src/cairo-path-stroke.c

   1 /* -*- Mode: c; tab-width: 8; c-basic-offset: 4; indent-tabs-mode: t; -*- */
   2 /* cairo - a vector graphics library with display and print output
   3  *
   4  * Copyright © 2002 University of Southern California
   5  *
   6  * This library is free software; you can redistribute it and/or
   7  * modify it either under the terms of the GNU Lesser General Public
   8  * License version 2.1 as published by the Free Software Foundation
   9  * (the "LGPL") or, at your option, under the terms of the Mozilla
  10  * Public License Version 1.1 (the "MPL"). If you do not alter this
  11  * notice, a recipient may use your version of this file under either
  12  * the MPL or the LGPL.
  13  *
  14  * You should have received a copy of the LGPL along with this library
  15  * in the file COPYING-LGPL-2.1; if not, write to the Free Software
  16  * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
  17  * You should have received a copy of the MPL along with this library
  18  * in the file COPYING-MPL-1.1
  19  *
  20  * The contents of this file are subject to the Mozilla Public License
  21  * Version 1.1 (the "License"); you may not use this file except in
  22  * compliance with the License. You may obtain a copy of the License at
  23  * http://www.mozilla.org/MPL/
  24  *
  25  * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
  26  * OF ANY KIND, either express or implied. See the LGPL or the MPL for
  27  * the specific language governing rights and limitations.
  28  *
  29  * The Original Code is the cairo graphics library.
  30  *
  31  * The Initial Developer of the Original Code is University of Southern
  32  * California.
  33  *
  34  * Contributor(s):
  35  *      Carl D. Worth <cworth@cworth.org>
  36  *      Chris Wilson <chris@chris-wilson.co.uk>
  37  */
  38
  39 #define _BSD_SOURCE /* for hypot() */
  40 #include "cairoint.h"
  41
  42 #include "cairo-box-inline.h"
  43 #include "cairo-boxes-private.h"
  44 #include "cairo-error-private.h"
  45 #include "cairo-path-fixed-private.h"
  46 #include "cairo-slope-private.h"
  47 #include "cairo-stroke-dash-private.h"
  48 #include "cairo-traps-private.h"
  49
  50 typedef struct cairo_stroker {
  51     cairo_stroke_style_t style;
  52
  53     const cairo_matrix_t *ctm;
  54     const cairo_matrix_t *ctm_inverse;
  55     double half_line_width;
  56     double tolerance;
  57     double spline_cusp_tolerance;
  58     double ctm_determinant;
  59     cairo_bool_t ctm_det_positive;
  60
  61     void *closure;
  62     cairo_status_t (*add_external_edge) (void *closure,
  63                                          const cairo_point_t *p1,
  64                                          const cairo_point_t *p2);
  65     cairo_status_t (*add_triangle) (void *closure,
  66                                     const cairo_point_t triangle[3]);
  67     cairo_status_t (*add_triangle_fan) (void *closure,
  68                                         const cairo_point_t *midpt,
  69                                         const cairo_point_t *points,
  70                                         int npoints);
  71     cairo_status_t (*add_convex_quad) (void *closure,
  72                                        const cairo_point_t quad[4]);
  73
  74     cairo_pen_t   pen;
  75
  76     cairo_point_t current_point;
  77     cairo_point_t first_point;
  78
  79     cairo_bool_t has_initial_sub_path;
  80
  81     cairo_bool_t has_current_face;
  82     cairo_stroke_face_t current_face;
  83
  84     cairo_bool_t has_first_face;
  85     cairo_stroke_face_t first_face;
  86
  87     cairo_stroker_dash_t dash;
  88
  89     cairo_bool_t has_bounds;
  90     cairo_box_t bounds;
  91 } cairo_stroker_t;
  92
  93 /*
  94  # to avoid warning : defined but not used [-Wunused-function]
  95 static cairo_bool_t
  96 _cairo_stroke_segment_intersect (cairo_point_t *p1, cairo_point_t *p2,
  97                  cairo_point_t *p3, cairo_point_t *p4,
  98                                  cairo_point_t *p)
  99 {
 100     double x1, y1, x2, y2, x3, y3, x4, y4;
 101     double pre, post;
 102     double x, y, d;
 103
 104     x1 = _cairo_fixed_to_double (p1->x);
 105     y1 = _cairo_fixed_to_double (p1->y);
 106     x2 = _cairo_fixed_to_double (p2->x);
 107     y2 = _cairo_fixed_to_double (p2->y);
 108     x3 = _cairo_fixed_to_double (p3->x);
 109     y3 = _cairo_fixed_to_double (p3->y);
 110     x4 = _cairo_fixed_to_double (p4->x);
 111     y4 = _cairo_fixed_to_double (p4->y);
 112
 113     d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
 114     if (d == 0)
 115         return FALSE;
 116
 117     pre = x1 * y2 - y1 * x2;
 118     post = x3 * y4 - y3 * x4;
 119     x = (pre * (x3 - x4) - (x1 - x2) * post) / d;
 120     y = (pre * (y3 - y4) - (y1 - y2) * post) / d;
 121
 122     // check if x, y are within both segments
 123     if (x < MIN (x1, x2) || x > MAX (x1, x2) ||
 124         x < MIN (x3, x4) || x > MAX (x3, x4))
 125     return FALSE;
 126     if (y < MIN (y1, y2) || y > MAX (y1, y2) ||
 127         y < MIN (y1, y2) || y > MAX (y3, y4))
 128     return FALSE;
 129
 130     p->x = _cairo_fixed_from_double (x);
 131     p->y = _cairo_fixed_from_double (y);
 132     return TRUE;
 133 }
 134 */
 135
 136 static void
 137 _cairo_stroker_limit (cairo_stroker_t *stroker,
 138                       const cairo_path_fixed_t *path,
 139                       const cairo_box_t *boxes,
 140                       int num_boxes)
 141 {
 142     double dx, dy;
 143     cairo_fixed_t fdx, fdy;
 144
 145     stroker->has_bounds = TRUE;
 146     _cairo_boxes_get_extents (boxes, num_boxes, &stroker->bounds);
 147
 148     /* Extend the bounds in each direction to account for the maximum area
 149      * we might generate trapezoids, to capture line segments that are outside
 150      * of the bounds but which might generate rendering that's within bounds.
 151      */
 152
 153     _cairo_stroke_style_max_distance_from_path (&stroker->style, path,
 154                                                 stroker->ctm, &dx, &dy);
 155
 156     fdx = _cairo_fixed_from_double (dx);
 157     fdy = _cairo_fixed_from_double (dy);
 158
 159     stroker->bounds.p1.x -= fdx;
 160     stroker->bounds.p2.x += fdx;
 161
 162     stroker->bounds.p1.y -= fdy;
 163     stroker->bounds.p2.y += fdy;
 164 }
 165
 166 static cairo_status_t
 167 _cairo_stroker_init (cairo_stroker_t            *stroker,
 168                      const cairo_path_fixed_t   *path,
 169                      const cairo_stroke_style_t *stroke_style,
 170                      const cairo_matrix_t       *ctm,
 171                      const cairo_matrix_t       *ctm_inverse,
 172                      double                      tolerance,
 173                      const cairo_box_t          *limits,
 174                      int                         num_limits)
 175 {
 176     cairo_status_t status;
 177
 178     stroker->style = *stroke_style;
 179     stroker->ctm = ctm;
 180     stroker->ctm_inverse = ctm_inverse;
 181     stroker->tolerance = tolerance;
 182     stroker->half_line_width = stroke_style->line_width / 2.0;
 183
 184     /* To test whether we need to join two segments of a spline using
 185      * a round-join or a bevel-join, we can inspect the angle between the
 186      * two segments. If the difference between the chord distance
 187      * (half-line-width times the cosine of the bisection angle) and the
 188      * half-line-width itself is greater than tolerance then we need to
 189      * inject a point.
 190      */
 191     stroker->spline_cusp_tolerance = 1 - tolerance / stroker->half_line_width;
 192     stroker->spline_cusp_tolerance *= stroker->spline_cusp_tolerance;
 193     stroker->spline_cusp_tolerance *= 2;
 194     stroker->spline_cusp_tolerance -= 1;
 195
 196     stroker->ctm_determinant = _cairo_matrix_compute_determinant (stroker->ctm);
 197     stroker->ctm_det_positive = stroker->ctm_determinant >= 0.0;
 198
 199     status = _cairo_pen_init (&stroker->pen,
 200                               stroker->half_line_width, tolerance, ctm);
 201     if (unlikely (status))
 202         return status;
 203
 204     stroker->has_current_face = FALSE;
 205     stroker->has_first_face = FALSE;
 206     stroker->has_initial_sub_path = FALSE;
 207
 208     _cairo_stroker_dash_init (&stroker->dash, stroke_style);
 209
 210     stroker->add_external_edge = NULL;
 211
 212     stroker->has_bounds = FALSE;
 213     if (num_limits)
 214         _cairo_stroker_limit (stroker, path, limits, num_limits);
 215
 216     return CAIRO_STATUS_SUCCESS;
 217 }
 218
 219 static void
 220 _cairo_stroker_fini (cairo_stroker_t *stroker)
 221 {
 222     _cairo_pen_fini (&stroker->pen);
 223 }
 224
 225 static void
 226 _translate_point (cairo_point_t *point, const cairo_point_t *offset)
 227 {
 228     point->x += offset->x;
 229     point->y += offset->y;
 230 }
 231
 232 static int
 233 _cairo_stroker_join_is_clockwise (const cairo_stroke_face_t *in,
 234                                   const cairo_stroke_face_t *out)
 235 {
 236     cairo_slope_t in_slope, out_slope;
 237
 238     _cairo_slope_init (&in_slope, &in->point, &in->cw);
 239     _cairo_slope_init (&out_slope, &out->point, &out->cw);
 240
 241     return _cairo_slope_compare (&in_slope, &out_slope) < 0;
 242 }
 243
 244 /**
 245  * _cairo_slope_compare_sgn:
 246  *
 247  * Return -1, 0 or 1 depending on the relative slopes of
 248  * two lines.
 249  **/
 250 static int
 251 _cairo_slope_compare_sgn (double dx1, double dy1, double dx2, double dy2)
 252 {
 253     double  c = (dx1 * dy2 - dx2 * dy1);
 254
 255     if (c > 0) return 1;
 256     if (c < 0) return -1;
 257     return 0;
 258 }
 259
 260 static inline int
 261 _range_step (int i, int step, int max)
 262 {
 263     i += step;
 264     if (i < 0)
 265         i = max - 1;
 266     if (i >= max)
 267         i = 0;
 268     return i;
 269 }
 270
 271 /*
 272  * Construct a fan around the midpoint using the vertices from pen between
 273  * inpt and outpt.
 274  */
 275 static cairo_status_t
 276 _tessellate_fan (cairo_stroker_t *stroker,
 277                  const cairo_slope_t *in_vector,
 278                  const cairo_slope_t *out_vector,
 279                  const cairo_point_t *midpt,
 280                  const cairo_point_t *inpt,
 281                  const cairo_point_t *outpt,
 282                  cairo_bool_t clockwise)
 283 {
 284     cairo_point_t stack_points[64], *points = stack_points;
 285     cairo_pen_t *pen = &stroker->pen;
 286     int start, stop, num_points = 0;
 287     cairo_status_t status = CAIRO_STATUS_SUCCESS;
 288
 289     if (stroker->has_bounds &&
 290         ! _cairo_box_contains_point (&stroker->bounds, midpt))
 291         goto BEVEL;
 292
 293     assert (stroker->pen.num_vertices);
 294
 295     if (clockwise) {
 296         _cairo_pen_find_active_ccw_vertices (pen,
 297                                              in_vector, out_vector,
 298                                              &start, &stop);
 299         if (stroker->add_external_edge) {
 300             cairo_point_t last;
 301             last = *inpt;
 302             while (start != stop) {
 303                 cairo_point_t p = *midpt;
 304                 _translate_point (&p, &pen->vertices[start].point);
 305
 306                 status = stroker->add_external_edge (stroker->closure,
 307                                                      &last, &p);
 308                 if (unlikely (status))
 309                     return status;
 310                 last = p;
 311
 312                 if (start-- == 0)
 313                     start += pen->num_vertices;
 314             }
 315             status = stroker->add_external_edge (stroker->closure,
 316                                                  &last, outpt);
 317         } else {
 318             if (start == stop)
 319                 goto BEVEL;
 320
 321             num_points = stop - start;
 322             if (num_points < 0)
 323                 num_points += pen->num_vertices;
 324             else
 325                 num_points = pen->num_vertices - stop + start;
 326             num_points += 2;
 327             if (num_points > ARRAY_LENGTH(stack_points)) {
 328                 points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
 329                 if (unlikely (points == NULL))
 330                     return _cairo_error (CAIRO_STATUS_NO_MEMORY);
 331             }
 332
 333             points[0] = *inpt;
 334             num_points = 1;
 335             while (start != stop) {
 336                 points[num_points] = *midpt;
 337                 _translate_point (&points[num_points], &pen->vertices[start].point);
 338                 num_points++;
 339
 340                 if (start-- == 0)
 341                     start += pen->num_vertices;
 342             }
 343             points[num_points++] = *outpt;
 344         }
 345     } else {
 346         _cairo_pen_find_active_cw_vertices (pen,
 347                                             in_vector, out_vector,
 348                                             &start, &stop);
 349         if (stroker->add_external_edge) {
 350             cairo_point_t last;
 351             last = *inpt;
 352             while (start != stop) {
 353                 cairo_point_t p = *midpt;
 354                 _translate_point (&p, &pen->vertices[start].point);
 355
 356                 status = stroker->add_external_edge (stroker->closure,
 357                                                      &p, &last);
 358                 if (unlikely (status))
 359                     return status;
 360                 last = p;
 361
 362                 if (++start == pen->num_vertices)
 363                     start = 0;
 364             }
 365             status = stroker->add_external_edge (stroker->closure,
 366                                                  outpt, &last);
 367         } else {
 368             if (start == stop)
 369                 goto BEVEL;
 370
 371             num_points = stop - start;
 372             if (num_points < 0)
 373                 num_points += pen->num_vertices;
 374             else
 375                 num_points = pen->num_vertices - stop + start;
 376             num_points += 2;
 377             if (num_points > ARRAY_LENGTH(stack_points)) {
 378                 points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
 379                 if (unlikely (points == NULL))
 380                     return _cairo_error (CAIRO_STATUS_NO_MEMORY);
 381             }
 382
 383             points[0] = *inpt;
 384             num_points = 1;
 385             while (start != stop) {
 386                 points[num_points] = *midpt;
 387                 _translate_point (&points[num_points], &pen->vertices[start].point);
 388                 num_points++;
 389
 390                 if (++start == pen->num_vertices)
 391                     start = 0;
 392             }
 393             points[num_points++] = *outpt;
 394         }
 395     }
 396
 397     if (num_points) {
 398         status = stroker->add_triangle_fan (stroker->closure,
 399                                             midpt, points, num_points);
 400     }
 401
 402     if (points != stack_points)
 403         free (points);
 404
 405     return status;
 406
 407 BEVEL:
 408     /* Ensure a leak free connection... */
 409     if (stroker->add_external_edge != NULL) {
 410         if (clockwise)
 411             return stroker->add_external_edge (stroker->closure, inpt, outpt);
 412         else
 413             return stroker->add_external_edge (stroker->closure, outpt, inpt);
 414     } else {
 415         stack_points[0] = *midpt;
 416         stack_points[1] = *inpt;
 417         stack_points[2] = *outpt;
 418         return stroker->add_triangle (stroker->closure, stack_points);
 419     }
 420 }
 421
 422 static cairo_status_t
 423 _cairo_stroker_join (cairo_stroker_t *stroker,
 424                      const cairo_stroke_face_t *in,
 425                      const cairo_stroke_face_t *out)
 426 {
 427     int  clockwise = _cairo_stroker_join_is_clockwise (out, in);
 428     const cairo_point_t *inpt, *outpt;
 429     cairo_point_t points[4];
 430     cairo_status_t status;
 431
 432     if (in->cw.x  == out->cw.x  && in->cw.y  == out->cw.y &&
 433         in->ccw.x == out->ccw.x && in->ccw.y == out->ccw.y)
 434     {
 435         return CAIRO_STATUS_SUCCESS;
 436     }
 437
 438     if (clockwise) {
 439         if (stroker->add_external_edge != NULL) {
 440             status = stroker->add_external_edge (stroker->closure,
 441                                                  &out->cw, &in->point);
 442             if (unlikely (status))
 443                 return status;
 444
 445             status = stroker->add_external_edge (stroker->closure,
 446                                                  &in->point, &in->cw);
 447             if (unlikely (status))
 448                 return status;
 449         }
 450
 451         inpt = &in->ccw;
 452         outpt = &out->ccw;
 453     } else {
 454         if (stroker->add_external_edge != NULL) {
 455             status = stroker->add_external_edge (stroker->closure,
 456                                                  &in->ccw, &in->point);
 457             if (unlikely (status))
 458                 return status;
 459
 460             status = stroker->add_external_edge (stroker->closure,
 461                                                  &in->point, &out->ccw);
 462             if (unlikely (status))
 463                 return status;
 464         }
 465
 466         inpt = &in->cw;
 467         outpt = &out->cw;
 468     }
 469
 470     switch (stroker->style.line_join) {
 471     case CAIRO_LINE_JOIN_ROUND:
 472         /* construct a fan around the common midpoint */
 473         return _tessellate_fan (stroker,
 474                                 &in->dev_vector,
 475                                 &out->dev_vector,
 476                                 &in->point, inpt, outpt,
 477                                 clockwise);
 478
 479     case CAIRO_LINE_JOIN_MITER:
 480     default: {
 481         /* dot product of incoming slope vector with outgoing slope vector */
 482         double  in_dot_out = -in->usr_vector.x * out->usr_vector.x +
 483                              -in->usr_vector.y * out->usr_vector.y;
 484         double  ml = stroker->style.miter_limit;
 485
 486         /* Check the miter limit -- lines meeting at an acute angle
 487          * can generate long miters, the limit converts them to bevel
 488          *
 489          * Consider the miter join formed when two line segments
 490          * meet at an angle psi:
 491          *
 492          *         /.\
 493          *        /. .\
 494          *       /./ \.\
 495          *      /./psi\.\
 496          *
 497          * We can zoom in on the right half of that to see:
 498          *
 499          *          |\
 500          *          | \ psi/2
 501          *          |  \
 502          *          |   \
 503          *          |    \
 504          *          |     \
 505          *        miter    \
 506          *       length     \
 507          *          |        \
 508          *          |        .\
 509          *          |    .     \
 510          *          |.   line   \
 511          *           \    width  \
 512          *            \           \
 513          *
 514          *
 515          * The right triangle in that figure, (the line-width side is
 516          * shown faintly with three '.' characters), gives us the
 517          * following expression relating miter length, angle and line
 518          * width:
 519          *
 520          *      1 /sin (psi/2) = miter_length / line_width
 521          *
 522          * The right-hand side of this relationship is the same ratio
 523          * in which the miter limit (ml) is expressed. We want to know
 524          * when the miter length is within the miter limit. That is
 525          * when the following condition holds:
 526          *
 527          *      1/sin(psi/2) <= ml
 528          *      1 <= ml sin(psi/2)
 529          *      1 <= ml² sin²(psi/2)
 530          *      2 <= ml² 2 sin²(psi/2)
 531          *                              2·sin²(psi/2) = 1-cos(psi)
 532          *      2 <= ml² (1-cos(psi))
 533          *
 534          *                              in · out = |in| |out| cos (psi)
 535          *
 536          * in and out are both unit vectors, so:
 537          *
 538          *                              in · out = cos (psi)
 539          *
 540          *      2 <= ml² (1 - in · out)
 541          *
 542          */
 543         if (2 <= ml * ml * (1 - in_dot_out)) {
 544             double              x1, y1, x2, y2;
 545             double              mx, my;
 546             double              dx1, dx2, dy1, dy2;
 547             double              ix, iy;
 548             double              fdx1, fdy1, fdx2, fdy2;
 549             double              mdx, mdy;
 550
 551             /*
 552              * we've got the points already transformed to device
 553              * space, but need to do some computation with them and
 554              * also need to transform the slope from user space to
 555              * device space
 556              */
 557             /* outer point of incoming line face */
 558             x1 = _cairo_fixed_to_double (inpt->x);
 559             y1 = _cairo_fixed_to_double (inpt->y);
 560             dx1 = in->usr_vector.x;
 561             dy1 = in->usr_vector.y;
 562             cairo_matrix_transform_distance (stroker->ctm, &dx1, &dy1);
 563
 564             /* outer point of outgoing line face */
 565             x2 = _cairo_fixed_to_double (outpt->x);
 566             y2 = _cairo_fixed_to_double (outpt->y);
 567             dx2 = out->usr_vector.x;
 568             dy2 = out->usr_vector.y;
 569             cairo_matrix_transform_distance (stroker->ctm, &dx2, &dy2);
 570
 571             /*
 572              * Compute the location of the outer corner of the miter.
 573              * That's pretty easy -- just the intersection of the two
 574              * outer edges.  We've got slopes and points on each
 575              * of those edges.  Compute my directly, then compute
 576              * mx by using the edge with the larger dy; that avoids
 577              * dividing by values close to zero.
 578              */
 579             my = (((x2 - x1) * dy1 * dy2 - y2 * dx2 * dy1 + y1 * dx1 * dy2) /
 580                   (dx1 * dy2 - dx2 * dy1));
 581             if (fabs (dy1) >= fabs (dy2))
 582                 mx = (my - y1) * dx1 / dy1 + x1;
 583             else
 584                 mx = (my - y2) * dx2 / dy2 + x2;
 585
 586             /*
 587              * When the two outer edges are nearly parallel, slight
 588              * perturbations in the position of the outer points of the lines
 589              * caused by representing them in fixed point form can cause the
 590              * intersection point of the miter to move a large amount. If
 591              * that moves the miter intersection from between the two faces,
 592              * then draw a bevel instead.
 593              */
 594
 595             ix = _cairo_fixed_to_double (in->point.x);
 596             iy = _cairo_fixed_to_double (in->point.y);
 597
 598             /* slope of one face */
 599             fdx1 = x1 - ix; fdy1 = y1 - iy;
 600
 601             /* slope of the other face */
 602             fdx2 = x2 - ix; fdy2 = y2 - iy;
 603
 604             /* slope from the intersection to the miter point */
 605             mdx = mx - ix; mdy = my - iy;
 606
 607             /*
 608              * Make sure the miter point line lies between the two
 609              * faces by comparing the slopes
 610              */
 611             if (_cairo_slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
 612                 _cairo_slope_compare_sgn (fdx2, fdy2, mdx, mdy))
 613             {
 614                 if (stroker->add_external_edge != NULL) {
 615                     points[0].x = _cairo_fixed_from_double (mx);
 616                     points[0].y = _cairo_fixed_from_double (my);
 617
 618                     if (clockwise) {
 619                         status = stroker->add_external_edge (stroker->closure,
 620                                                              inpt, &points[0]);
 621                         if (unlikely (status))
 622                             return status;
 623
 624                         status = stroker->add_external_edge (stroker->closure,
 625                                                              &points[0], outpt);
 626                         if (unlikely (status))
 627                             return status;
 628                     } else {
 629                         status = stroker->add_external_edge (stroker->closure,
 630                                                              outpt, &points[0]);
 631                         if (unlikely (status))
 632                             return status;
 633
 634                         status = stroker->add_external_edge (stroker->closure,
 635                                                              &points[0], inpt);
 636                         if (unlikely (status))
 637                             return status;
 638                     }
 639
 640                     return CAIRO_STATUS_SUCCESS;
 641                 } else {
 642                     points[0] = in->point;
 643                     points[1] = *inpt;
 644                     points[2].x = _cairo_fixed_from_double (mx);
 645                     points[2].y = _cairo_fixed_from_double (my);
 646                     points[3] = *outpt;
 647
 648                     return stroker->add_convex_quad (stroker->closure, points);
 649                 }
 650             }
 651         }
 652     }
 653
 654     /* fall through ... */
 655
 656     case CAIRO_LINE_JOIN_BEVEL:
 657         if (stroker->add_external_edge != NULL) {
 658             if (clockwise) {
 659                 return stroker->add_external_edge (stroker->closure,
 660                                                    inpt, outpt);
 661             } else {
 662                 return stroker->add_external_edge (stroker->closure,
 663                                                    outpt, inpt);
 664             }
 665         } else {
 666             points[0] = in->point;
 667             points[1] = *inpt;
 668             points[2] = *outpt;
 669
 670             return stroker->add_triangle (stroker->closure, points);
 671         }
 672     }
 673 }
 674
 675 static cairo_status_t
 676 _cairo_stroker_add_cap (cairo_stroker_t *stroker,
 677                         const cairo_stroke_face_t *f)
 678 {
 679     switch (stroker->style.line_cap) {
 680     case CAIRO_LINE_CAP_ROUND: {
 681         cairo_slope_t slope;
 682
 683         slope.dx = -f->dev_vector.dx;
 684         slope.dy = -f->dev_vector.dy;
 685
 686         return _tessellate_fan (stroker,
 687                                 &f->dev_vector,
 688                                 &slope,
 689                                 &f->point, &f->cw, &f->ccw,
 690                                 FALSE);
 691
 692     }
 693
 694     case CAIRO_LINE_CAP_SQUARE: {
 695         double dx, dy;
 696         cairo_slope_t   fvector;
 697         cairo_point_t   quad[4];
 698
 699         dx = f->usr_vector.x;
 700         dy = f->usr_vector.y;
 701         dx *= stroker->half_line_width;
 702         dy *= stroker->half_line_width;
 703         cairo_matrix_transform_distance (stroker->ctm, &dx, &dy);
 704         fvector.dx = _cairo_fixed_from_double (dx);
 705         fvector.dy = _cairo_fixed_from_double (dy);
 706
 707         quad[0] = f->ccw;
 708         quad[1].x = f->ccw.x + fvector.dx;
 709         quad[1].y = f->ccw.y + fvector.dy;
 710         quad[2].x = f->cw.x + fvector.dx;
 711         quad[2].y = f->cw.y + fvector.dy;
 712         quad[3] = f->cw;
 713
 714         if (stroker->add_external_edge != NULL) {
 715             cairo_status_t status;
 716
 717             status = stroker->add_external_edge (stroker->closure,
 718                                                  &quad[0], &quad[1]);
 719             if (unlikely (status))
 720                 return status;
 721
 722             status = stroker->add_external_edge (stroker->closure,
 723                                                  &quad[1], &quad[2]);
 724             if (unlikely (status))
 725                 return status;
 726
 727             status = stroker->add_external_edge (stroker->closure,
 728                                                  &quad[2], &quad[3]);
 729             if (unlikely (status))
 730                 return status;
 731
 732             return CAIRO_STATUS_SUCCESS;
 733         } else {
 734             return stroker->add_convex_quad (stroker->closure, quad);
 735         }
 736     }
 737
 738     case CAIRO_LINE_CAP_BUTT:
 739     default:
 740         if (stroker->add_external_edge != NULL) {
 741             return stroker->add_external_edge (stroker->closure,
 742                                                &f->ccw, &f->cw);
 743         } else {
 744             return CAIRO_STATUS_SUCCESS;
 745         }
 746     }
 747 }
 748
 749 static cairo_status_t
 750 _cairo_stroker_add_leading_cap (cairo_stroker_t     *stroker,
 751                                 const cairo_stroke_face_t *face)
 752 {
 753     cairo_stroke_face_t reversed;
 754     cairo_point_t t;
 755
 756     reversed = *face;
 757
 758     /* The initial cap needs an outward facing vector. Reverse everything */
 759     reversed.usr_vector.x = -reversed.usr_vector.x;
 760     reversed.usr_vector.y = -reversed.usr_vector.y;
 761     reversed.dev_vector.dx = -reversed.dev_vector.dx;
 762     reversed.dev_vector.dy = -reversed.dev_vector.dy;
 763     t = reversed.cw;
 764     reversed.cw = reversed.ccw;
 765     reversed.ccw = t;
 766
 767     return _cairo_stroker_add_cap (stroker, &reversed);
 768 }
 769
 770 static cairo_status_t
 771 _cairo_stroker_add_trailing_cap (cairo_stroker_t     *stroker,
 772                                  const cairo_stroke_face_t *face)
 773 {
 774     return _cairo_stroker_add_cap (stroker, face);
 775 }
 776
 777 static inline cairo_bool_t
 778 _compute_normalized_device_slope (double *dx, double *dy,
 779                                   const cairo_matrix_t *ctm_inverse,
 780                                   double *mag_out)
 781 {
 782     double dx0 = *dx, dy0 = *dy;
 783     double mag;
 784
 785     cairo_matrix_transform_distance (ctm_inverse, &dx0, &dy0);
 786
 787     if (dx0 == 0.0 && dy0 == 0.0) {
 788         if (mag_out)
 789             *mag_out = 0.0;
 790         return FALSE;
 791     }
 792
 793     if (dx0 == 0.0) {
 794         *dx = 0.0;
 795         if (dy0 > 0.0) {
 796             mag = dy0;
 797             *dy = 1.0;
 798         } else {
 799             mag = -dy0;
 800             *dy = -1.0;
 801         }
 802     } else if (dy0 == 0.0) {
 803         *dy = 0.0;
 804         if (dx0 > 0.0) {
 805             mag = dx0;
 806             *dx = 1.0;
 807         } else {
 808             mag = -dx0;
 809             *dx = -1.0;
 810         }
 811     } else {
 812         mag = hypot (dx0, dy0);
 813         *dx = dx0 / mag;
 814         *dy = dy0 / mag;
 815     }
 816
 817     if (mag_out)
 818         *mag_out = mag;
 819
 820     return TRUE;
 821 }
 822
 823 static void
 824 _compute_face (const cairo_point_t *point,
 825                const cairo_slope_t *dev_slope,
 826                double slope_dx,
 827                double slope_dy,
 828                cairo_stroker_t *stroker,
 829                cairo_stroke_face_t *face)
 830 {
 831     double face_dx, face_dy;
 832     cairo_point_t offset_ccw, offset_cw;
 833
 834     /*
 835      * rotate to get a line_width/2 vector along the face, note that
 836      * the vector must be rotated the right direction in device space,
 837      * but by 90° in user space. So, the rotation depends on
 838      * whether the ctm reflects or not, and that can be determined
 839      * by looking at the determinant of the matrix.
 840      */
 841     if (stroker->ctm_det_positive)
 842     {
 843         face_dx = - slope_dy * stroker->half_line_width;
 844         face_dy = slope_dx * stroker->half_line_width;
 845     }
 846     else
 847     {
 848         face_dx = slope_dy * stroker->half_line_width;
 849         face_dy = - slope_dx * stroker->half_line_width;
 850     }
 851
 852     /* back to device space */
 853     cairo_matrix_transform_distance (stroker->ctm, &face_dx, &face_dy);
 854
 855     offset_ccw.x = _cairo_fixed_from_double (face_dx);
 856     offset_ccw.y = _cairo_fixed_from_double (face_dy);
 857     offset_cw.x = -offset_ccw.x;
 858     offset_cw.y = -offset_ccw.y;
 859
 860     face->ccw = *point;
 861     _translate_point (&face->ccw, &offset_ccw);
 862
 863     face->point = *point;
 864
 865     face->cw = *point;
 866     _translate_point (&face->cw, &offset_cw);
 867
 868     face->usr_vector.x = slope_dx;
 869     face->usr_vector.y = slope_dy;
 870
 871     face->dev_vector = *dev_slope;
 872 }
 873
 874 static cairo_status_t
 875 _cairo_stroker_add_caps (cairo_stroker_t *stroker)
 876 {
 877     cairo_status_t status;
 878
 879     /* check for a degenerative sub_path */
 880     if (stroker->has_initial_sub_path
 881         && ! stroker->has_first_face
 882         && ! stroker->has_current_face
 883         && stroker->style.line_cap == CAIRO_LINE_CAP_ROUND)
 884     {
 885         /* pick an arbitrary slope to use */
 886         double dx = 1.0, dy = 0.0;
 887         cairo_slope_t slope = { CAIRO_FIXED_ONE, 0 };
 888         cairo_stroke_face_t face;
 889         face.length = 0.0;
 890
 891         _compute_normalized_device_slope (&dx, &dy,
 892                                           stroker->ctm_inverse, NULL);
 893
 894         /* arbitrarily choose first_point
 895          * first_point and current_point should be the same */
 896         _compute_face (&stroker->first_point, &slope, dx, dy, stroker, &face);
 897
 898         status = _cairo_stroker_add_leading_cap (stroker, &face);
 899         if (unlikely (status))
 900             return status;
 901
 902         status = _cairo_stroker_add_trailing_cap (stroker, &face);
 903         if (unlikely (status))
 904             return status;
 905     }
 906
 907     if (stroker->has_first_face) {
 908         status = _cairo_stroker_add_leading_cap (stroker,
 909                                                  &stroker->first_face);
 910         if (unlikely (status))
 911             return status;
 912     }
 913
 914     if (stroker->has_current_face) {
 915         status = _cairo_stroker_add_trailing_cap (stroker,
 916                                                   &stroker->current_face);
 917         if (unlikely (status))
 918             return status;
 919     }
 920
 921     return CAIRO_STATUS_SUCCESS;
 922 }
 923
 924 static cairo_status_t
 925 _cairo_stroker_add_sub_edge (cairo_stroker_t *stroker,
 926                              const cairo_point_t *p1,
 927                              const cairo_point_t *p2,
 928                              cairo_slope_t *dev_slope,
 929                              double slope_dx, double slope_dy,
 930                              cairo_stroke_face_t *start,
 931                              cairo_stroke_face_t *end)
 932 {
 933     _compute_face (p1, dev_slope, slope_dx, slope_dy, stroker, start);
 934     *end = *start;
 935
 936     if (p1->x == p2->x && p1->y == p2->y)
 937         return CAIRO_STATUS_SUCCESS;
 938
 939     end->point = *p2;
 940     end->ccw.x += p2->x - p1->x;
 941     end->ccw.y += p2->y - p1->y;
 942     end->cw.x += p2->x - p1->x;
 943     end->cw.y += p2->y - p1->y;
 944
 945     if (stroker->add_external_edge != NULL) {
 946         cairo_status_t status;
 947
 948         status = stroker->add_external_edge (stroker->closure,
 949                                              &end->cw, &start->cw);
 950         if (unlikely (status))
 951             return status;
 952
 953         status = stroker->add_external_edge (stroker->closure,
 954                                              &start->ccw, &end->ccw);
 955         if (unlikely (status))
 956             return status;
 957
 958         return CAIRO_STATUS_SUCCESS;
 959     } else {
 960         cairo_point_t quad[4];
 961
 962         quad[0] = start->cw;
 963         quad[1] = end->cw;
 964         quad[2] = end->ccw;
 965         quad[3] = start->ccw;
 966
 967         return stroker->add_convex_quad (stroker->closure, quad);
 968     }
 969 }
 970
 971 static cairo_status_t
 972 _cairo_stroker_move_to (void *closure,
 973                         const cairo_point_t *point)
 974 {
 975     cairo_stroker_t *stroker = closure;
 976     cairo_status_t status;
 977
 978     /* reset the dash pattern for new sub paths */
 979     _cairo_stroker_dash_start (&stroker->dash);
 980
 981     /* Cap the start and end of the previous sub path as needed */
 982     status = _cairo_stroker_add_caps (stroker);
 983     if (unlikely (status))
 984         return status;
 985
 986     stroker->first_point = *point;
 987     stroker->current_point = *point;
 988
 989     stroker->has_first_face = FALSE;
 990     stroker->has_current_face = FALSE;
 991     stroker->has_initial_sub_path = FALSE;
 992
 993     return CAIRO_STATUS_SUCCESS;
 994 }
 995
 996 static cairo_status_t
 997 _cairo_stroker_line_to (void *closure,
 998                         const cairo_point_t *point)
 999 {
1000     cairo_stroker_t *stroker = closure;
1001     cairo_stroke_face_t start, end;
1002     cairo_point_t *p1 = &stroker->current_point;
1003     cairo_slope_t dev_slope;
1004     double slope_dx, slope_dy;
1005     cairo_status_t status;
1006     start.length = 0.0;
1007
1008     stroker->has_initial_sub_path = TRUE;
1009
1010     if (p1->x == point->x && p1->y == point->y)
1011         return CAIRO_STATUS_SUCCESS;
1012
1013     _cairo_slope_init (&dev_slope, p1, point);
1014     slope_dx = _cairo_fixed_to_double (point->x - p1->x);
1015     slope_dy = _cairo_fixed_to_double (point->y - p1->y);
1016     _compute_normalized_device_slope (&slope_dx, &slope_dy,
1017                                       stroker->ctm_inverse, NULL);
1018
1019     status = _cairo_stroker_add_sub_edge (stroker,
1020                                           p1, point,
1021                                           &dev_slope,
1022                                           slope_dx, slope_dy,
1023                                           &start, &end);
1024     if (unlikely (status))
1025         return status;
1026
1027     if (stroker->has_current_face) {
1028         /* Join with final face from previous segment */
1029         status = _cairo_stroker_join (stroker,
1030                                       &stroker->current_face,
1031                                       &start);
1032         if (unlikely (status))
1033             return status;
1034     } else if (! stroker->has_first_face) {
1035         /* Save sub path's first face in case needed for closing join */
1036         stroker->first_face = start;
1037         stroker->has_first_face = TRUE;
1038     }
1039     stroker->current_face = end;
1040     stroker->has_current_face = TRUE;
1041
1042     stroker->current_point = *point;
1043
1044     return CAIRO_STATUS_SUCCESS;
1045 }
1046
1047 static cairo_status_t
1048 _cairo_stroker_spline_to (void *closure,
1049                           const cairo_point_t *point,
1050                           const cairo_slope_t *tangent)
1051 {
1052     cairo_stroker_t *stroker = closure;
1053     cairo_stroke_face_t new_face;
1054     double slope_dx, slope_dy;
1055     cairo_point_t points[3];
1056     cairo_point_t intersect_point;
1057     cairo_line_join_t line_join_save;
1058     cairo_status_t status;
1059
1060     stroker->has_initial_sub_path = TRUE;
1061     new_face.length = 0.0;
1062
1063     if (stroker->current_point.x == point->x &&
1064         stroker->current_point.y == point->y)
1065         return CAIRO_STATUS_SUCCESS;
1066
1067     slope_dx = _cairo_fixed_to_double (tangent->dx);
1068     slope_dy = _cairo_fixed_to_double (tangent->dy);
1069
1070     if (! _compute_normalized_device_slope (&slope_dx, &slope_dy,
1071                                             stroker->ctm_inverse, NULL))
1072         return CAIRO_STATUS_SUCCESS;
1073
1074     _compute_face (point, tangent,
1075                    slope_dx, slope_dy,
1076                    stroker, &new_face);
1077
1078     assert (stroker->has_current_face);
1079
1080     if ((new_face.dev_slope.x * stroker->current_face.dev_slope.x +
1081          new_face.dev_slope.y * stroker->current_face.dev_slope.y) < stroker->spline_cusp_tolerance) {
1082
1083         const cairo_point_t *inpt, *outpt;
1084         int clockwise = _cairo_stroker_join_is_clockwise (&new_face,
1085                                                           &stroker->current_face);
1086
1087         if (clockwise) {
1088             inpt = &stroker->current_face.cw;
1089             outpt = &new_face.cw;
1090         } else {
1091             inpt = &stroker->current_face.ccw;
1092             outpt = &new_face.ccw;
1093         }
1094
1095         _tessellate_fan (stroker,
1096                          &stroker->current_face.dev_vector,
1097                          &new_face.dev_vector,
1098                          &stroker->current_face.point,
1099                          inpt, outpt,
1100                          clockwise);
1101     }
1102
1103     if (_slow_segment_intersection (&stroker->current_face.cw,
1104                                     &stroker->current_face.ccw,
1105                                     &new_face.cw,
1106                                     &new_face.ccw,
1107                                     &intersect_point)) {
1108         points[0] = stroker->current_face.ccw;
1109         points[1] = new_face.ccw;
1110         points[2] = intersect_point;
1111         stroker->add_triangle (stroker->closure, points);
1112
1113         points[0] = stroker->current_face.cw;
1114         points[1] = new_face.cw;
1115         stroker->add_triangle (stroker->closure, points);
1116     } else {
1117         points[0] = stroker->current_face.ccw;
1118         points[1] = stroker->current_face.cw;
1119         points[2] = new_face.cw;
1120         stroker->add_triangle (stroker->closure, points);
1121
1122         points[0] = stroker->current_face.ccw;
1123         points[1] = new_face.cw;
1124         points[2] = new_face.ccw;
1125         stroker->add_triangle (stroker->closure, points);
1126     }
1127
1128     /* compute join */
1129     /* Temporarily modify the stroker to use round joins to guarantee
1130      * smooth stroked curves. */
1131     line_join_save = stroker->style.line_join;
1132     stroker->style.line_join = CAIRO_LINE_JOIN_ROUND;
1133
1134     if (! stroker->dash.dashed || stroker->dash.dash_on) {
1135         if (stroker->has_current_face) {
1136             status = _cairo_stroker_join (stroker,
1137                                           &stroker->current_face, &new_face);
1138             if (unlikely (status))
1139                 return status;
1140         }
1141     }
1142
1143     stroker->style.line_join = line_join_save;
1144
1145     stroker->current_face = new_face;
1146     stroker->has_current_face = TRUE;
1147     stroker->current_point = *point;
1148
1149     return CAIRO_STATUS_SUCCESS;
1150 }
1151
1152 /*
1153  * Dashed lines.  Cap each dash end, join around turns when on
1154  */
1155 static cairo_status_t
1156 _cairo_stroker_line_to_dashed (void *closure,
1157                                const cairo_point_t *p2)
1158 {
1159     cairo_stroker_t *stroker = closure;
1160     double mag, remain, step_length = 0;
1161     double slope_dx, slope_dy;
1162     double dx2, dy2;
1163     cairo_stroke_face_t sub_start, sub_end;
1164     cairo_point_t *p1 = &stroker->current_point;
1165     cairo_slope_t dev_slope;
1166     cairo_line_t segment;
1167     cairo_bool_t fully_in_bounds;
1168     cairo_status_t status;
1169     sub_start.length = 0.0;
1170
1171     stroker->has_initial_sub_path = stroker->dash.dash_starts_on;
1172
1173     if (p1->x == p2->x && p1->y == p2->y)
1174         return CAIRO_STATUS_SUCCESS;
1175
1176     fully_in_bounds = TRUE;
1177     if (stroker->has_bounds &&
1178         (! _cairo_box_contains_point (&stroker->bounds, p1) ||
1179          ! _cairo_box_contains_point (&stroker->bounds, p2)))
1180     {
1181         fully_in_bounds = FALSE;
1182     }
1183
1184     _cairo_slope_init (&dev_slope, p1, p2);
1185
1186     slope_dx = _cairo_fixed_to_double (p2->x - p1->x);
1187     slope_dy = _cairo_fixed_to_double (p2->y - p1->y);
1188
1189     if (! _compute_normalized_device_slope (&slope_dx, &slope_dy,
1190                                             stroker->ctm_inverse, &mag))
1191     {
1192         return CAIRO_STATUS_SUCCESS;
1193     }
1194
1195     remain = mag;
1196     segment.p1 = *p1;
1197     while (remain) {
1198         step_length = MIN (stroker->dash.dash_remain, remain);
1199         remain -= step_length;
1200         dx2 = slope_dx * (mag - remain);
1201         dy2 = slope_dy * (mag - remain);
1202         cairo_matrix_transform_distance (stroker->ctm, &dx2, &dy2);
1203         segment.p2.x = _cairo_fixed_from_double (dx2) + p1->x;
1204         segment.p2.y = _cairo_fixed_from_double (dy2) + p1->y;
1205
1206         if (stroker->dash.dash_on &&
1207             (fully_in_bounds ||
1208              (! stroker->has_first_face && stroker->dash.dash_starts_on) ||
1209              _cairo_box_intersects_line_segment (&stroker->bounds, &segment)))
1210         {
1211             status = _cairo_stroker_add_sub_edge (stroker,
1212                                                   &segment.p1, &segment.p2,
1213                                                   &dev_slope,
1214                                                   slope_dx, slope_dy,
1215                                                   &sub_start, &sub_end);
1216             if (unlikely (status))
1217                 return status;
1218
1219             if (stroker->has_current_face)
1220             {
1221                 /* Join with final face from previous segment */
1222                 status = _cairo_stroker_join (stroker,
1223                                               &stroker->current_face,
1224                                               &sub_start);
1225                 if (unlikely (status))
1226                     return status;
1227
1228                 stroker->has_current_face = FALSE;
1229             }
1230             else if (! stroker->has_first_face &&
1231                        stroker->dash.dash_starts_on)
1232             {
1233                 /* Save sub path's first face in case needed for closing join */
1234                 stroker->first_face = sub_start;
1235                 stroker->has_first_face = TRUE;
1236             }
1237             else
1238             {
1239                 /* Cap dash start if not connecting to a previous segment */
1240                 status = _cairo_stroker_add_leading_cap (stroker, &sub_start);
1241                 if (unlikely (status))
1242                     return status;
1243             }
1244
1245             if (remain) {
1246                 /* Cap dash end if not at end of segment */
1247                 status = _cairo_stroker_add_trailing_cap (stroker, &sub_end);
1248                 if (unlikely (status))
1249                     return status;
1250             } else {
1251                 stroker->current_face = sub_end;
1252                 stroker->has_current_face = TRUE;
1253             }
1254         } else {
1255             if (stroker->has_current_face) {
1256                 /* Cap final face from previous segment */
1257                 status = _cairo_stroker_add_trailing_cap (stroker,
1258                                                           &stroker->current_face);
1259                 if (unlikely (status))
1260                     return status;
1261
1262                 stroker->has_current_face = FALSE;
1263             }
1264         }
1265
1266         _cairo_stroker_dash_step (&stroker->dash, step_length);
1267         segment.p1 = segment.p2;
1268     }
1269
1270     if (stroker->dash.dash_on && ! stroker->has_current_face) {
1271         /* This segment ends on a transition to dash_on, compute a new face
1272          * and add cap for the beginning of the next dash_on step.
1273          *
1274          * Note: this will create a degenerate cap if this is not the last line
1275          * in the path. Whether this behaviour is desirable or not is debatable.
1276          * On one side these degenerate caps can not be reproduced with regular
1277          * path stroking.
1278          * On the other hand, Acroread 7 also produces the degenerate caps.
1279          */
1280         _compute_face (p2, &dev_slope,
1281                        slope_dx, slope_dy,
1282                        stroker,
1283                        &stroker->current_face);
1284
1285         status = _cairo_stroker_add_leading_cap (stroker,
1286                                                  &stroker->current_face);
1287         if (unlikely (status))
1288             return status;
1289
1290         stroker->has_current_face = TRUE;
1291     }
1292
1293     stroker->current_point = *p2;
1294
1295     return CAIRO_STATUS_SUCCESS;
1296 }
1297 static cairo_status_t
1298 _cairo_stroker_curve_to (void *closure,
1299                          const cairo_point_t *b,
1300                          const cairo_point_t *c,
1301                          const cairo_point_t *d)
1302 {
1303     cairo_stroker_t *stroker = closure;
1304     cairo_spline_t spline;
1305     cairo_line_join_t line_join_save;
1306     cairo_stroke_face_t face;
1307     double slope_dx, slope_dy;
1308     cairo_spline_add_point_func_t line_to;
1309     cairo_spline_add_point_func_t spline_to;
1310     cairo_status_t status = CAIRO_STATUS_SUCCESS;
1311     face.length = 0.0;
1312
1313     line_to = stroker->dash.dashed ?
1314         (cairo_spline_add_point_func_t) _cairo_stroker_line_to_dashed :
1315         (cairo_spline_add_point_func_t) _cairo_stroker_line_to;
1316
1317     /* spline_to is only capable of rendering non-degenerate splines. */
1318     spline_to = stroker->dash.dashed ?
1319         (cairo_spline_add_point_func_t) _cairo_stroker_line_to_dashed :
1320         (cairo_spline_add_point_func_t) _cairo_stroker_spline_to;
1321
1322     if (! _cairo_spline_init (&spline,
1323                               spline_to,
1324                               stroker,
1325                               &stroker->current_point, b, c, d))
1326     {
1327         cairo_slope_t fallback_slope;
1328         _cairo_slope_init (&fallback_slope, &stroker->current_point, d);
1329         return line_to (closure, d, &fallback_slope);
1330     }
1331
1332     /* If the line width is so small that the pen is reduced to a
1333        single point, then we have nothing to do. */
1334     if (stroker->pen.num_vertices <= 1)
1335         return CAIRO_STATUS_SUCCESS;
1336
1337     /* Compute the initial face */
1338     if (! stroker->dash.dashed || stroker->dash.dash_on) {
1339         slope_dx = _cairo_fixed_to_double (spline.initial_slope.dx);
1340         slope_dy = _cairo_fixed_to_double (spline.initial_slope.dy);
1341         if (_compute_normalized_device_slope (&slope_dx, &slope_dy,
1342                                               stroker->ctm_inverse, NULL))
1343         {
1344             _compute_face (&stroker->current_point,
1345                            &spline.initial_slope,
1346                            slope_dx, slope_dy,
1347                            stroker, &face);
1348         }
1349         if (stroker->has_current_face) {
1350             status = _cairo_stroker_join (stroker,
1351                                           &stroker->current_face, &face);
1352             if (unlikely (status))
1353                 return status;
1354         } else if (! stroker->has_first_face) {
1355             stroker->first_face = face;
1356             stroker->has_first_face = TRUE;
1357         }
1358
1359         stroker->current_face = face;
1360         stroker->has_current_face = TRUE;
1361     }
1362
1363     /* Temporarily modify the stroker to use round joins to guarantee
1364      * smooth stroked curves. */
1365     line_join_save = stroker->style.line_join;
1366     stroker->style.line_join = CAIRO_LINE_JOIN_ROUND;
1367
1368     status = _cairo_spline_decompose (&spline, stroker->tolerance);
1369     if (unlikely (status))
1370         return status;
1371
1372     /* And join the final face */
1373     if (! stroker->dash.dashed || stroker->dash.dash_on) {
1374         slope_dx = _cairo_fixed_to_double (spline.final_slope.dx);
1375         slope_dy = _cairo_fixed_to_double (spline.final_slope.dy);
1376         if (_compute_normalized_device_slope (&slope_dx, &slope_dy,
1377                                               stroker->ctm_inverse, NULL))
1378         {
1379             _compute_face (&stroker->current_point,
1380                            &spline.final_slope,
1381                            slope_dx, slope_dy,
1382                            stroker, &face);
1383         }
1384
1385         status = _cairo_stroker_join (stroker, &stroker->current_face, &face);
1386         if (unlikely (status))
1387             return status;
1388
1389         stroker->current_face = face;
1390     }
1391
1392     stroker->style.line_join = line_join_save;
1393
1394     return CAIRO_STATUS_SUCCESS;
1395 }
1396
1397 static cairo_status_t
1398 _cairo_stroker_close_path (void *closure)
1399 {
1400     cairo_stroker_t *stroker = closure;
1401     cairo_status_t status;
1402
1403     if (stroker->dash.dashed)
1404         status = _cairo_stroker_line_to_dashed (stroker, &stroker->first_point);
1405     else
1406         status = _cairo_stroker_line_to (stroker, &stroker->first_point);
1407     if (unlikely (status))
1408         return status;
1409
1410     if (stroker->has_first_face && stroker->has_current_face) {
1411         /* Join first and final faces of sub path */
1412         status = _cairo_stroker_join (stroker,
1413                                       &stroker->current_face,
1414                                       &stroker->first_face);
1415         if (unlikely (status))
1416             return status;
1417     } else {
1418         /* Cap the start and end of the sub path as needed */
1419         status = _cairo_stroker_add_caps (stroker);
1420         if (unlikely (status))
1421             return status;
1422     }
1423
1424     stroker->has_initial_sub_path = FALSE;
1425     stroker->has_first_face = FALSE;
1426     stroker->has_current_face = FALSE;
1427
1428     return CAIRO_STATUS_SUCCESS;
1429 }
1430
1431 cairo_status_t
1432 _cairo_path_fixed_stroke_to_shaper (cairo_path_fixed_t  *path,
1433                                     const cairo_stroke_style_t  *stroke_style,
1434                                     const cairo_matrix_t        *ctm,
1435                                     const cairo_matrix_t        *ctm_inverse,
1436                                     double               tolerance,
1437                                     cairo_status_t (*add_triangle) (void *closure,
1438                                                                     const cairo_point_t triangle[3]),
1439                                     cairo_status_t (*add_triangle_fan) (void *closure,
1440                                                                         const cairo_point_t *midpt,
1441                                                                         const cairo_point_t *points,
1442                                                                         int npoints),
1443                                     cairo_status_t (*add_convex_quad) (void *closure,
1444                                                                        const cairo_point_t quad[4]),
1445                                     void *closure)
1446 {
1447     cairo_stroker_t stroker;
1448     cairo_status_t status;
1449
1450     status = _cairo_stroker_init (&stroker, path, stroke_style,
1451                                   ctm, ctm_inverse, tolerance,
1452                                   NULL, 0);
1453     if (unlikely (status))
1454         return status;
1455
1456     stroker.add_triangle = add_triangle;
1457     stroker.add_triangle_fan = add_triangle_fan;
1458     stroker.add_convex_quad = add_convex_quad;
1459     stroker.closure = closure;
1460
1461     status = _cairo_path_fixed_interpret (path,
1462                                           _cairo_stroker_move_to,
1463                                           stroker.dash.dashed ?
1464                                           _cairo_stroker_line_to_dashed :
1465                                           _cairo_stroker_line_to,
1466                                           _cairo_stroker_curve_to,
1467                                           _cairo_stroker_close_path,
1468                                           &stroker);
1469
1470     if (unlikely (status))
1471         goto BAIL;
1472
1473     /* Cap the start and end of the final sub path as needed */
1474     status = _cairo_stroker_add_caps (&stroker);
1475
1476 BAIL:
1477     _cairo_stroker_fini (&stroker);
1478
1479     return status;
1480 }
1481
1482 cairo_status_t
1483 _cairo_path_fixed_stroke_dashed_to_polygon (const cairo_path_fixed_t    *path,
1484                                             const cairo_stroke_style_t  *stroke_style,
1485                                             const cairo_matrix_t        *ctm,
1486                                             const cairo_matrix_t        *ctm_inverse,
1487                                             double               tolerance,
1488                                             cairo_polygon_t *polygon)
1489 {
1490     cairo_stroker_t stroker;
1491     cairo_status_t status;
1492
1493     status = _cairo_stroker_init (&stroker, path, stroke_style,
1494                                   ctm, ctm_inverse, tolerance,
1495                                   polygon->limits, polygon->num_limits);
1496     if (unlikely (status))
1497         return status;
1498
1499     stroker.add_external_edge = _cairo_polygon_add_external_edge,
1500     stroker.closure = polygon;
1501
1502     status = _cairo_path_fixed_interpret (path,
1503                                           _cairo_stroker_move_to,
1504                                           stroker.dash.dashed ?
1505                                           _cairo_stroker_line_to_dashed :
1506                                           _cairo_stroker_line_to,
1507                                           _cairo_stroker_curve_to,
1508                                           _cairo_stroker_close_path,
1509                                           &stroker);
1510
1511     if (unlikely (status))
1512         goto BAIL;
1513
1514     /* Cap the start and end of the final sub path as needed */
1515     status = _cairo_stroker_add_caps (&stroker);
1516
1517 BAIL:
1518     _cairo_stroker_fini (&stroker);
1519
1520     return status;
1521 }
1522
1523 cairo_int_status_t
1524 _cairo_path_fixed_stroke_polygon_to_traps (const cairo_path_fixed_t     *path,
1525                                            const cairo_stroke_style_t   *stroke_style,
1526                                            const cairo_matrix_t *ctm,
1527                                            const cairo_matrix_t *ctm_inverse,
1528                                            double                tolerance,
1529                                            cairo_traps_t        *traps)
1530 {
1531     cairo_int_status_t status;
1532     cairo_polygon_t polygon;
1533
1534     _cairo_polygon_init (&polygon, traps->limits, traps->num_limits);
1535     status = _cairo_path_fixed_stroke_to_polygon (path,
1536                                                   stroke_style,
1537                                                   ctm,
1538                                                   ctm_inverse,
1539                                                   tolerance,
1540                                                   &polygon);
1541     if (unlikely (status))
1542         goto BAIL;
1543
1544     status = _cairo_polygon_status (&polygon);
1545     if (unlikely (status))
1546         goto BAIL;
1547
1548     status = _cairo_bentley_ottmann_tessellate_polygon (traps, &polygon,
1549                                                         CAIRO_FILL_RULE_WINDING);
1550
1551 BAIL:
1552     _cairo_polygon_fini (&polygon);
1553
1554     return status;
1555 }