--- /dev/null
+#include <stdio.h>
+/*
+ * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
+ * ALL RIGHTS RESERVED
+ * Permission to use, copy, modify, and distribute this software for
+ * any purpose and without fee is hereby granted, provided that the above
+ * copyright notice appear in all copies and that both the copyright notice
+ * and this permission notice appear in supporting documentation, and that
+ * the name of Silicon Graphics, Inc. not be used in advertising
+ * or publicity pertaining to distribution of the software without specific,
+ * written prior permission.
+ *
+ * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
+ * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
+ * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
+ * FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON
+ * GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
+ * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
+ * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
+ * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
+ * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN
+ * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
+ * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * US Government Users Restricted Rights
+ * Use, duplication, or disclosure by the Government is subject to
+ * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
+ * (c)(1)(ii) of the Rights in Technical Data and Computer Software
+ * clause at DFARS 252.227-7013 and/or in similar or successor
+ * clauses in the FAR or the DOD or NASA FAR Supplement.
+ * Unpublished-- rights reserved under the copyright laws of the
+ * United States. Contractor/manufacturer is Silicon Graphics,
+ * Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311.
+ *
+ * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
+ */
+/*
+ * Trackball code:
+ *
+ * Implementation of a virtual trackball.
+ * Implemented by Gavin Bell, lots of ideas from Thant Tessman and
+ * the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
+ *
+ * Vector manip code:
+ *
+ * Original code from:
+ * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
+ *
+ * Much mucking with by:
+ * Gavin Bell
+ */
+#if defined(_WIN32)
+#pragma warning (disable:4244) /* disable bogus conversion warnings */
+#endif
+#include <math.h>
+#include "trackball.h"
+
+/*
+ * This size should really be based on the distance from the center of
+ * rotation to the point on the object underneath the mouse. That
+ * point would then track the mouse as closely as possible. This is a
+ * simple example, though, so that is left as an Exercise for the
+ * Programmer.
+ */
+#define TRACKBALLSIZE (0.8f)
+
+/*
+ * Local function prototypes (not defined in trackball.h)
+ */
+static float tb_project_to_sphere(float, float, float);
+static void normalize_quat(float [4]);
+
+static void
+vzero(float v[3])
+{
+ v[0] = 0.0;
+ v[1] = 0.0;
+ v[2] = 0.0;
+}
+
+static void
+vset(float v[3], float x, float y, float z)
+{
+ v[0] = x;
+ v[1] = y;
+ v[2] = z;
+}
+
+static void
+vsub(const float src1[3], const float src2[3], float dst[3])
+{
+ dst[0] = src1[0] - src2[0];
+ dst[1] = src1[1] - src2[1];
+ dst[2] = src1[2] - src2[2];
+}
+
+static void
+vcopy(const float v1[3], float v2[3])
+{
+ register int i;
+ for (i = 0 ; i < 3 ; i++)
+ v2[i] = v1[i];
+}
+
+static void
+vcross(const float v1[3], const float v2[3], float cross[3])
+{
+ float temp[3];
+
+ temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
+ temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
+ temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
+ vcopy(temp, cross);
+}
+
+static float
+vlength(const float v[3])
+{
+ return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
+}
+
+static void
+vscale(float v[3], float div)
+{
+ v[0] *= div;
+ v[1] *= div;
+ v[2] *= div;
+}
+
+static void
+vnormal(float v[3])
+{
+ vscale(v,1.0/vlength(v));
+}
+
+static float
+vdot(const float v1[3], const float v2[3])
+{
+ return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
+}
+
+static void
+vadd(const float src1[3], const float src2[3], float dst[3])
+{
+ dst[0] = src1[0] + src2[0];
+ dst[1] = src1[1] + src2[1];
+ dst[2] = src1[2] + src2[2];
+}
+
+/*
+ * Ok, simulate a track-ball. Project the points onto the virtual
+ * trackball, then figure out the axis of rotation, which is the cross
+ * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
+ * Note: This is a deformed trackball-- is a trackball in the center,
+ * but is deformed into a hyperbolic sheet of rotation away from the
+ * center. This particular function was chosen after trying out
+ * several variations.
+ *
+ * It is assumed that the arguments to this routine are in the range
+ * (-1.0 ... 1.0)
+ */
+void
+trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
+{
+ float a[3]; /* Axis of rotation */
+ float phi; /* how much to rotate about axis */
+ float p1[3], p2[3], d[3];
+ float t;
+
+ if (p1x == p2x && p1y == p2y) {
+ /* Zero rotation */
+ vzero(q);
+ q[3] = 1.0;
+ return;
+ }
+
+ /*
+ * First, figure out z-coordinates for projection of P1 and P2 to
+ * deformed sphere
+ */
+ vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
+ vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
+
+ /*
+ * Now, we want the cross product of P1 and P2
+ */
+ vcross(p2,p1,a);
+
+ /*
+ * Figure out how much to rotate around that axis.
+ */
+ vsub(p1,p2,d);
+ t = vlength(d) / (2.0*TRACKBALLSIZE);
+
+ /*
+ * Avoid problems with out-of-control values...
+ */
+ if (t > 1.0) t = 1.0;
+ if (t < -1.0) t = -1.0;
+ phi = 2.0 * asin(t);
+
+ axis_to_quat(a,phi,q);
+}
+
+/*
+ * Given an axis and angle, compute quaternion.
+ */
+void
+axis_to_quat(const float a[3], float phi, float q[4])
+{
+ vcopy(a,q);
+ vnormal(q);
+ vscale(q, sin(phi/2.0));
+ q[3] = cos(phi/2.0);
+}
+
+/*
+ * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
+ * if we are away from the center of the sphere.
+ */
+static float
+tb_project_to_sphere(float r, float x, float y)
+{
+ float d, t, z;
+
+ d = sqrt(x*x + y*y);
+ if (d < r * 0.70710678118654752440) { /* Inside sphere */
+ z = sqrt(r*r - d*d);
+ } else { /* On hyperbola */
+ t = r / 1.41421356237309504880;
+ z = t*t / d;
+ }
+ return z;
+}
+
+/*
+ * Given two rotations, e1 and e2, expressed as quaternion rotations,
+ * figure out the equivalent single rotation and stuff it into dest.
+ *
+ * This routine also normalizes the result every RENORMCOUNT times it is
+ * called, to keep error from creeping in.
+ *
+ * NOTE: This routine is written so that q1 or q2 may be the same
+ * as dest (or each other).
+ */
+
+#define RENORMCOUNT 97
+
+void
+add_quats(const float q1[4], const float q2[4], float dest[4])
+{
+ static int count=0;
+ float t1[4], t2[4], t3[4];
+ float tf[4];
+
+#if 0
+printf("q1 = %f %f %f %f\n", q1[0], q1[1], q1[2], q1[3]);
+printf("q2 = %f %f %f %f\n", q2[0], q2[1], q2[2], q2[3]);
+#endif
+
+ vcopy(q1,t1);
+ vscale(t1,q2[3]);
+
+ vcopy(q2,t2);
+ vscale(t2,q1[3]);
+
+ vcross(q2,q1,t3);
+ vadd(t1,t2,tf);
+ vadd(t3,tf,tf);
+ tf[3] = q1[3] * q2[3] - vdot(q1,q2);
+
+#if 0
+printf("tf = %f %f %f %f\n", tf[0], tf[1], tf[2], tf[3]);
+#endif
+
+ dest[0] = tf[0];
+ dest[1] = tf[1];
+ dest[2] = tf[2];
+ dest[3] = tf[3];
+
+ if (++count > RENORMCOUNT) {
+ count = 0;
+ normalize_quat(dest);
+ }
+}
+
+/*
+ * Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0
+ * If they don't add up to 1.0, dividing by their magnitued will
+ * renormalize them.
+ *
+ * Note: See the following for more information on quaternions:
+ *
+ * - Shoemake, K., Animating rotation with quaternion curves, Computer
+ * Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
+ * - Pletinckx, D., Quaternion calculus as a basic tool in computer
+ * graphics, The Visual Computer 5, 2-13, 1989.
+ */
+static void
+normalize_quat(float q[4])
+{
+ int i;
+ float mag;
+
+ mag = sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
+ for (i = 0; i < 4; i++)
+ q[i] /= mag;
+}
+
+/*
+ * Build a rotation matrix, given a quaternion rotation.
+ *
+ */
+void
+build_rotmatrix(float m[4][4], const float q[4])
+{
+ m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
+ m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
+ m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
+ m[0][3] = 0.0;
+
+ m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
+ m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
+ m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
+ m[1][3] = 0.0;
+
+ m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
+ m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
+ m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
+ m[2][3] = 0.0;
+
+ m[3][0] = 0.0;
+ m[3][1] = 0.0;
+ m[3][2] = 0.0;
+ m[3][3] = 1.0;
+}
+
--- /dev/null
+/*
+ * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
+ * ALL RIGHTS RESERVED
+ * Permission to use, copy, modify, and distribute this software for
+ * any purpose and without fee is hereby granted, provided that the above
+ * copyright notice appear in all copies and that both the copyright notice
+ * and this permission notice appear in supporting documentation, and that
+ * the name of Silicon Graphics, Inc. not be used in advertising
+ * or publicity pertaining to distribution of the software without specific,
+ * written prior permission.
+ *
+ * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
+ * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
+ * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
+ * FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON
+ * GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
+ * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
+ * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
+ * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
+ * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN
+ * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
+ * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * US Government Users Restricted Rights
+ * Use, duplication, or disclosure by the Government is subject to
+ * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
+ * (c)(1)(ii) of the Rights in Technical Data and Computer Software
+ * clause at DFARS 252.227-7013 and/or in similar or successor
+ * clauses in the FAR or the DOD or NASA FAR Supplement.
+ * Unpublished-- rights reserved under the copyright laws of the
+ * United States. Contractor/manufacturer is Silicon Graphics,
+ * Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311.
+ *
+ * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
+ */
+/*
+ * trackball.h
+ * A virtual trackball implementation
+ * Written by Gavin Bell for Silicon Graphics, November 1988.
+ */
+
+#ifndef TRACKBALL_H
+#define TRACKBALL_H
+
+
+/*
+ * Pass the x and y coordinates of the last and current positions of
+ * the mouse, scaled so they are from (-1.0 ... 1.0).
+ *
+ * The resulting rotation is returned as a quaternion rotation in the
+ * first paramater.
+ */
+void
+trackball(float q[4], float p1x, float p1y, float p2x, float p2y);
+
+/*
+ * Given two quaternions, add them together to get a third quaternion.
+ * Adding quaternions to get a compound rotation is analagous to adding
+ * translations to get a compound translation. When incrementally
+ * adding rotations, the first argument here should be the new
+ * rotation, the second and third the total rotation (which will be
+ * over-written with the resulting new total rotation).
+ */
+void
+add_quats(const float q1[4], const float q2[4], float dest[4]);
+
+/*
+ * A useful function, builds a rotation matrix in Matrix based on
+ * given quaternion.
+ */
+void
+build_rotmatrix(float m[4][4], const float q[4]);
+
+/*
+ * This function computes a quaternion based on an axis (defined by
+ * the given vector) and an angle about which to rotate. The angle is
+ * expressed in radians. The result is put into the third argument.
+ */
+void
+axis_to_quat(const float a[3], float phi, float q[4]);
+
+
+#endif /* TRACKBALL_H */
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