433}, {45.5550553, 43.8144668}, {89.743077, 11.8944428}},
+{{49.5466436, 30.4382438}, {56.3292139, 44.3383274}, {58.8653675, 50.331813}},
+{{58.8653675, 50.331813}, {61.106944, 55.5655329}, {61.7133948, 56.0247083}},
+{{61.7133948, 56.0247083}, {62.3198455, 56.4838837}, {62.7466525, 53.2705356}},
+{{62.7466525, 53.2705356}, {63.1064311, 47.7098594}, {68.2227928, 36.1296005}},
+{{68.2227928, 36.1296005}, {73.3391545, 24.5493417}, {89.743077, 11.8944428}},
+</div>
+
+<div id="cubic5x6">
+{{24.3042985, 82.344259}, {59.9615856, 74.3697725}, {32.7666043, 8.31767205}, {95.114078, 82.3081283}},
+{{24.3042985, 82.344259}, {33.0316107, 80.3924607}, {38.6135161, 73.199581}},
+{{38.6135161, 73.199581}, {41.8734961, 68.9987494}, {45.7986582, 59.6541823}},
+{{45.7986582, 59.6541823}, {49.7161349, 50.3279117}, {52.6598645, 48.50717}},
+{{52.6598645, 48.50717}, {57.3512738, 45.6054619}, {66.2796867, 52.394109}},
+{{66.2796867, 52.394109}, {76.3758191, 60.0706222}, {95.114078, 82.3081283}},
+</div>
+
+<div id="cubic5x6x">
+{{24.3042985, 82.344259}, {59.9615856, 74.3697725}, {32.7666043, 8.31767205}, {95.114078, 82.3081283}},
+{{24.3042985, 82.344259}, {33.965356, 79.8151924}, {38.6135161, 73.199581}},
+{{38.6135161, 73.199581}, {43.2616761, 66.5839696}, {45.7986582, 59.6541823}},
+{{45.7986582, 59.6541823}, {48.5966015, 51.6963295}, {52.6598645, 48.50717}},
+{{52.6598645, 48.50717}, {56.7231274, 45.3180106}, {66.2796867, 52.394109}},
+{{66.2796867, 52.394109}, {75.8362459, 59.4702074}, {95.114078, 82.3081283}},
+</div>
+
+<div id="cubic5x7">
+{{14.6365061, 95.7588134}, {18.3773411, 67.9719648}, {4.8126874, 86.837213}, {73.0391371, 68.7771361}},
+{{14.6365061, 95.7588134}, {15.2275148, 91.3688129}, {15.5044612, 85.7525859}},
+{{15.5044612, 85.7525859}, {15.7576453, 80.618239}, {16.904617, 79.6508905}},
+{{16.904617, 79.6508905}, {18.0515887, 78.683542}, {24.680235, 78.0137979}},
+{{24.680235, 78.0137979}, {33.9302732, 77.0791942}, {41.7459023, 75.745697}},
+{{41.7459023, 75.745697}, {55.7221394, 73.3610813}, {73.0391371, 68.7771361}},
+</div>
+
+<div id="cubic5x7x">
+{{14.6365061, 95.7588134}, {18.3773411, 67.9719648}, {4.8126874, 86.837213}, {73.0391371, 68.7771361}},
+{{14.6365061, 95.7588134}, {15.4253236, 89.2562084}, {15.5044612, 85.7525859}},
+{{15.5044612, 85.7525859}, {15.4709024, 80.8600761}, {16.904617, 79.6508905}},
+{{16.904617, 79.6508905}, {18.3383317, 78.4417048}, {24.680235, 78.0137979}},
+{{24.680235, 78.0137979}, {30.2055996, 77.5914828}, {41.7459023, 75.745697}},
+{{41.7459023, 75.745697}, {53.2862049, 73.8999113}, {73.0391371, 68.7771361}},
+</div>
+
+<div id="cubic5x8">
+{{11.3940197, 99.2884769}, {41.4314282, 38.0142946}, {6.25007991, 45.0930539}, {78.9565565, 22.8458219}},
+{{11.3940197, 99.2884769}, {17.9356966, 85.9439202}, {21.7417223, 74.0130457}},
+{{21.7417223, 74.0130457}, {23.9251358, 67.1686272}, {26.0700343, 57.3329391}},
+{{26.0700343, 57.3329391}, {28.2750992, 47.2213507}, {30.7090957, 43.764797}},
+{{30.7090957, 43.764797}, {34.2237869, 38.7735329}, {44.5059747, 34.4313542}},
+{{44.5059747, 34.4313542}, {53.4825656, 30.6405304}, {78.9565565, 22.8458219}},
+</div>
+
+<div id="cubic5x8x">
+{{11.3940197, 99.2884769}, {41.4314282, 38.0142946}, {6.25007991, 45.0930539}, {78.9565565, 22.8458219}},
+{{11.3940197, 99.2884769}, {18.6635437, 84.168545}, {21.7417223, 74.0130457}},
+{{21.7417223, 74.0130457}, {24.8199009, 63.8575464}, {26.0700343, 57.3329391}},
+{{26.0700343, 57.3329391}, {27.5370962, 48.6793447}, {30.7090957, 43.764797}},
+{{30.7090957, 43.764797}, {33.8810951, 38.8502494}, {44.5059747, 34.4313542}},
+{{44.5059747, 34.4313542}, {55.1308542, 30.012459}, {78.9565565, 22.8458219}},
+</div>
+
+<div id="cubic5x9">
+{{69.7292014, 38.6877352}, {24.7648688, 23.1501713}, {84.9283191, 90.2588441}, {80.392774, 61.3533852}},
+{{69.7292014, 38.6877352}, {57.2585085, 34.3784487}, {54.0073216, 37.8534623}},
+{{54.0073216, 37.8534623}, {51.2791269, 40.7694784}, {55.3644243, 48.2785885}},
+{{55.3644243, 48.2785885}, {59.0228346, 55.0030454}, {65.6488241, 61.3874162}},
+{{65.6488241, 61.3874162}, {72.4185069, 67.9102405}, {76.7088359, 68.6042477}},
+{{76.7088359, 68.6042477}, {81.6560742, 69.4045171}, {80.392774, 61.3533852}},
+</div>
+
+<div id="cubic5x9x">
+{{69.7292014, 38.6877352}, {24.7648688, 23.1501713}, {84.9283191, 90.2588441}, {80.392774, 61.3533852}},
+{{69.7292014, 38.6877352}, {56.5795552, 34.3837867}, {54.0073216, 37.8534623}},
+{{54.0073216, 37.8534623}, {51.4350879, 41.3231378}, {55.3644243, 48.2785885}},
+{{55.3644243, 48.2785885}, {59.2937606, 55.2340392}, {65.6488241, 61.3874162}},
+{{65.6488241, 61.3874162}, {72.0038877, 67.5407932}, {76.7088359, 68.6042477}},
+{{76.7088359, 68.6042477}, {81.413784, 69.6677022}, {80.392774, 61.3533852}},
+</div>
+
+<div id="cubic6x0">
+{{60.7765365, 71.2493073}, {87.1078942, 22.3776699}, {1.49747543, 68.0695699}, {45.2619466, 17.5360766}},
+{{60.7765365, 71.2493073}, {66.8034381, 60.063232}, {65.7606554, 53.9755229}},
+{{65.7606554, 53.9755229}, {64.9026034, 48.9662616}, {59.0403561, 46.9365029}},
+{{59.0403561, 46.9365029}, {55.5624487, 45.7323037}, {47.0319968, 45.0593685}},
+{{47.0319968, 45.0593685}, {38.6438055, 44.3976557}, {35.915024, 43.1681828}},
+{{35.915024, 43.1681828}, {31.4270492, 41.1460923}, {32.9921574, 35.8381417}},
+{{32.9921574, 35.8381417}, {34.8405988, 29.5692874}, {45.2619466, 17.5360766}},
+</div>
+
+<div id="cubic6x0x">
+{{60.7765365, 71.2493073}, {87.1078942, 22.3776699}, {1.49747543, 68.0695699}, {45.2619466, 17.5360766}},
+{{60.7765365, 71.2493073}, {66.9967453, 59.4196142}, {65.7606554, 53.9755229}},
+{{65.7606554, 53.9755229}, {64.5245656, 48.5314316}, {59.0403561, 46.9365029}},
+{{59.0403561, 46.9365029}, {53.5561467, 45.3415741}, {47.0319968, 45.0593685}},
+{{47.0319968, 45.0593685}, {40.2998025, 44.7818435}, {35.915024, 43.1681828}},
+{{35.915024, 43.1681828}, {31.5302455, 41.5545222}, {32.9921574, 35.8381417}},
+{{32.9921574, 35.8381417}, {34.4540694, 30.1217612}, {45.2619466, 17.5360766}},
+</div>
+
+<div id="cubic6x1">
+{{7.56463181, 38.7667716}, {53.1298274, 53.009038}, {22.9012888, 1.96013199}, {43.9383991, 72.6733402}},
+{{7.56463181, 38.7667716}, {18.0499753, 42.0441646}, {24.9041761, 41.2832621}},
+{{24.9041761, 41.2832621}, {30.0084481, 40.7166236}, {32.7855974, 37.9676099}},
+{{32.7855974, 37.9676099}, {34.25762, 36.5105005}, {35.0000192, 34.4010014}},
+{{35.0000192, 34.4010014}, {35.1477005, 33.9813707}, {35.2051475, 34.7029855}},
+{{35.2051475, 34.7029855}, {35.5299907, 38.7834725}, {36.7160087, 44.7150792}},
+{{36.7160087, 44.7150792}, {38.9607709, 55.9417619}, {43.9383991, 72.6733402}},
+</div>
+
+<div id="cubic6x1x">
+{{7.56463181, 38.7667716}, {53.1298274, 53.009038}, {22.9012888, 1.96013199}, {43.9383991, 72.6733402}},
+{{7.56463181, 38.7667716}, {19.0728251, 42.1807008}, {24.9041761, 41.2832621}},
+{{24.9041761, 41.2832621}, {30.7355271, 40.3858233}, {32.7855974, 37.9676099}},
+{{32.7855974, 37.9676099}, {34.8356678, 35.5493964}, {35.0000192, 34.4010014}},
+{{35.0000192, 34.4010014}, {35.1702591, 33.6960593}, {35.2051475, 34.7029855}},
+{{35.2051475, 34.7029855}, {35.1391248, 36.1152585}, {36.7160087, 44.7150792}},
+{{36.7160087, 44.7150792}, {38.2928925, 53.3148999}, {43.9383991, 72.6733402}},
+</div>
+
+<div id="cubic6x2">
+{{53.4808373, 52.4330519}, {42.3039286, 2.12741392}, {55.4457253, 76.3045082}, {49.8689114, 46.7937026}},
+{{53.4808373, 52.4330519}, {50.9719376, 41.1408598}, {49.8115514, 36.9274013}},
+{{49.8115514, 36.9274013}, {48.82027, 33.3279765}, {48.8115145, 34.8928161}},
+{{48.8115145, 34.8928161}, {48.8045445, 36.1385203}, {49.4292469, 40.7546742}},
+{{49.4292469, 40.7546742}, {49.7879548, 43.4052983}, {50.613269, 48.9383534}},
+{{50.613269, 48.9383534}, {51.3518777, 53.8901197}, {51.31236, 53.9808933}},
+{{51.31236, 53.9808933}, {51.2529165, 54.1174374}, {49.8689114, 46.7937026}},
+</div>
+
+<div id="cubic6x2x">
+{{53.4808373, 52.4330519}, {42.3039286, 2.12741392}, {55.4457253, 76.3045082}, {49.8689114, 46.7937026}},
+{{53.4808373, 52.4330519}, {50.8474472, 40.6156325}, {49.8115514, 36.9274013}},
+{{49.8115514, 36.9274013}, {48.7756556, 33.2391701}, {48.8115145, 34.8928161}},
+{{48.8115145, 34.8928161}, {48.8473733, 36.5464621}, {49.4292469, 40.7546742}},
+{{49.4292469, 40.7546742}, {50.0111204, 44.9628863}, {50.613269, 48.9383534}},
+{{50.613269, 48.9383534}, {51.3082301, 53.5085713}, {51.31236, 53.9808933}},
+{{51.31236, 53.9808933}, {51.31649, 54.4532153}, {49.8689114, 46.7937026}},
+</div>
+
+<div id="cubic6x3">
+{{30.270176, 50.8484091}, {9.21238377, 32.534054}, {99.8452993, 99.9447358}, {71.1751053, 39.994736}},
+{{30.270176, 50.8484091}, {26.1998702, 47.3083881}, {27.3542845, 47.6109361}},
+{{27.3542845, 47.6109361}, {28.1421178, 47.8174109}, {33.7377536, 50.9254737}},
+{{33.7377536, 50.9254737}, {43.6710144, 56.4428448}, {49.5826034, 59.2306974}},
+{{49.5826034, 59.2306974}, {60.0794163, 64.1809007}, {66.5061178, 65.1608314}},
+{{66.5061178, 65.1608314}, {74.7232814, 66.4137682}, {76.404788, 61.2406021}},
+{{76.404788, 61.2406021}, {78.4000331, 55.1022173}, {71.1751053, 39.994736}},
+</div>
+
+<div id="cubic6x3x">
+{{30.270176, 50.8484091}, {9.21238377, 32.534054}, {99.8452993, 99.9447358}, {71.1751053, 39.994736}},
+{{30.270176, 50.8484091}, {26.0151068, 47.1560011}, {27.3542845, 47.6109361}},
+{{27.3542845, 47.6109361}, {28.6934622, 48.0658712}, {33.7377536, 50.9254737}},
+{{33.7377536, 50.9254737}, {40.3775737, 54.7374488}, {49.5826034, 59.2306974}},
+{{49.5826034, 59.2306974}, {58.787633, 63.723946}, {66.5061178, 65.1608314}},
+{{66.5061178, 65.1608314}, {74.2246025, 66.5977168}, {76.404788, 61.2406021}},
+{{76.404788, 61.2406021}, {78.5849735, 55.8834875}, {71.1751053, 39.994736}},
+</div>
+
+<div id="cubic6x4">
+{{52.3256249, 36.7777584}, {23.7859194, 69.9470399}, {99.9000587, 20.2858463}, {44.2180221, 72.2977287}},
+{{52.3256249, 36.7777584}, {46.323817, 43.7531512}, {45.7451821, 46.7544892}},
+{{45.7451821, 46.7544892}, {45.2655359, 49.2423797}, {48.551811, 49.2476269}},
+{{48.551811, 49.2476269}, {50.5144448, 49.2507606}, {55.9087216, 48.0313516}},
+{{55.9087216, 48.0313516}, {62.3329105, 46.5791247}, {63.9943433, 47.0044226}},
+{{63.9943433, 47.0044226}, {66.7468982, 47.7090289}, {62.987381, 52.8381772}},
+{{62.987381, 52.8381772}, {58.5075376, 58.9500739}, {44.2180221, 72.2977287}},
+</div>
+
+<div id="cubic6x4x">
+{{52.3256249, 36.7777584}, {23.7859194, 69.9470399}, {99.9000587, 20.2858463}, {44.2180221, 72.2977287}},
+{{52.3256249, 36.7777584}, {46.0840368, 44.1087946}, {45.7451821, 46.7544892}},
+{{45.7451821, 46.7544892}, {45.4063273, 49.4001838}, {48.551811, 49.2476269}},
+{{48.551811, 49.2476269}, {51.6972946, 49.09507}, {55.9087216, 48.0313516}},
+{{55.9087216, 48.0313516}, {61.1409519, 46.6483554}, {63.9943433, 47.0044226}},
+{{63.9943433, 47.0044226}, {66.8477347, 47.3604898}, {62.987381, 52.8381772}},
+{{62.987381, 52.8381772}, {59.1270273, 58.3158645}, {44.2180221, 72.2977287}},
+</div>
+
+<div id="cubic6x5">
+{{42.9059103, 19.6341859}, {91.762872, 58.5903164}, {27.4474096, 8.61261101}, {52.1532298, 39.3337672}},
+{{42.9059103, 19.6341859}, {54.1145994, 28.5714415}, {58.004639, 31.7917065}},
+{{58.004639, 31.7917065}, {62.019725, 35.1154878}, {61.7728162, 35.2682181}},
+{{61.7728162, 35.2682181}, {61.6064162, 35.3711481}, {58.4041375, 33.5820691}},
+{{58.4041375, 33.5820691}, {53.244257, 30.6992989}, {50.8183004, 29.6863137}},
+{{50.8183004, 29.6863137}, {46.5331956, 27.8970204}, {46.2915313, 29.5538521}},
+{{46.2915313, 29.5538521}, {45.9839754, 31.662432}, {52.1532298, 39.3337672}},
+</div>
+
+<div id="cubic6x5x">
+{{42.9059103, 19.6341859}, {91.762872, 58.5903164}, {27.4474096, 8.61261101}, {52.1532298, 39.3337672}},
+{{42.9059103, 19.6341859}, {53.8121244, 28.322992}, {58.004639, 31.7917065}},
+{{58.004639, 31.7917065}, {62.1971535, 35.260421}, {61.7728162, 35.2682181}},
+{{61.7728162, 35.2682181}, {61.3484789, 35.2760153}, {58.4041375, 33.5820691}},
+{{58.4041375, 33.5820691}, {54.7626269, 31.4620033}, {50.8183004, 29.6863137}},
+{{50.8183004, 29.6863137}, {46.8739739, 27.9106241}, {46.2915313, 29.5538521}},
+{{46.2915313, 29.5538521}, {45.7090887, 31.1970802}, {52.1532298, 39.3337672}},
+</div>
+
+<div id="cubic6x6">
+{{73.4375576, 65.030414}, {66.1679208, 84.2450892}, {7.2134248, 36.0306381}, {66.9352454, 80.6694031}},
+{{73.4375576, 65.030414}, {71.5866063, 69.9227391}, {65.0188473, 69.7835224}},
+{{65.0188473, 69.7835224}, {60.0105733, 69.677362}, {52.4355896, 66.6514651}},
+{{52.4355896, 66.6514651}, {48.2960051, 64.9978699}, {42.4281173, 61.975806}},
+{{42.4281173, 61.975806}, {40.1794784, 60.817718}, {40.5562709, 61.1722188}},
+{{40.5562709, 61.1722188}, {40.9330633, 61.5267196}, {45.4424567, 64.8118124}},
+{{45.4424567, 64.8118124}, {56.3732534, 72.774897}, {66.9352454, 80.6694031}},
+</div>
+
+<div id="cubic6x6x">
+{{73.4375576, 65.030414}, {66.1679208, 84.2450892}, {7.2134248, 36.0306381}, {66.9352454, 80.6694031}},
+{{73.4375576, 65.030414}, {71.1118808, 70.1709551}, {65.0188473, 69.7835224}},
+{{65.0188473, 69.7835224}, {58.9258137, 69.3960897}, {52.4355896, 66.6514651}},
+{{52.4355896, 66.6514651}, {45.9453656, 63.9068405}, {42.4281173, 61.975806}},
+{{42.4281173, 61.975806}, {40.0852803, 60.7290928}, {40.5562709, 61.1722188}},
+{{40.5562709, 61.1722188}, {41.0272614, 61.6153448}, {45.4424567, 64.8118124}},
+{{45.4424567, 64.8118124}, {51.3278432, 69.0492921}, {66.9352454, 80.6694031}},
+</div>
+
+<div id="cubic6x7">
+{{46.6695473, 75.0819435}, {2.22400357, 78.828021}, {62.548768, 57.1436195}, {12.8128845, 46.150303}},
+{{46.6695473, 75.0819435}, {36.8374139, 75.9106415}, {32.735691, 75.1220326}},
+{{32.735691, 75.1220326}, {29.1601585, 74.4345905}, {29.1402184, 72.2922743}},
+{{29.1402184, 72.2922743}, {29.1278273, 70.9609985}, {31.0504514, 67.4052326}},
+{{31.0504514, 67.4052326}, {33.5289159, 62.8214769}, {33.7777617, 60.3248048}},
+{{33.7777617, 60.3248048}, {34.2044612, 56.0437252}, {30.1210496, 52.8325143}},
+{{30.1210496, 52.8325143}, {25.0685705, 48.8592251}, {12.8128845, 46.150303}},
+</div>
+
+<div id="cubic6x7x">
+{{46.6695473, 75.0819435}, {2.22400357, 78.828021}, {62.548768, 57.1436195}, {12.8128845, 46.150303}},
+{{46.6695473, 75.0819435}, {36.5139384, 75.9210204}, {32.735691, 75.1220326}},
+{{32.735691, 75.1220326}, {28.9574435, 74.3230448}, {29.1402184, 72.2922743}},
+{{29.1402184, 72.2922743}, {29.3229933, 70.2615038}, {31.0504514, 67.4052326}},
+{{31.0504514, 67.4052326}, {33.1016834, 64.1207271}, {33.7777617, 60.3248048}},
+{{33.7777617, 60.3248048}, {34.45384, 56.5288825}, {30.1210496, 52.8325143}},
+{{30.1210496, 52.8325143}, {25.7882591, 49.1361461}, {12.8128845, 46.150303}},
+</div>
+
+<div id="cubic6x8">
+{{55.3467924, 13.540705}, {78.628494, 9.09824134}, {14.1422475, 88.7534345}, {78.9736115, 9.48816133}},
+{{55.3467924, 13.540705}, {60.6017653, 12.5379851}, {60.6776079, 17.0952733}},
+{{60.6776079, 17.0952733}, {60.7373059, 20.6824519}, {57.5541656, 27.8149349}},
+{{57.5541656, 27.8149349}, {55.7485732, 31.8607373}, {51.7778474, 39.2052874}},
+{{51.7778474, 39.2052874}, {48.7947857, 44.7229805}, {49.1759091, 44.7804774}},
+{{49.1759091, 44.7804774}, {49.7203899, 44.8626187}, {56.152876, 37.2125188}},
+{{56.152876, 37.2125188}, {61.4648441, 30.8950413}, {78.9736115, 9.48816133}},
+</div>
+
+<div id="cubic6x8x">
+{{55.3467924, 13.540705}, {78.628494, 9.09824134}, {14.1422475, 88.7534345}, {78.9736115, 9.48816133}},
+{{55.3467924, 13.540705}, {60.8509374, 12.7149155}, {60.6776079, 17.0952733}},
+{{60.6776079, 17.0952733}, {60.5042785, 21.475631}, {57.5541656, 27.8149349}},
+{{57.5541656, 27.8149349}, {54.6040527, 34.1542387}, {51.7778474, 39.2052874}},
+{{51.7778474, 39.2052874}, {48.8652599, 44.4020133}, {49.1759091, 44.7804774}},
+{{49.1759091, 44.7804774}, {49.4865584, 45.1589416}, {56.152876, 37.2125188}},
+{{56.152876, 37.2125188}, {62.8191937, 29.2660961}, {78.9736115, 9.48816133}},
+</div>
+
+<div id="cubic6x9">
+{{6.436938, 85.6170305}, {65.4323691, 21.8280372}, {63.8217439, 52.0501321}, {6.57091737, 37.4082543}},
+{{6.436938, 85.6170305}, {18.3889022, 72.6939321}, {29.5730232, 62.1640306}},
+{{29.5730232, 62.1640306}, {35.8331919, 56.2700528}, {44.0352491, 49.2100734}},
+{{44.0352491, 49.2100734}, {50.0664784, 44.0186496}, {50.0976641, 43.1465107}},
+{{50.0976641, 43.1465107}, {50.1288498, 42.2743718}, {44.2847347, 42.2329622}},
+{{44.2847347, 42.2329622}, {36.0580615, 42.1746705}, {29.7656368, 41.5603994}},
+{{29.7656368, 41.5603994}, {18.5096561, 40.4615824}, {6.57091737, 37.4082543}},
+</div>
+
+<div id="cubic6x9x">
+{{6.436938, 85.6170305}, {65.4323691, 21.8280372}, {63.8217439, 52.0501321}, {6.57091737, 37.4082543}},
+{{6.436938, 85.6170305}, {20.1874324, 70.8746109}, {29.5730232, 62.1640306}},
+{{29.5730232, 62.1640306}, {38.958614, 53.4534502}, {44.0352491, 49.2100734}},
+{{44.0352491, 49.2100734}, {50.058682, 44.2366844}, {50.0976641, 43.1465107}},
+{{50.0976641, 43.1465107}, {50.1366462, 42.0563371}, {44.2847347, 42.2329622}},
+{{44.2847347, 42.2329622}, {39.2093652, 42.3394209}, {29.7656368, 41.5603994}},
+{{29.7656368, 41.5603994}, {20.3219083, 40.7813779}, {6.57091737, 37.4082543}},
+</div>
+
+<div id="cubic7x0">
+{{47.0675449, 64.2273128}, {68.4467872, 85.1524572}, {57.3478562, 45.4193099}, {62.340955, 64.4298956}},
+{{47.0675449, 64.2273128}, {52.2209452, 69.2712543}, {55.5069225, 70.2618397}},
+{{55.5069225, 70.2618397}, {58.2344663, 71.0840808}, {59.6132451, 69.0985913}},
+{{59.6132451, 69.0985913}, {60.6680756, 67.5795987}, {60.901578, 64.4621115}},
+{{60.901578, 64.4621115}, {61.029698, 62.7515845}, {60.8869865, 60.0769443}},
+{{60.8869865, 60.0769443}, {60.8258684, 58.931493}, {60.9363129, 59.2030029}},
+{{60.9363129, 59.2030029}, {61.0467573, 59.4745129}, {61.7705423, 62.2490239}},
+{{61.7705423, 62.2490239}, {62.1209644, 63.5923097}, {62.340955, 64.4298956}},
+</div>
+
+<div id="cubic7x0x">
+{{47.0675449, 64.2273128}, {68.4467872, 85.1524572}, {57.3478562, 45.4193099}, {62.340955, 64.4298956}},
+{{47.0675449, 64.2273128}, {52.5598806, 69.5095881}, {55.5069225, 70.2618397}},
+{{55.5069225, 70.2618397}, {58.4539644, 71.0140913}, {59.6132451, 69.0985913}},
+{{59.6132451, 69.0985913}, {60.7725259, 67.1830912}, {60.901578, 64.4621115}},
+{{60.901578, 64.4621115}, {61.0306302, 61.7411317}, {60.8869865, 60.0769443}},
+{{60.8869865, 60.0769443}, {60.7982573, 58.8636155}, {60.9363129, 59.2030029}},
+{{60.9363129, 59.2030029}, {61.0743684, 59.5423904}, {61.7705423, 62.2490239}},
+{{61.7705423, 62.2490239}, {62.0120077, 63.1760698}, {62.340955, 64.4298956}},
+</div>
+
+<div id="cubic7x1">
+{{44.6639438, 66.9040647}, {56.6149349, 27.2102873}, {23.2993796, 92.6723405}, {44.026369, 51.1832799}},
+{{44.6639438, 66.9040647}, {47.1627908, 58.6044453}, {47.3201686, 55.4528932}},
+{{47.3201686, 55.4528932}, {47.4533435, 52.7860125}, {45.9070214, 53.8259442}},
+{{45.9070214, 53.8259442}, {44.6909451, 54.6437792}, {42.4058247, 57.7914576}},
+{{42.4058247, 57.7914576}, {41.1108979, 59.5751769}, {38.7979012, 63.1176732}},
+{{38.7979012, 63.1176732}, {37.2505608, 65.4875199}, {37.097116, 65.5770977}},
+{{37.097116, 65.5770977}, {36.8720355, 65.7084948}, {38.3585854, 62.6270533}},
+{{38.3585854, 62.6270533}, {39.7438195, 59.7556272}, {44.026369, 51.1832799}},
+</div>
+
+<div id="cubic7x1x">
+{{44.6639438, 66.9040647}, {56.6149349, 27.2102873}, {23.2993796, 92.6723405}, {44.026369, 51.1832799}},
+{{44.6639438, 66.9040647}, {47.2570645, 58.1934532}, {47.3201686, 55.4528932}},
+{{47.3201686, 55.4528932}, {47.3832726, 52.7123331}, {45.9070214, 53.8259442}},
+{{45.9070214, 53.8259442}, {44.4307701, 54.9395554}, {42.4058247, 57.7914576}},
+{{42.4058247, 57.7914576}, {40.3808794, 60.6433599}, {38.7979012, 63.1176732}},
+{{38.7979012, 63.1176732}, {37.3874524, 65.3142201}, {37.097116, 65.5770977}},
+{{37.097116, 65.5770977}, {36.8067796, 65.8399752}, {38.3585854, 62.6270533}},
+{{38.3585854, 62.6270533}, {39.9103912, 59.4141313}, {44.026369, 51.1832799}},
+</div>
+
+<div id="cubic7x2">
+{{8.53545089, 55.3230609}, {14.6846658, 5.17757498}, {19.5026836, 81.6040195}, {18.7564744, 40.0648544}},
+{{8.53545089, 55.3230609}, {9.80938657, 44.9343975}, {11.1496907, 40.6303968}},
+{{11.1496907, 40.6303968}, {12.2999484, 36.9366756}, {13.510145, 37.7040519}},
+{{13.510145, 37.7040519}, {14.4789672, 38.3183745}, {15.5359245, 41.871143}},
+{{15.5359245, 41.871143}, {16.1464176, 43.9232035}, {17.1461401, 48.4587871}},
+{{17.1461401, 48.4587871}, {17.9290951, 52.0109309}, {18.2017805, 52.6665884}},
+{{18.2017805, 52.6665884}, {18.6299694, 53.6961462}, {18.7604053, 51.1306715}},
+{{18.7604053, 51.1306715}, {18.904388, 48.2987505}, {18.7564744, 40.0648544}},
+</div>
+
+<div id="cubic7x2x">
+{{8.53545089, 55.3230609}, {14.6846658, 5.17757498}, {19.5026836, 81.6040195}, {18.7564744, 40.0648544}},
+{{8.53545089, 55.3230609}, {9.89590602, 44.4510387}, {11.1496907, 40.6303968}},
+{{11.1496907, 40.6303968}, {12.4034754, 36.8097549}, {13.510145, 37.7040519}},
+{{13.510145, 37.7040519}, {14.6168146, 38.5983488}, {15.5359245, 41.871143}},
+{{15.5359245, 41.871143}, {16.4550345, 45.1439372}, {17.1461401, 48.4587871}},
+{{17.1461401, 48.4587871}, {17.7900216, 51.5253445}, {18.2017805, 52.6665884}},
+{{18.2017805, 52.6665884}, {18.6135393, 53.8078322}, {18.7604053, 51.1306715}},
+{{18.7604053, 51.1306715}, {18.9072713, 48.4535108}, {18.7564744, 40.0648544}},
+</div>
+
+<div id="cubic7x3">
+{{77.2429303, 21.9290386}, {61.3518447, 40.4530391}, {94.2286334, 0.642292155}, {95.0042533, 36.4855481}},
+{{77.2429303, 21.9290386}, {76.5648343, 22.7194849}, {75.4687566, 23.992131}},
+{{75.4687566, 23.992131}, {73.1344126, 26.702517}, {72.9524614, 27.0039848}},
+{{72.9524614, 27.0039848}, {72.7705102, 27.3054527}, {74.013147, 26.4038735}},
+{{74.013147, 26.4038735}, {76.9396956, 24.2805538}, {79.071521, 23.1293275}},
+{{79.071521, 23.1293275}, {82.9580525, 21.0305265}, {85.9547875, 20.9037075}},
+{{85.9547875, 20.9037075}, {89.8728448, 20.737899}, {92.1150103, 23.9485892}},
+{{92.1150103, 23.9485892}, {94.8166786, 27.8172686}, {95.0042533, 36.4855481}},
+</div>
+
+<div id="cubic7x3x">
+{{77.2429303, 21.9290386}, {61.3518447, 40.4530391}, {94.2286334, 0.642292155}, {95.0042533, 36.4855481}},
+{{77.2429303, 21.9290386}, {76.2273572, 23.1121054}, {75.4687566, 23.992131}},
+{{75.4687566, 23.992131}, {73.1799004, 26.6271501}, {72.9524614, 27.0039848}},
+{{72.9524614, 27.0039848}, {72.7250224, 27.3808196}, {74.013147, 26.4038735}},
+{{74.013147, 26.4038735}, {75.7676189, 25.0320659}, {79.071521, 23.1293275}},
+{{79.071521, 23.1293275}, {82.3754232, 21.226589}, {85.9547875, 20.9037075}},
+{{85.9547875, 20.9037075}, {89.5341519, 20.580826}, {92.1150103, 23.9485892}},
+{{92.1150103, 23.9485892}, {94.6958688, 27.3163524}, {95.0042533, 36.4855481}},
+</div>
+
+<div id="cubic7x4">
+{{85.1880251, 55.1384624}, {12.1381459, 5.8187271}, {95.3464197, 87.2766355}, {58.4136199, 57.7104629}},
+{{85.1880251, 55.1384624}, {69.4954757, 44.5436142}, {61.7319269, 40.861468}},
+{{61.7319269, 40.861468}, {55.009991, 37.6733448}, {54.1223283, 39.6260005}},
+{{54.1223283, 39.6260005}, {53.4043154, 41.2054652}, {56.5289517, 46.3315706}},
+{{56.5289517, 46.3315706}, {58.3527212, 49.323546}, {63.1215192, 55.8776895}},
+{{63.1215192, 55.8776895}, {66.7797089, 60.9054346}, {67.68997, 62.4640064}},
+{{67.68997, 62.4640064}, {69.1578236, 64.9773019}, {67.3518779, 64.1520255}},
+{{67.3518779, 64.1520255}, {65.2740366, 63.2024988}, {58.4136199, 57.7104629}},
+</div>
+
+<div id="cubic7x4x">
+{{85.1880251, 55.1384624}, {12.1381459, 5.8187271}, {95.3464197, 87.2766355}, {58.4136199, 57.7104629}},
+{{85.1880251, 55.1384624}, {68.7695663, 44.1020224}, {61.7319269, 40.861468}},
+{{61.7319269, 40.861468}, {54.6942874, 37.6209137}, {54.1223283, 39.6260005}},
+{{54.1223283, 39.6260005}, {53.5503693, 41.6310872}, {56.5289517, 46.3315706}},
+{{56.5289517, 46.3315706}, {59.5075341, 51.032054}, {63.1215192, 55.8776895}},
+{{63.1215192, 55.8776895}, {66.1706775, 59.9915119}, {67.68997, 62.4640064}},
+{{67.68997, 62.4640064}, {69.2092626, 64.9365008}, {67.3518779, 64.1520255}},
+{{67.3518779, 64.1520255}, {65.4944933, 63.3675501}, {58.4136199, 57.7104629}},
+</div>
+
+<div id="cubic7x5">
+{{8.65591127, 79.9006976}, {91.0247206, 52.4786449}, {8.58452539, 80.1182901}, {48.1023732, 56.5861463}},
+{{8.65591127, 79.9006976}, {10.1949106, 79.3883372}, {13.1021747, 78.4205896}},
+{{13.1021747, 78.4205896}, {33.3914306, 71.6668594}, {38.6134953, 69.8848279}},
+{{38.6134953, 69.8848279}, {45.9243859, 67.3899838}, {46.7629899, 66.8658296}},
+{{46.7629899, 66.8658296}, {47.3619928, 66.4914338}, {44.5359397, 66.7758818}},
+{{44.5359397, 66.7758818}, {40.3498242, 67.197223}, {38.6707421, 67.0021236}},
+{{38.6707421, 67.0021236}, {35.6941333, 66.6562593}, {37.1605001, 64.6054153}},
+{{37.1605001, 64.6054153}, {39.032712, 61.9869609}, {48.1023732, 56.5861463}},
+</div>
+
+<div id="cubic7x5x">
+{{8.65591127, 79.9006976}, {91.0247206, 52.4786449}, {8.58452539, 80.1182901}, {48.1023732, 56.5861463}},
+{{8.65591127, 79.9006976}, {10.9639426, 79.1323302}, {13.1021747, 78.4205896}},
+{{13.1021747, 78.4205896}, {31.0714516, 72.4500538}, {38.6134953, 69.8848279}},
+{{38.6134953, 69.8848279}, {46.155539, 67.319602}, {46.7629899, 66.8658296}},
+{{46.7629899, 66.8658296}, {47.3704409, 66.4120572}, {44.5359397, 66.7758818}},
+{{44.5359397, 66.7758818}, {41.5267469, 67.1697889}, {38.6707421, 67.0021236}},
+{{38.6707421, 67.0021236}, {35.8147372, 66.8344583}, {37.1605001, 64.6054153}},
+{{37.1605001, 64.6054153}, {38.5062629, 62.3763723}, {48.1023732, 56.5861463}},
+</div>
+
+<div id="cubic7x6">
+{{42.8441148, 81.0382013}, {9.0486696, 80.9900212}, {99.2855478, 92.2020003}, {39.0193165, 97.6524087}},
+{{42.8441148, 81.0382013}, {36.5292256, 81.0291985}, {35.3205259, 81.5652507}},
+{{35.3205259, 81.5652507}, {34.274399, 82.0292026}, {36.9288084, 83.0293311}},
+{{36.9288084, 83.0293311}, {38.5699459, 83.647679}, {43.916545, 85.1977854}},
+{{43.916545, 85.1977854}, {50.735588, 87.1747884}, {53.7318941, 88.2602772}},
+{{53.7318941, 88.2602772}, {58.8545207, 90.11608}, {59.9920782, 91.5927712}},
+{{59.9920782, 91.5927712}, {61.3953813, 93.4144333}, {56.9901885, 94.8414282}},
+{{56.9901885, 94.8414282}, {51.9120881, 96.4864013}, {39.0193165, 97.6524087}},
+</div>
+
+<div id="cubic7x6x">
+{{42.8441148, 81.0382013}, {9.0486696, 80.9900212}, {99.2855478, 92.2020003}, {39.0193165, 97.6524087}},
+{{42.8441148, 81.0382013}, {36.3303003, 81.0383861}, {35.3205259, 81.5652507}},
+{{35.3205259, 81.5652507}, {34.3107514, 82.0921153}, {36.9288084, 83.0293311}},
+{{36.9288084, 83.0293311}, {39.5468653, 83.9665469}, {43.916545, 85.1977854}},
+{{43.916545, 85.1977854}, {48.9996472, 86.6173008}, {53.7318941, 88.2602772}},
+{{53.7318941, 88.2602772}, {58.4641409, 89.9032535}, {59.9920782, 91.5927712}},
+{{59.9920782, 91.5927712}, {61.5200154, 93.2822889}, {56.9901885, 94.8414282}},
+{{56.9901885, 94.8414282}, {52.4603617, 96.4005675}, {39.0193165, 97.6524087}},
+</div>
+
+<div id="cubic7x7">
+{{70.2955832, 57.867012}, {70.8709129, 27.4331047}, {68.1912432, 90.2241446}, {97.1991291, 25.763215}},
+{{70.2955832, 57.867012}, {70.3286385, 56.1184463}, {70.3691418, 53.5027125}},
+{{70.3691418, 53.5027125}, {70.4294268, 49.6094598}, {70.5008735, 49.1586526}},
+{{70.5008735, 49.1586526}, {70.5723202, 48.7078455}, {70.9407155, 49.8962556}},
+{{70.9407155, 49.8962556}, {71.8329974, 52.7746761}, {72.7964345, 54.1820074}},
+{{72.7964345, 54.1820074}, {74.5546706, 56.7503333}, {77.0780289, 56.0896348}},
+{{77.0780289, 56.0896348}, {80.3799099, 55.2250934}, {84.85557, 48.8673125}},
+{{84.85557, 48.8673125}, {90.2513448, 41.2024868}, {97.1991291, 25.763215}},
+</div>
+
+<div id="cubic7x7x">
+{{70.2955832, 57.867012}, {70.8709129, 27.4331047}, {68.1912432, 90.2241446}, {97.1991291, 25.763215}},
+{{70.2955832, 57.867012}, {70.3435094, 55.2546173}, {70.3691418, 53.5027125}},
+{{70.3691418, 53.5027125}, {70.4115651, 49.7221615}, {70.5008735, 49.1586526}},
+{{70.5008735, 49.1586526}, {70.5901819, 48.5951437}, {70.9407155, 49.8962556}},
+{{70.9407155, 49.8962556}, {71.3958651, 51.7896844}, {72.7964345, 54.1820074}},
+{{72.7964345, 54.1820074}, {74.1970039, 56.5743304}, {77.0780289, 56.0896348}},
+{{77.0780289, 56.0896348}, {79.9590538, 55.6049393}, {84.85557, 48.8673125}},
+{{84.85557, 48.8673125}, {89.7520861, 42.1296858}, {97.1991291, 25.763215}},
+</div>
+
+<div id="cubic7x8">
+{{50.528201, 27.4745214}, {64.2810473, 71.5620589}, {43.5236709, 2.33669765}, {72.8774712, 51.6581711}},
+{{50.528201, 27.4745214}, {53.3761101, 36.6040713}, {54.38742, 39.6099548}},
+{{54.38742, 39.6099548}, {55.5064406, 42.9359834}, {55.7720854, 42.9677817}},
+{{55.7720854, 42.9677817}, {55.9546136, 42.9896307}, {55.8827854, 40.8375726}},
+{{55.8827854, 40.8375726}, {55.7725733, 37.5354848}, {55.9802468, 35.9707481}},
+{{55.9802468, 35.9707481}, {56.3474228, 33.2042239}, {57.7009449, 33.0167369}},
+{{57.7009449, 33.0167369}, {59.424989, 32.7779259}, {62.7612346, 36.6782932}},
+{{62.7612346, 36.6782932}, {66.7088662, 41.293425}, {72.8774712, 51.6581711}},
+</div>
+
+<div id="cubic7x8x">
+{{50.528201, 27.4745214}, {64.2810473, 71.5620589}, {43.5236709, 2.33669765}, {72.8774712, 51.6581711}},
+{{50.528201, 27.4745214}, {53.2265224, 36.1478361}, {54.38742, 39.6099548}},
+{{54.38742, 39.6099548}, {55.5483175, 43.0720735}, {55.7720854, 42.9677817}},
+{{55.7720854, 42.9677817}, {55.9958532, 42.8634898}, {55.8827854, 40.8375726}},
+{{55.8827854, 40.8375726}, {55.7402514, 38.5138013}, {55.9802468, 35.9707481}},
+{{55.9802468, 35.9707481}, {56.2202423, 33.4276949}, {57.7009449, 33.0167369}},
+{{57.7009449, 33.0167369}, {59.1816474, 32.6057789}, {62.7612346, 36.6782932}},
+{{62.7612346, 36.6782932}, {66.3408218, 40.7508075}, {72.8774712, 51.6581711}},
+</div>
+
+<div id="cubic7x9">
+{{30.3413925, 47.7835835}, {98.6874047, 39.210338}, {8.15117029, 96.7190508}, {57.0872154, 64.8290379}},
+{{30.3413925, 47.7835835}, {46.0782555, 45.8095694}, {52.5540659, 48.2453346}},
+{{52.5540659, 48.2453346}, {57.9511897, 50.2753703}, {56.8130484, 55.3244869}},
+{{56.8130484, 55.3244869}, {55.9369414, 59.2111449}, {51.1961195, 64.811489}},
+{{51.1961195, 64.811489}, {48.5753558, 67.9074035}, {43.7810591, 72.4967897}},
+{{43.7810591, 72.4967897}, {41.2648644, 74.905441}, {42.230691, 74.4021224}},
+{{42.230691, 74.4021224}, {43.1965176, 73.8988039}, {51.5076718, 68.470241}},
+{{51.5076718, 68.470241}, {54.9756852, 66.2050527}, {57.0872154, 64.8290379}},
+</div>
+
+<div id="cubic7x9x">
+{{30.3413925, 47.7835835}, {98.6874047, 39.210338}, {8.15117029, 96.7190508}, {57.0872154, 64.8290379}},
+{{30.3413925, 47.7835835}, {46.9458744, 45.8339148}, {52.5540659, 48.2453346}},
+{{52.5540659, 48.2453346}, {58.1622574, 50.6567543}, {56.8130484, 55.3244869}},
+{{56.8130484, 55.3244869}, {55.4638393, 59.9922194}, {51.1961195, 64.811489}},
+{{51.1961195, 64.811489}, {46.9283998, 69.6307587}, {43.7810591, 72.4967897}},
+{{43.7810591, 72.4967897}, {41.0234077, 75.0312707}, {42.230691, 74.4021224}},
+{{42.230691, 74.4021224}, {43.4379742, 73.7729742}, {51.5076718, 68.470241}},
+{{51.5076718, 68.470241}, {53.9259122, 66.8899375}, {57.0872154, 64.8290379}},
+</div>
+
+<div id="cubic8x0">
+{{42.5967063, 22.8420382}, {6.13525533, 15.2363991}, {78.1588409, 15.6382141}, {31.4640028, 15.4944166}},
+{{42.5967063, 22.8420382}, {34.7914244, 21.2139034}, {32.6593413, 19.878761}},
+{{32.6593413, 19.878761}, {30.8695713, 18.7579803}, {33.1023831, 17.8591237}},
+{{33.1023831, 17.8591237}, {34.8391625, 17.1599535}, {39.0195021, 16.5984277}},
+{{39.0195021, 16.5984277}, {41.3590736, 16.2841638}, {45.5043686, 15.9119743}},
+{{45.5043686, 15.9119743}, {47.7538437, 15.7100029}, {47.8024311, 15.6545014}},
+{{47.8024311, 15.6545014}, {47.8704535, 15.5767993}, {44.9932779, 15.5487509}},
+{{44.9932779, 15.5487509}, {42.9381525, 15.5287163}, {34.6690635, 15.5040796}},
+{{34.6690635, 15.5040796}, {32.6017407, 15.4979203}, {31.4640028, 15.4944166}},
+</div>
+
+<div id="cubic8x0x">
+{{42.5967063, 22.8420382}, {6.13525533, 15.2363991}, {78.1588409, 15.6382141}, {31.4640028, 15.4944166}},
+{{42.5967063, 22.8420382}, {34.4196308, 21.1014023}, {32.6593413, 19.878761}},
+{{32.6593413, 19.878761}, {30.8990517, 18.6561197}, {33.1023831, 17.8591237}},
+{{33.1023831, 17.8591237}, {35.3057145, 17.0621277}, {39.0195021, 16.5984277}},
+{{39.0195021, 16.5984277}, {42.7332897, 16.1347277}, {45.5043686, 15.9119743}},
+{{45.5043686, 15.9119743}, {47.6292231, 15.7339768}, {47.8024311, 15.6545014}},
+{{47.8024311, 15.6545014}, {47.9756391, 15.575026}, {44.9932779, 15.5487509}},
+{{44.9932779, 15.5487509}, {42.0109167, 15.5224759}, {34.6690635, 15.5040796}},
+{{34.6690635, 15.5040796}, {33.169788, 15.4996412}, {31.4640028, 15.4944166}},
+</div>
+
+<div id="cubic8x1">
+{{29.0323957, 47.4745379}, {4.55778772, 2.73824763}, {21.7278637, 80.2053625}, {11.5269861, 34.0549996}},
+{{29.0323957, 47.4745379}, {23.6693619, 37.6716337}, {20.3221199, 34.4936205}},
+{{20.3221199, 34.4936205}, {17.5126817, 31.826221}, {16.162445, 33.8631071}},
+{{16.162445, 33.8631071}, {15.1123784, 35.4471745}, {14.9546458, 39.8886357}},
+{{14.9546458, 39.8886357}, {14.8663892, 42.3737787}, {15.0999972, 46.8758445}},
+{{15.0999972, 46.8758445}, {15.2259779, 49.3037298}, {15.1224749, 49.3309043}},
+{{15.1224749, 49.3309043}, {14.9775707, 49.3689487}, {14.2215808, 46.1220869}},
+{{14.2215808, 46.1220869}, {13.6815881, 43.8028999}, {11.62512, 34.4989774}},
+{{11.62512, 34.4989774}, {11.559983, 34.2042829}, {11.5269861, 34.0549996}},
+</div>
+
+<div id="cubic8x1x">
+{{29.0323957, 47.4745379}, {4.55778772, 2.73824763}, {21.7278637, 80.2053625}, {11.5269861, 34.0549996}},
+{{29.0323957, 47.4745379}, {23.339767, 37.184683}, {20.3221199, 34.4936205}},
+{{20.3221199, 34.4936205}, {17.3044729, 31.802558}, {16.162445, 33.8631071}},
+{{16.162445, 33.8631071}, {15.0204171, 35.9236561}, {14.9546458, 39.8886357}},
+{{14.9546458, 39.8886357}, {14.8888745, 43.8536153}, {15.0999972, 46.8758445}},
+{{15.0999972, 46.8758445}, {15.2455546, 49.1755419}, {15.1224749, 49.3309043}},
+{{15.1224749, 49.3309043}, {14.9993952, 49.4862668}, {14.2215808, 46.1220869}},
+{{14.2215808, 46.1220869}, {13.4437665, 42.757907}, {11.62512, 34.4989774}},
+{{11.62512, 34.4989774}, {11.5764809, 34.2789225}, {11.5269861, 34.0549996}},
+</div>
+
+<div id="cubic8x2">
+{{30.5187597, 28.7944151}, {47.7341773, 68.3182353}, {24.579915, 14.6321317}, {22.237118, 39.2417454}},
+{{30.5187597, 28.7944151}, {30.823715, 29.4945431}, {31.3959629, 30.8080078}},
+{{31.3959629, 30.8080078}, {34.9281707, 38.9153861}, {35.7821411, 40.9504208}},
+{{35.7821411, 40.9504208}, {36.9776996, 43.7994693}, {36.8148424, 43.845334}},
+{{36.8148424, 43.845334}, {36.6985159, 43.8780945}, {35.3792396, 41.9741019}},
+{{35.3792396, 41.9741019}, {33.3589087, 39.0583404}, {32.0725075, 37.4554574}},
+{{32.0725075, 37.4554574}, {29.7893226, 34.6105606}, {28.0338583, 33.4024856}},
+{{28.0338583, 33.4024856}, {25.7901854, 31.8584352}, {24.3823693, 32.9522328}},
+{{24.3823693, 32.9522328}, {22.7123482, 34.2497498}, {22.237118, 39.2417454}},
+</div>
+
+<div id="cubic8x2x">
+{{30.5187597, 28.7944151}, {47.7341773, 68.3182353}, {24.579915, 14.6321317}, {22.237118, 39.2417454}},
+{{30.5187597, 28.7944151}, {30.9761076, 29.8443688}, {31.3959629, 30.8080078}},
+{{31.3959629, 30.8080078}, {34.5380678, 38.0012585}, {35.7821411, 40.9504208}},
+{{35.7821411, 40.9504208}, {37.0262144, 43.899583}, {36.8148424, 43.845334}},
+{{36.8148424, 43.845334}, {36.6034705, 43.791085}, {35.3792396, 41.9741019}},
+{{35.3792396, 41.9741019}, {34.0487375, 39.9904922}, {32.0725075, 37.4554574}},
+{{32.0725075, 37.4554574}, {30.0962775, 34.9204225}, {28.0338583, 33.4024856}},
+{{28.0338583, 33.4024856}, {25.9714391, 31.8845487}, {24.3823693, 32.9522328}},
+{{24.3823693, 32.9522328}, {22.7932996, 34.019917}, {22.237118, 39.2417454}},
+</div>
+
+<div id="cubic8x3">
+{{44.0194731, 35.2849254}, {33.7413378, 90.6639866}, {89.6236054, 3.93610117}, {54.0523993, 58.6752083}},
+{{44.0194731, 35.2849254}, {41.8034025, 47.2252151}, {43.4093427, 51.8147312}},
+{{43.4093427, 51.8147312}, {44.7573046, 55.6669869}, {48.7793294, 54.2868164}},
+{{48.7793294, 54.2868164}, {51.9073817, 53.2134153}, {56.6514498, 48.9586591}},
+{{56.6514498, 48.9586591}, {59.3060696, 46.5778416}, {63.5477208, 42.0877376}},
+{{63.5477208, 42.0877376}, {65.8388976, 39.6623562}, {66.0159848, 39.6831127}},
+{{66.0159848, 39.6831127}, {66.2639069, 39.7121719}, {64.0479481, 43.2239426}},
+{{64.0479481, 43.2239426}, {62.4651204, 45.7323502}, {55.9567221, 55.7452241}},
+{{55.9567221, 55.7452241}, {54.718939, 57.649497}, {54.0523993, 58.6752083}},
+</div>
+
+<div id="cubic8x3x">
+{{44.0194731, 35.2849254}, {33.7413378, 90.6639866}, {89.6236054, 3.93610117}, {54.0523993, 58.6752083}},
+{{44.0194731, 35.2849254}, {41.7846308, 47.8464432}, {43.4093427, 51.8147312}},
+{{43.4093427, 51.8147312}, {45.0340547, 55.7830192}, {48.7793294, 54.2868164}},
+{{48.7793294, 54.2868164}, {52.524604, 52.7906136}, {56.6514498, 48.9586591}},
+{{56.6514498, 48.9586591}, {60.7782955, 45.1267046}, {63.5477208, 42.0877376}},
+{{63.5477208, 42.0877376}, {65.6800669, 39.7784361}, {66.0159848, 39.6831127}},
+{{66.0159848, 39.6831127}, {66.3519027, 39.5877893}, {64.0479481, 43.2239426}},
+{{64.0479481, 43.2239426}, {61.7439935, 46.8600958}, {55.9567221, 55.7452241}},
+{{55.9567221, 55.7452241}, {55.0519496, 57.1371078}, {54.0523993, 58.6752083}},
+</div>
+
+<div id="cubic8x4">
+{{34.4823321, 44.5556425}, {46.6831036, 2.92242272}, {17.1586486, 85.4072306}, {39.3243103, 23.6824388}},
+{{34.4823321, 44.5556425}, {36.9549821, 36.1181121}, {37.4421857, 33.458373}},
+{{37.4421857, 33.458373}, {37.852416, 31.2188464}, {36.8498458, 33.1020754}},
+{{36.8498458, 33.1020754}, {36.0666826, 34.5731701}, {34.4114682, 38.5859621}},
+{{34.4114682, 38.5859621}, {33.4805756, 40.8427565}, {31.8332086, 45.009246}},
+{{31.8332086, 45.009246}, {30.8106719, 47.5954265}, {30.8033416, 47.5462886}},
+{{30.8033416, 47.5462886}, {30.793079, 47.4774956}, {32.1835801, 43.5816708}},
+{{32.1835801, 43.5816708}, {33.1767952, 40.7989388}, {37.1569859, 29.7171487}},
+{{37.1569859, 29.7171487}, {38.5382511, 25.8713805}, {39.3243103, 23.6824388}},
+</div>
+
+<div id="cubic8x4x">
+{{34.4823321, 44.5556425}, {46.6831036, 2.92242272}, {17.1586486, 85.4072306}, {39.3243103, 23.6824388}},
+{{34.4823321, 44.5556425}, {37.0635768, 35.7091664}, {37.4421857, 33.458373}},
+{{37.4421857, 33.458373}, {37.8207947, 31.2075797}, {36.8498458, 33.1020754}},
+{{36.8498458, 33.1020754}, {35.878897, 34.996571}, {34.4114682, 38.5859621}},
+{{34.4114682, 38.5859621}, {32.9440394, 42.1753532}, {31.8332086, 45.009246}},
+{{31.8332086, 45.009246}, {30.8636314, 47.4784019}, {30.8033416, 47.5462886}},
+{{30.8033416, 47.5462886}, {30.7430517, 47.6141753}, {32.1835801, 43.5816708}},
+{{32.1835801, 43.5816708}, {33.6241085, 39.5491663}, {37.1569859, 29.7171487}},
+{{37.1569859, 29.7171487}, {38.146263, 26.9628595}, {39.3243103, 23.6824388}},
+</div>
+
+<div id="cubic8x5">
+{{67.1009526, 65.7102964}, {92.9511368, 29.7558215}, {6.09136899, 77.6386629}, {73.0077305, 40.9268787}},
+{{67.1009526, 65.7102964}, {72.234988, 58.569475}, {72.0584002, 54.9887776}},
+{{72.0584002, 54.9887776}, {71.9092626, 51.9646911}, {67.9699024, 51.5063347}},
+{{67.9699024, 51.5063347}, {64.8799872, 51.1468138}, {59.401457, 52.3770387}},
+{{59.401457, 52.3770387}, {56.3059837, 53.072139}, {50.919062, 54.7149606}},
+{{50.919062, 54.7149606}, {47.1095083, 55.8767404}, {47.0889098, 55.6405516}},
+{{47.0889098, 55.6405516}, {47.0600718, 55.3098873}, {52.2780952, 52.3607383}},
+{{52.2780952, 52.3607383}, {56.0052548, 50.2542034}, {70.9344915, 42.0642523}},
+{{70.9344915, 42.0642523}, {72.2995322, 41.3154119}, {73.0077305, 40.9268787}},
+</div>
+
+<div id="cubic8x5x">
+{{67.1009526, 65.7102964}, {92.9511368, 29.7558215}, {6.09136899, 77.6386629}, {73.0077305, 40.9268787}},
+{{67.1009526, 65.7102964}, {72.4119125, 58.1790269}, {72.0584002, 54.9887776}},
+{{72.0584002, 54.9887776}, {71.7048879, 51.7985283}, {67.9699024, 51.5063347}},
+{{67.9699024, 51.5063347}, {64.2349168, 51.2141411}, {59.401457, 52.3770387}},
+{{59.401457, 52.3770387}, {54.5679971, 53.5399363}, {50.919062, 54.7149606}},
+{{50.919062, 54.7149606}, {47.3051356, 55.8776986}, {47.0889098, 55.6405516}},
+{{47.0889098, 55.6405516}, {46.8726839, 55.4034046}, {52.2780952, 52.3607383}},
+{{52.2780952, 52.3607383}, {57.6835065, 49.3180721}, {70.9344915, 42.0642523}},
+{{70.9344915, 42.0642523}, {71.9455119, 41.5096286}, {73.0077305, 40.9268787}},
+</div>
+
+<div id="cubic8x6">
+{{34.6917773, 64.7007906}, {26.1879157, 40.299837}, {19.3601908, 86.7271998}, {24.0468774, 55.867852}},
+{{34.6917773, 64.7007906}, {32.8936408, 59.5412235}, {30.9809892, 57.9762826}},
+{{30.9809892, 57.9762826}, {29.3733084, 56.6608702}, {27.7048898, 57.9022642}},
+{{27.7048898, 57.9022642}, {26.4047253, 58.8696572}, {25.0679408, 61.4005651}},
+{{25.0679408, 61.4005651}, {24.3182009, 62.820033}, {23.2746043, 65.3930147}},
+{{23.2746043, 65.3930147}, {22.674283, 66.8731035}, {22.5736375, 66.8767729}},
+{{22.5736375, 66.8767729}, {22.4327337, 66.88191}, {22.7095685, 64.8303341}},
+{{22.7095685, 64.8303341}, {22.9073076, 63.3649228}, {23.7989097, 57.4996081}},
+{{23.7989097, 57.4996081}, {23.9603141, 56.4378254}, {24.0468774, 55.867852}},
+</div>
+
+<div id="cubic8x6x">
+{{34.6917773, 64.7007906}, {26.1879157, 40.299837}, {19.3601908, 86.7271998}, {24.0468774, 55.867852}},
+{{34.6917773, 64.7007906}, {32.7532689, 59.2911428}, {30.9809892, 57.9762826}},
+{{30.9809892, 57.9762826}, {29.2087096, 56.6614223}, {27.7048898, 57.9022642}},
+{{27.7048898, 57.9022642}, {26.2010699, 59.1431061}, {25.0679408, 61.4005651}},
+{{25.0679408, 61.4005651}, {23.9348117, 63.658024}, {23.2746043, 65.3930147}},
+{{23.2746043, 65.3930147}, {22.7294605, 66.7981817}, {22.5736375, 66.8767729}},
+{{22.5736375, 66.8767729}, {22.4178145, 66.955364}, {22.7095685, 64.8303341}},
+{{22.7095685, 64.8303341}, {23.0013225, 62.7053042}, {23.7989097, 57.4996081}},
+{{23.7989097, 57.4996081}, {23.9170479, 56.7225788}, {24.0468774, 55.867852}},
+</div>
+
+<div id="cubic8x7">
+{{33.7213174, 54.1809799}, {19.7290722, 86.516309}, {79.6055485, 30.4535282}, {32.4492169, 73.9888241}},
+{{33.7213174, 54.1809799}, {30.929259, 60.6332771}, {31.7178101, 63.1685506}},
+{{31.7178101, 63.1685506}, {32.3822203, 65.3046982}, {35.5832592, 64.6365068}},
+{{35.5832592, 64.6365068}, {38.0860576, 64.1140676}, {42.1661464, 61.8599641}},
+{{42.1661464, 61.8599641}, {44.4631798, 60.5909351}, {48.3149537, 58.1140379}},
+{{48.3149537, 58.1140379}, {50.7761073, 56.5313841}, {50.8756876, 56.6229029}},
+{{50.8756876, 56.6229029}, {51.0150999, 56.7510292}, {48.1271345, 59.4792497}},
+{{48.1271345, 59.4792497}, {46.064302, 61.4279786}, {37.7133917, 69.1313755}},
+{{37.7133917, 69.1313755}, {34.3790695, 72.2071608}, {32.4492169, 73.9888241}},
+</div>
+
+<div id="cubic8x7x">
+{{33.7213174, 54.1809799}, {19.7290722, 86.516309}, {79.6055485, 30.4535282}, {32.4492169, 73.9888241}},
+{{33.7213174, 54.1809799}, {30.8583849, 60.9640583}, {31.7178101, 63.1685506}},
+{{31.7178101, 63.1685506}, {32.5772353, 65.3730429}, {35.5832592, 64.6365068}},
+{{35.5832592, 64.6365068}, {38.589283, 63.8999708}, {42.1661464, 61.8599641}},
+{{42.1661464, 61.8599641}, {45.7430098, 59.8199575}, {48.3149537, 58.1140379}},
+{{48.3149537, 58.1140379}, {50.6281545, 56.5876371}, {50.8756876, 56.6229029}},
+{{50.8756876, 56.6229029}, {51.1232206, 56.6581687}, {48.1271345, 59.4792497}},
+{{48.1271345, 59.4792497}, {45.1310483, 62.3003307}, {37.7133917, 69.1313755}},
+{{37.7133917, 69.1313755}, {35.340896, 71.3195506}, {32.4492169, 73.9888241}},
+</div>
+
+<div id="cubic8x8">
+{{53.9853472, 31.729689}, {80.8833995, 7.2950833}, {8.46509939, 72.9253675}, {56.6511208, 35.3872682}},
+{{53.9853472, 31.729689}, {54.6892116, 31.0902877}, {55.8968586, 29.9930402}},
+{{55.8968586, 29.9930402}, {59.7242319, 26.5155538}, {60.0744106, 26.2078693}},
+{{60.0744106, 26.2078693}, {60.4245892, 25.9001849}, {58.6982878, 27.5315648}},
+{{58.6982878, 27.5315648}, {54.8548255, 31.1636922}, {52.2592609, 33.6639071}},
+{{52.2592609, 33.6639071}, {47.5369986, 38.2126941}, {44.5524326, 41.278553}},
+{{44.5524326, 41.278553}, {40.6568202, 45.2802731}, {39.8604011, 46.6125979}},
+{{39.8604011, 46.6125979}, {38.901811, 48.2162178}, {42.4657645, 45.9031378}},
+{{42.4657645, 45.9031378}, {46.5800498, 43.232881}, {56.6511208, 35.3872682}},
+</div>
+
+<div id="cubic8x8x">
+{{53.9853472, 31.729689}, {80.8833995, 7.2950833}, {8.46509939, 72.9253675}, {56.6511208, 35.3872682}},
+{{53.9853472, 31.729689}, {55.0401587, 30.7714526}, {55.8968586, 29.9930402}},
+{{55.8968586, 29.9930402}, {59.6366873, 26.5924749}, {60.0744106, 26.2078693}},
+{{60.0744106, 26.2078693}, {60.5121339, 25.8232638}, {58.6982878, 27.5315648}},
+{{58.6982878, 27.5315648}, {56.3310494, 29.756797}, {52.2592609, 33.6639071}},
+{{52.2592609, 33.6639071}, {48.1874723, 37.5710172}, {44.5524326, 41.278553}},
+{{44.5524326, 41.278553}, {40.9173929, 44.9860887}, {39.8604011, 46.6125979}},
+{{39.8604011, 46.6125979}, {38.8034093, 48.2391072}, {42.4657645, 45.9031378}},
+{{42.4657645, 45.9031378}, {46.1281196, 43.5671684}, {56.6511208, 35.3872682}},
+</div>
+
+<div id="cubic8x9">
+{{73.1810322, 53.6088109}, {3.28446082, 1.93300047}, {87.9389074, 89.2160727}, {54.5340817, 54.3107021}},
+{{73.1810322, 53.6088109}, {58.5574459, 42.7973267}, {51.3867695, 38.9320081}},
+{{51.3867695, 38.9320081}, {45.1924119, 35.5929695}, {44.6615376, 37.4897176}},
+{{44.6615376, 37.4897176}, {44.2222697, 39.0591673}, {47.6643015, 44.1654891}},
+{{47.6643015, 44.1654891}, {50.2846557, 48.0528359}, {55.0540263, 53.8428721}},
+{{55.0540263, 53.8428721}, {57.6549797, 57.0004406}, {61.4896769, 61.4054165}},
+{{61.4896769, 61.4054165}, {62.8763033, 62.9982556}, {62.6160157, 62.7489128}},
+{{62.6160157, 62.7489128}, {62.3557281, 62.49957}, {59.4073763, 59.4106743}},
+{{59.4073763, 59.4106743}, {56.5808171, 56.449377}, {54.5340817, 54.3107021}},
+</div>
+
+<div id="cubic8x9x">
+{{73.1810322, 53.6088109}, {3.28446082, 1.93300047}, {87.9389074, 89.2160727}, {54.5340817, 54.3107021}},
+{{73.1810322, 53.6088109}, {57.8490138, 42.3222252}, {51.3867695, 38.9320081}},
+{{51.3867695, 38.9320081}, {44.9245252, 35.5417911}, {44.6615376, 37.4897176}},
+{{44.6615376, 37.4897176}, {44.3985499, 39.4376442}, {47.6643015, 44.1654891}},
+{{47.6643015, 44.1654891}, {50.9300531, 48.893334}, {55.0540263, 53.8428721}},
+{{55.0540263, 53.8428721}, {59.1779995, 58.7924103}, {61.4896769, 61.4054165}},
+{{61.4896769, 61.4054165}, {62.9413752, 63.0605913}, {62.6160157, 62.7489128}},
+{{62.6160157, 62.7489128}, {62.2906562, 62.4372343}, {59.4073763, 59.4106743}},
+{{59.4073763, 59.4106743}, {57.5885087, 57.5036974}, {54.5340817, 54.3107021}},
+</div>
+
+<div id="cubic4">
+{{24.2578299, 1.34695745}, {6.77689729, 99.312693}, {3.18338154, 3.09354817}, {59.132973, 47.8778685}},
+{{38.313885, 41.465269}, {48.4308047, 76.5337766}, {93.264044, 88.7879534}, {83.3354337, 18.6335197}}
+</div>
+
+<div id="cubic5">
+{{24.0062249, 72.6211198}, {22.3913226, 30.9587957}, {80.7539402, 31.4736433}, {99.6348716, 63.2867312}},
+{{43.1612821, 11.6690897}, {24.4801394, 37.7033828}, {77.5229567, 28.3334108}, {60.0910899, 50.9480224}}
+$6 = {{x = 24.006224853920855, y = 72.621119847810419}, {x = 24.119692298829129, y = 51.890688643515688}, {x = 38.700154924642845, y = 44.614929583485953}}
+(gdb) p q2
+$7 = {{x = 24.006224853920855, y = 72.621119847810419}, {x = 29.758671200376888, y = 31.764642512385173}, {x = 71.277052443896736, y = 42.309313461363033}}
+</div>
+
+<div id="quad1">
+{{x = 34.879150914024962, y = 83.862726601601125}, {x = 35.095810134304429, y = 83.693473210169543}, {x = 35.359284111931586, y = 83.488069234177502}}
+{{x = 54.503204203015471, y = 76.094098492518242}, {x = 51.366889541918894, y = 71.609856061299155}, {x = 46.53086955445437, y = 69.949863036494207}}
+</div>
+
+<div id="cubic6">
+{{x = 54.080923997834752, y = 38.089631608729078}, {x = 10.447347774378651, y = 88.574043981998258}, {x = 33.294667831293616, y = 83.482240551841556}, {x = 25.649263209500006, y = 87.166762066617025}}
+</div>
+
+<div id="quad2">
+{{x = 25.367434474345036, y = 50.4712103169743}, {x = 17.865013304933097, y = 37.356741010559439}, {x = 16.818988838905465, y = 37.682915484123129}}
+{{x = 16.818988838905465, y = 37.682915484123129}, {x = 15.772964372877833, y = 38.009089957686811}, {x = 20.624104547604965, y = 41.825131596683121}}
+</div>
+
+<div id="cubic7">
+{{x = 25.367434474345036, y = 50.4712103169743}, {x = 5.2367042308844178, y = 13.28800847441331}, {x = 21.031375239152169, y = 74.32364443052731}, {x = 60.821163496384933, y = 21.294883741668837}}
+</div>
+
+<div id="quad3">
+{{x = 36.148792695174222, y = 70.336952793070424}, {x = 36.141613037691357, y = 70.711654739870085}, {x = 36.154708826402597, y = 71.088492662905836}}
+{{x = 35.216235592661825, y = 70.580199617313212}, {x = 36.244476835123969, y = 71.010897787304074}, {x = 37.230244263238326, y = 71.423156953613102}}
+</div>
+
+<div id="quad4">
+{{x = 369.84860200000003, y = 145.68026699999999}, {x = 382.36041299999999, y = 121.298294}, {x = 406.20770299999998, y = 121.298294}}
+{{x = 369.850525, y = 145.67596399999999}, {x = 382.36291499999999, y = 121.29286999999999}, {x = 406.21127300000001, y = 121.29286999999999}}
+</div>
+
+<div id="quad5">
+{{x = 67.25299631583178, y = 21.109080184767524}, {x = 43.617595267398613, y = 33.658034168577529}, {x = 33.38371819435676, y = 44.214192553988745}}
+{{x = 40.476838859398541, y = 39.543209911285999}, {x = 36.701186108431131, y = 34.8817994016458}, {x = 30.102144288878023, y = 26.739063172945315}}
+</div>
+
+<div id="quad6">
+{{x = 59.981867574297752, y = 19.243986850744687}, {x = 59.992798861020468, y = 19.257454808070786}, {x = 60.003741189575571, y = 19.270930807443623}}
+{{x = 47.800898294803176, y = 89.697640756935641}, {x = 38.74069898238357, y = 58.416865487251982}, {x = 37.639862598936119, y = 44.208141075385868}}
+</div>
+
+<div id="cubic8">
+{{x = 53.674595921148828, y = 8.9336467482771944}, {x = 48.248201817389678, y = 7.5279448682106773}, {x = 89.942031162763953, y = 55.717752573880254}, {x = 81.402728418541486, y = 35.656530426655216}}
+{{x = 47.800898294803176, y = 89.697640756935641}, {x = 22.169400016856102, y = 1.1060833004797266}, {x = 48.267509205391399, y = 32.027215013293187}, {x = 79.306880794142785, y = 10.745507157754854}}
+</div>
+
+<div id="quad7">
+{{x = 33.567436351153468, y = 62.336347586395924}, {x = 35.200980274619084, y = 65.038561460144479}, {x = 36.479571811084995, y = 67.632178905412445}}
+{{x = 41.349524945572696, y = 67.886658677862641}, {x = 39.125562529359087, y = 67.429772735149214}, {x = 35.600314083992416, y = 66.705372160552685}}
+</div>
+
+<div id="quad8">
+{{x = 36.148792695174222, y = 70.336952793070424}, {x = 36.141613037691357, y = 70.711654739870085}, {x = 36.154708826402597, y = 71.088492662905836}}
+{{x = 35.216235592661825, y = 70.580199617313212}, {x = 36.244476835123969, y = 71.010897787304074}, {x = 37.230244263238326, y = 71.423156953613102}}
+</div>
+
+<div id="quad9">
+{{353.2948,194.351074}, {353.2948,173.767563}, {364.167572,160.819855}},
+{{360.416077,166.795715}, {370.126831,147.872162}, {388.635406,147.872162}},
+</div>
+
+<div id="quad10">
+    {{8, 8}, {10, 10}, {8, -10}},
+    {{8, 8}, {12, 12}, {14, 4}},
+</div>
+
+<div id="quad11">
+{{x = 50.934805397717923, y = 51.52391952648901}, {x = 56.803308902971423, y = 44.246234610627596}, {x = 69.776888596721406, y = 40.166645096692555}}
+{{x = 50.230212796400401, y = 38.386469101526998}, {x = 49.855620812184917, y = 38.818990392153609}, {x = 56.356567496227363, y = 47.229909093319407}}
+</div>
+
+<div id="cubic9">
+{{18.1312339, 31.6473732}, {95.5711034, 63.5350219}, {92.3283165, 62.0158945}, {18.5656052, 32.1268808}},
+{{97.402018, 35.7169972}, {33.1127443, 25.8935163}, {1.13970027, 54.9424981}, {56.4860195, 60.529264}},
+</div>
+
+<div id="cubic10">
+{{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}},
+{{61.3365082, 82.6931328}, {44.6393809, 54.0748258}, {16.8156155, 20.0497047}, {41.866885, 56.7355037}},
+</div>
+
+<div id="cubic11">
+{{40.3684631, 72.7588382}, {85.2198593, 90.174892}, {31.9101421, 13.7580149}, {72.0483425, 16.4930846}},
+{{57.7943379, 49.4368549}, {69.4103137, 79.1415428}, {30.9563231, 82.9221187}, {99.2731298, 83.4922981}},
+</div>
+
+<div id="cubic12">
+{{98.3415562, 26.5353662}, {15.3721551, 59.8107939}, {77.1895742, 25.1742572}, {11.7326863, 91.2589209}},
+{{79.899867, 77.0640431}, {40.0129651, 97.9042774}, {3.74105489, 75.9095456}, {88.6837571, 7.90615282}},
+</div>
+
+<div id="cubic13">
+{{95.6513419, 12.1029701}, {63.4801516, 10.9081754}, {41.0209588, 39.2537121}, {65.9441362, 23.0970739}},
+{{14.6179238, 83.4452002}, {33.7032426, 50.3981092}, {37.1399002, 10.3032037}, {92.5218685, 15.0431467}},
+</div>
+
+<div id="cubic14">
+{{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}},
+{{61.3365082, 82.6931328}, {44.6393809, 54.0748258}, {16.8156155, 20.0497047}, {41.866885, 56.7355037}},
+{{67.4265481,37.9937726}, {51.1295132,57.5422812}, {44.5947482,65.6442673}},
+{{44.5947482,65.6442673}, {35.2387481,77.3910511}, {43.2346162,66.2224493}},
+{{43.2346162,66.2224493}, {51.8234203,54.2750917}, {75.3863417,18.24489}},
+{{61.3365082,82.6931328}, {54.8250789,71.6639328}, {47.7274442,61.4049645}},
+{{47.7274442,61.4049645}, {40.6298095,51.1459962}, {35.9460478,45.2252785}},
+{{35.9460478,45.2252785}, {31.2622861,39.3045608}, {31.9924758,41.2901124}},
+{{31.9924758,41.2901124}, {32.7226655,43.275664}, {41.866885,56.7355037}},
+</div>
+
+<div id="quad12">
+{{x = 67.426548091427676, y = 37.993772624988935}, {x = 51.129513170665042, y = 57.542281234563646}, {x = 44.594748190899182, y = 65.644267382683879}}
+{{x = 61.336508189019057, y = 82.693132843213675}, {x = 54.825078921449354, y = 71.663932799212432}, {x = 47.727444217558926, y = 61.4049645128392}}
+</div>
+
+<div id="quad13">
+{{x = 53.774852327053594, y = 53.318060789841951}, {x = 45.787877803416805, y = 51.393492026284981}, {x = 46.703936967162392, y = 53.06860709822206}}
+{{x = 46.703936967162392, y = 53.06860709822206}, {x = 47.619996130907957, y = 54.74372217015916}, {x = 53.020051653535361, y = 48.633140968832024}}
+</div>
+
+<div id="cubic15">
+{{40.3684631, 72.7588382}, {85.2198593, 90.174892}, {31.9101421, 13.7580149}, {72.0483425, 16.4930846}},
+{{57.7943379, 49.4368549}, {69.4103137, 79.1415428}, {30.9563231, 82.9221187}, {99.2731298, 83.4922981}},
+</div>
+
+<div id="cubic16">
+{{98.3415562, 26.5353662}, {15.3721551, 59.8107939}, {77.1895742, 25.1742572}, {11.7326863, 91.2589209}},
+{{79.899867, 77.0640431}, {40.0129651, 97.9042774}, {3.74105489, 75.9095456}, {88.6837571, 7.90615282}},
+</div>
+
+<div id="cubic17">
+{{95.6513419, 12.1029701}, {63.4801516, 10.9081754}, {41.0209588, 39.2537121}, {65.9441362, 23.0970739}},
+{{14.6179238, 83.4452002}, {33.7032426, 50.3981092}, {37.1399002, 10.3032037}, {92.5218685, 15.0431467}},
+{{95.6513419,12.1029701}, {79.216947,12.1911515}, {68.1126831,18.0126375}},
+{{68.1126831,18.0126375}, {57.0084192,23.8341235}, {55.4198832,27.1619689}},
+{{55.4198832,27.1619689}, {53.8313472,30.4898143}, {65.9441362,23.0970739}},
+{{14.6179238,83.4452002}, {20.3825754,73.0912112}, {25.0377248,62.5209893}},
+{{25.0377248,62.5209893}, {33.2090045,41.6303758}, {46.9147771,27.3313746}},
+{{46.9147771,27.3313746}, {60.6205496,13.0323735}, {92.5218685,15.0431467}},
+</div>
+
+<div id="cubic18">
+{{55.7513494, 12.929877}, {46.4296358, 42.8887602}, {16.8160022, 26.5487217}, {4.93643419, 66.6494508}},
+{{12.4426199, 23.1121812}, {31.3921366, 7.64067448}, {4.36561578, 72.9044408}, {77.3190123, 0.63959742}},
+
+{{55.7513494,12.929877}, {52.399261,23.0070161}, {46.4958203,27.5595279}},
+{{46.4958203,27.5595279}, {40.5923795,32.1120397}, {33.5495747,34.9548738}},
+{{33.5495747,34.9548738}, {25.3214643,38.1279717}, {17.6150117,44.5570525}},
+{{17.6150117,44.5570525}, {9.90855921,50.9861334}, {4.93643419,66.6494508}},
+
+{{12.4426199,23.1121812}, {17.0040168,19.5021098}, {18.7553606,21.0894159}},
+{{18.7553606,21.0894159}, {20.5067044,22.676722}, {21.4650431,26.4450934}},
+{{21.4650431,26.4450934}, {22.5692754,31.7464864}, {26.4671516,34.648351}},
+{{26.4671516,34.648351}, {30.3650278,37.5502156}, {41.873704,30.8489321}},
+{{41.873704,30.8489321}, {53.3823801,24.1476487}, {77.3190123,0.63959742}},
+</div>
+
+</div>
+
+<script type="text/javascript">
+
+var testDivs = [
+    cubic18,
+    cubic17,
+    cubic16,
+    cubic15,
+    quad13,
+    quad12,
+    cubic14,
+    cubic13,
+    cubic12,
+    cubic11,
+    cubic10,
+    cubic9,
+    quad11,
+    quad10,
+    quad9,
+    quad8,
+    quad7,
+    cubic8,
+    quad6,
+    quad5,
+    quad4,
+    quad3,
+    cubic7,
+    quad2,
+    cubic6,
+    quad1,
+    cubic5,
+    cubic4,
+    cubic1x0,
+    cubic1x0x,
+    cubic1x1,
+    cubic1x1x,
+    cubic1x2,
+    cubic1x2x,
+    cubic1x3,
+    cubic1x3x,
+    cubic1x4,
+    cubic1x4x,
+    cubic1x5,
+    cubic1x5x,
+    cubic1x6,
+    cubic1x6x,
+    cubic1x7,
+    cubic1x7x,
+    cubic1x8,
+    cubic1x8x,
+    cubic1x9,
+    cubic1x9x,
+    cubic2x0,
+    cubic2x0x,
+    cubic2x1,
+    cubic2x1x,
+    cubic2x2,
+    cubic2x2x,
+    cubic2x3,
+    cubic2x3x,
+    cubic2x4,
+    cubic2x4x,
+    cubic2x5,
+    cubic2x5x,
+    cubic2x6,
+    cubic2x6x,
+    cubic2x7,
+    cubic2x7x,
+    cubic2x8,
+    cubic2x8x,
+    cubic2x9,
+    cubic2x9x,
+    cubic3x0,
+    cubic3x0x,
+    cubic3x1,
+    cubic3x1x,
+    cubic3x2,
+    cubic3x2x,
+    cubic3x3,
+    cubic3x3x,
+    cubic3x4,
+    cubic3x4x,
+    cubic3x5,
+    cubic3x5x,
+    cubic3x6,
+    cubic3x6x,
+    cubic3x7,
+    cubic3x7x,
+    cubic3x8,
+    cubic3x8x,
+    cubic3x9,
+    cubic3x9x,
+    cubic4x0,
+    cubic4x0x,
+    cubic4x1,
+    cubic4x1x,
+    cubic4x2,
+    cubic4x2x,
+    cubic4x3,
+    cubic4x3x,
+    cubic4x4,
+    cubic4x4x,
+    cubic4x5,
+    cubic4x5x,
+    cubic4x6,
+    cubic4x6x,
+    cubic4x7,
+    cubic4x7x,
+    cubic4x8,
+    cubic4x8x,
+    cubic4x9,
+    cubic4x9x,
+    cubic5x0,
+    cubic5x0x,
+    cubic5x1,
+    cubic5x1x,
+    cubic5x2,
+    cubic5x2x,
+    cubic5x3,
+    cubic5x3x,
+    cubic5x4,
+    cubic5x4x,
+    cubic5x5,
+    cubic5x5x,
+    cubic5x6,
+    cubic5x6x,
+    cubic5x7,
+    cubic5x7x,
+    cubic5x8,
+    cubic5x8x,
+    cubic5x9,
+    cubic5x9x,
+    cubic6x0,
+    cubic6x0x,
+    cubic6x1,
+    cubic6x1x,
+    cubic6x2,
+    cubic6x2x,
+    cubic6x3,
+    cubic6x3x,
+    cubic6x4,
+    cubic6x4x,
+    cubic6x5,
+    cubic6x5x,
+    cubic6x6,
+    cubic6x6x,
+    cubic6x7,
+    cubic6x7x,
+    cubic6x8,
+    cubic6x8x,
+    cubic6x9,
+    cubic6x9x,
+    cubic7x0,
+    cubic7x0x,
+    cubic7x1,
+    cubic7x1x,
+    cubic7x2,
+    cubic7x2x,
+    cubic7x3,
+    cubic7x3x,
+    cubic7x4,
+    cubic7x4x,
+    cubic7x5,
+    cubic7x5x,
+    cubic7x6,
+    cubic7x6x,
+    cubic7x7,
+    cubic7x7x,
+    cubic7x8,
+    cubic7x8x,
+    cubic7x9,
+    cubic7x9x,
+    cubic8x0,
+    cubic8x0x,
+    cubic8x1,
+    cubic8x1x,
+    cubic8x2,
+    cubic8x2x,
+    cubic8x3,
+    cubic8x3x,
+    cubic8x4,
+    cubic8x4x,
+    cubic8x5,
+    cubic8x5x,
+    cubic8x6,
+    cubic8x6x,
+    cubic8x7,
+    cubic8x7x,
+    cubic8x8,
+    cubic8x8x,
+    cubic8x9,
+    cubic8x9x,
+    cubic3,
+    cubic2,
+    cubic1,
+];
+
+var scale, columns, rows, xStart, yStart;
+
+var ticks = 10;
+var at_x = 13 + 0.5;
+var at_y = 23 + 0.5;
+var init_decimal_places = 1; // make this 3 to show more precision
+var decimal_places;
+var tests = [];
+var testTitles = [];
+var testIndex = 0;
+var ctx;
+var minScale = 1;
+var subscale = 1;
+var curveT = -1;
+var drawCubics = true;
+var drawQuads = true;
+var drawControlLines = true;
+
+function parse(test, title) {
+    var curveStrs = test.split("{{");
+    if (curveStrs.length == 1)
+        curveStrs = test.split("=(");
+    var pattern = /[a-z$=]?-?\d+\.*\d*/g;
+    var curves = [];
+    for (var c in curveStrs) {
+        var curveStr = curveStrs[c];
+        var points = curveStr.match(pattern);
+        var pts = [];
+        for (var wd in points) {
+            var num = parseFloat(points[wd]);
+            if (isNaN(num)) continue;
+            pts.push(num);
+        }
+        if (pts.length > 2)
+            curves.push(pts);
+    }
+    if (curves.length >= 1) {
+        tests.push(curves);
+        testTitles.push(title);
+    }
+}
+
+function init(test) {
+    var canvas = document.getElementById('canvas');
+    if (!canvas.getContext) return;
+    canvas.width = window.innerWidth - at_x;
+    canvas.height = window.innerHeight - at_y;
+    ctx = canvas.getContext('2d');
+    var xmin = Infinity;
+    var xmax = -Infinity;
+    var ymin = Infinity;
+    var ymax = -Infinity;
+    for (var curves in test) {
+        var curve = test[curves];
+        var last = curve.length;
+        for (var idx = 0; idx < last; idx += 2) {
+            xmin = Math.min(xmin, curve[idx]);
+            xmax = Math.max(xmax, curve[idx]);
+            ymin = Math.min(ymin, curve[idx + 1]);
+            ymax = Math.max(ymax, curve[idx + 1]);
+        }
+    }
+    var testW = xmax - xmin;
+    var testH = ymax - ymin;
+    subscale = 1;
+    while (testW * subscale < 0.1 && testH * subscale < 0.1) {
+        subscale *= 10;
+    }
+    while (testW * subscale > 10 && testH * subscale > 10) {
+        subscale /= 10;
+    }
+    xStart = Math.floor(xmin * subscale) / subscale;
+    yStart = Math.floor(ymin * subscale) / subscale;
+    var xEnd = Math.ceil(xmin * subscale) / subscale;
+    var yEnd = Math.ceil(ymin * subscale) / subscale;
+    var cCelsW = Math.floor(ctx.canvas.width / 10);
+    var cCelsH = Math.floor(ctx.canvas.height / 10);
+    testW = xEnd - xStart;
+    testH = yEnd - yStart; 
+    var scaleWH = 1;
+    while (cCelsW > testW * scaleWH * 10 && cCelsH > testH * scaleWH * 10) {
+        scaleWH *= 10;
+    }
+    while (cCelsW * 10 < testW * scaleWH && cCelsH * 10 < testH * scaleWH) {
+        scaleWH /= 10;
+    }
+    
+    columns = Math.ceil(xmax * subscale) - Math.floor(xmin * subscale) + 1;
+    rows = Math.ceil(ymax * subscale) - Math.floor(ymin * subscale) + 1;
+    
+    var hscale = ctx.canvas.width / columns / ticks;
+    var vscale = ctx.canvas.height / rows / ticks;
+    minScale = Math.floor(Math.min(hscale, vscale));
+    scale = minScale * subscale;
+}
+
+function drawPoint(px, py, xoffset, yoffset, unit) {
+    var label = px.toFixed(decimal_places) + ", " + py.toFixed(decimal_places);
+    var _px = px * unit + xoffset;
+    var _py = py * unit + yoffset;
+    ctx.beginPath();
+    ctx.arc(_px, _py, 3, 0, Math.PI*2, true);
+    ctx.closePath();
+    ctx.fill();
+    ctx.fillText(label, _px + 5, _py);
+}
+
+function draw(test, title, scale) {
+    ctx.fillStyle = "rgba(0,0,0, 0.1)";
+    ctx.font = "normal 50px Arial";
+    ctx.fillText(title, 50, 50);
+    ctx.font = "normal 10px Arial";
+
+    var unit = scale * ticks;
+    ctx.lineWidth = 1;
+    var i;
+    for (i = 0; i <= rows * ticks; ++i) {
+        ctx.strokeStyle = (i % ticks) != 0 ? "rgb(200,200,200)" : "black";
+        ctx.beginPath();
+        ctx.moveTo(at_x + 0, at_y + i * minScale);
+        ctx.lineTo(at_x + ticks * columns * minScale, at_y + i * minScale);
+        ctx.stroke();
+    }
+    for (i = 0; i <= columns * ticks; ++i) {
+        ctx.strokeStyle = (i % ticks) != 0 ? "rgb(200,200,200)" : "black";
+        ctx.beginPath();
+        ctx.moveTo(at_x + i * minScale, at_y + 0);
+        ctx.lineTo(at_x + i * minScale, at_y + ticks * rows * minScale);
+        ctx.stroke();
+    }
+ 
+    var xoffset = xStart * -unit + at_x;
+    var yoffset = yStart * -unit + at_y;
+
+    ctx.fillStyle = "rgb(40,80,60)"
+    for (i = 0; i <= columns; i += 1)
+    {
+        num = xStart + i / subscale; 
+        ctx.fillText(num.toFixed(decimal_places), xoffset + num * unit - 5, 10);
+    }
+    for (i = 0; i <= rows; i += 1)
+    {
+        num = yStart + i / subscale; 
+        ctx.fillText(num.toFixed(decimal_places), 0, yoffset + num * unit + 0);
+    }
+    var curves, pts;
+    for (curves in test) {
+        var curve = test[curves];
+        if (curve.length == 6 && !drawQuads) {
+            continue;
+        }
+        if (curve.length == 8 && !drawCubics) {
+            continue;
+        }
+        ctx.beginPath();
+        ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit);
+        switch (curve.length) {
+            case 6:
+                ctx.quadraticCurveTo(
+                    xoffset + curve[2] * unit, yoffset + curve[3] * unit,
+                    xoffset + curve[4] * unit, yoffset + curve[5] * unit);
+                break;
+            case 8:
+                ctx.bezierCurveTo(
+                    xoffset + curve[2] * unit, yoffset + curve[3] * unit,
+                    xoffset + curve[4] * unit, yoffset + curve[5] * unit,
+                    xoffset + curve[6] * unit, yoffset + curve[7] * unit);
+                break;
+        }
+        if (curves == 2) ctx.strokeStyle = curves ? "red" : "blue";
+        ctx.stroke();
+        if (drawControlLines) {
+            ctx.strokeStyle = "rgba(0,0,0, 0.3)";
+            ctx.beginPath();
+            ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit);
+            ctx.lineTo(xoffset + curve[2] * unit, yoffset + curve[3] * unit);
+            ctx.lineTo(xoffset + curve[4] * unit, yoffset + curve[5] * unit);
+            if (curve.length == 8)
+                ctx.lineTo(xoffset + curve[6] * unit, yoffset + curve[7] * unit);
+            ctx.stroke();
+        }
+        if (curveT >= 0 && curveT <= 1) {
+            var x, y;
+            var t = curveT;
+            switch (curve.length) {
+                case 6:
+                    var one_t = 1 - t;
+                    var a = one_t * one_t;
+                    var b = 2 * one_t * t;
+                    var c = t * t;
+                    x = a * curve[0] + b * curve[2] + c * curve[4];
+                    y = a * curve[1] + b * curve[3] + c * curve[5];
+                    break;
+                case 8:
+                    var one_t = 1 - t;
+                    var one_t2 = one_t * one_t;
+                    var a = one_t2 * one_t;
+                    var b = 3 * one_t2 * t;
+                    var t2 = t * t;
+                    var c = 3 * one_t * t2;
+                    var d = t2 * t;
+                    x = a * curve[0] + b * curve[2] + c * curve[4] + d * curve[6];
+                    y = a * curve[1] + b * curve[3] + c * curve[5] + d * curve[7];
+                    break;
+            }
+            drawPoint(x, y, xoffset, yoffset, unit);
+            var num = curveT.toFixed(3);
+            ctx.beginPath();
+            ctx.rect(200,10,200,10);
+            ctx.fillStyle="white";
+            ctx.fill();
+            ctx.fillStyle="black";
+            ctx.fillText(num, 230, 18);
+            if (curve.length == 8) {
+                var one_t = 1 - t;
+                var a = curve[0];
+                var b = curve[2];
+                var c = curve[4];
+                var d = curve[6];
+                var dx = (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
+                a = curve[1];
+                b = curve[3];
+                c = curve[5];
+                d = curve[7];
+                var dy = (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
+                ctx.beginPath();
+                ctx.moveTo(xoffset + (x - dx) * unit, yoffset + (y - dy) * unit);
+                ctx.lineTo(xoffset + (x + dx) * unit, yoffset + (y + dy) * unit);
+                ctx.stroke();
+            }
+        }
+    }
+}
+
+function drawTop() {
+    init(tests[testIndex]);
+    redraw();
+}
+
+function redraw() {
+    ctx.beginPath();
+    ctx.rect(0, 0, ctx.canvas.width, ctx.canvas.height);
+    ctx.fillStyle="white";
+    ctx.fill();
+    draw(tests[testIndex], testTitles[testIndex], scale);
+}
+
+function doKeyPress(evt) {
+    var char = String.fromCharCode(evt.charCode);
+    switch (char) {
+    case 'c':
+        drawCubics ^= true;
+        redraw();
+        break;
+    case 'l':
+        drawControlLines ^= true;
+        redraw();
+        break;
+    case 'N':
+        testIndex += 9;
+    case 'n':
+        if (++testIndex >= tests.length)
+            testIndex = 0;
+        mouseX = Infinity;
+        drawTop();
+        break;
+    case 'P':
+        testIndex -= 9;
+    case 'p':
+        if (--testIndex < 0)
+            testIndex = tests.length - 1;
+        mouseX = Infinity;
+        drawTop();
+        break;
+    case 'q':
+        drawQuads ^= true;
+        redraw();
+        break;
+    case 'x':
+        drawCubics ^= true;
+        drawQuads ^= true;
+        redraw();
+        break;
+    }
+}
+
+function handleMouseClick() {
+    var e = window.event;
+	var tgt = e.target || e.srcElement;
+    var min = tgt.offsetTop + Math.ceil(at_y);
+    var max = min + ticks * rows * minScale;
+    curveT = (e.clientY - min) / (max - min);
+    redraw();
+}
+
+function calcXY() {
+    var e = window.event;
+	var tgt = e.target || e.srcElement;
+    var left = tgt.offsetLeft;
+    var top = tgt.offsetTop;
+    var unit = scale * ticks;
+    mouseX = (e.clientX - left - Math.ceil(at_x) + 1) / unit + xStart;
+    mouseY = (e.clientY - top - Math.ceil(at_y)) / unit + yStart;
+}
+
+function handleMouseOver() {
+    calcXY();
+    var num = mouseX.toFixed(3) + ", " + mouseY.toFixed(3);
+    ctx.beginPath();
+    ctx.rect(30,10,200,10);
+    ctx.fillStyle="white";
+    ctx.fill();
+    ctx.fillStyle="black";
+    ctx.fillText(num, 30, 18);
+}
+
+function start() {
+    for (i = 0; i < testDivs.length; ++i) {
+        var title = testDivs[i].id.toString();
+        var str = testDivs[i].firstChild.data;
+        parse(str, title);
+    }
+    drawTop();
+    window.addEventListener('keypress', doKeyPress, true);
+    window.onresize = function() {
+        drawTop();
+    }
+}
+
+</script>
+</head>
+
+<body onLoad="start();">
+<canvas id="canvas" width="750" height="500"
+    onmousemove="handleMouseOver()"
+    onclick="handleMouseClick()"
+    ></canvas >
+</body>
+</html>
-- 
2.7.4