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cairo-path-stroke.c

/* -*- Mode: c; tab-width: 8; c-basic-offset: 4; indent-tabs-mode: t; -*- */
/* cairo - a vector graphics library with display and print output
 *
 * Copyright © 2002 University of Southern California
 *
 * This library is free software; you can redistribute it and/or
 * modify it either under the terms of the GNU Lesser General Public
 * License version 2.1 as published by the Free Software Foundation
 * (the "LGPL") or, at your option, under the terms of the Mozilla
 * Public License Version 1.1 (the "MPL"). If you do not alter this
 * notice, a recipient may use your version of this file under either
 * the MPL or the LGPL.
 *
 * You should have received a copy of the LGPL along with this library
 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
 * You should have received a copy of the MPL along with this library
 * in the file COPYING-MPL-1.1
 *
 * The contents of this file are subject to the Mozilla Public License
 * Version 1.1 (the "License"); you may not use this file except in
 * compliance with the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
 * the specific language governing rights and limitations.
 *
 * The Original Code is the cairo graphics library.
 *
 * The Initial Developer of the Original Code is University of Southern
 * California.
 *
 * Contributor(s):
 *    Carl D. Worth <cworth@cworth.org>
 *    Chris Wilson <chris@chris-wilson.co.uk>
 */

#define _BSD_SOURCE /* for hypot() */
#include "cairoint.h"

#include "cairo-boxes-private.h"
#include "cairo-error-private.h"
#include "cairo-path-fixed-private.h"
#include "cairo-slope-private.h"

00047 typedef struct _cairo_stroker_dash {
    cairo_bool_t dashed;
    unsigned int dash_index;
    cairo_bool_t dash_on;
    cairo_bool_t dash_starts_on;
    double dash_remain;

    double dash_offset;
    const double *dashes;
    unsigned int num_dashes;
} cairo_stroker_dash_t;

00059 typedef struct cairo_stroker {
    cairo_stroke_style_t style;

    const cairo_matrix_t *ctm;
    const cairo_matrix_t *ctm_inverse;
    double tolerance;
    double ctm_determinant;
    cairo_bool_t ctm_det_positive;

    void *closure;
    cairo_status_t (*add_external_edge) (void *closure,
                               const cairo_point_t *p1,
                               const cairo_point_t *p2);
    cairo_status_t (*add_triangle) (void *closure,
                            const cairo_point_t triangle[3]);
    cairo_status_t (*add_triangle_fan) (void *closure,
                              const cairo_point_t *midpt,
                              const cairo_point_t *points,
                              int npoints);
    cairo_status_t (*add_convex_quad) (void *closure,
                               const cairo_point_t quad[4]);

    cairo_pen_t     pen;

    cairo_point_t current_point;
    cairo_point_t first_point;

    cairo_bool_t has_initial_sub_path;

    cairo_bool_t has_current_face;
    cairo_stroke_face_t current_face;

    cairo_bool_t has_first_face;
    cairo_stroke_face_t first_face;

    cairo_stroker_dash_t dash;

    cairo_bool_t has_bounds;
    cairo_box_t bounds;
} cairo_stroker_t;

static void
_cairo_stroker_dash_start (cairo_stroker_dash_t *dash)
{
    double offset;
    cairo_bool_t on = TRUE;
    unsigned int i = 0;

    if (! dash->dashed)
      return;

    offset = dash->dash_offset;

    /* We stop searching for a starting point as soon as the
       offset reaches zero.  Otherwise when an initial dash
       segment shrinks to zero it will be skipped over. */
    while (offset > 0.0 && offset >= dash->dashes[i]) {
      offset -= dash->dashes[i];
      on = !on;
      if (++i == dash->num_dashes)
          i = 0;
    }

    dash->dash_index = i;
    dash->dash_on = dash->dash_starts_on = on;
    dash->dash_remain = dash->dashes[i] - offset;
}

static void
_cairo_stroker_dash_step (cairo_stroker_dash_t *dash, double step)
{
    dash->dash_remain -= step;
    if (dash->dash_remain <= 0.) {
      if (++dash->dash_index == dash->num_dashes)
          dash->dash_index = 0;

      dash->dash_on = ! dash->dash_on;
      dash->dash_remain = dash->dashes[dash->dash_index];
    }
}

static void
_cairo_stroker_dash_init (cairo_stroker_dash_t *dash,
                    const cairo_stroke_style_t *style)
{
    dash->dashed = style->dash != NULL;
    if (! dash->dashed)
      return;

    dash->dashes = style->dash;
    dash->num_dashes = style->num_dashes;
    dash->dash_offset = style->dash_offset;

    _cairo_stroker_dash_start (dash);
}

static cairo_status_t
_cairo_stroker_init (cairo_stroker_t            *stroker,
                 const cairo_stroke_style_t     *stroke_style,
                 const cairo_matrix_t     *ctm,
                 const cairo_matrix_t     *ctm_inverse,
                 double              tolerance)
{
    cairo_status_t status;

    stroker->style = *stroke_style;
    stroker->ctm = ctm;
    stroker->ctm_inverse = ctm_inverse;
    stroker->tolerance = tolerance;

    stroker->ctm_determinant = _cairo_matrix_compute_determinant (stroker->ctm);
    stroker->ctm_det_positive = stroker->ctm_determinant >= 0.0;

    status = _cairo_pen_init (&stroker->pen,
                          stroke_style->line_width / 2.0,
                        tolerance, ctm);
    if (unlikely (status))
      return status;

    stroker->has_bounds = FALSE;

    stroker->has_current_face = FALSE;
    stroker->has_first_face = FALSE;
    stroker->has_initial_sub_path = FALSE;

    _cairo_stroker_dash_init (&stroker->dash, stroke_style);

    stroker->add_external_edge = NULL;

    return CAIRO_STATUS_SUCCESS;
}

static void
_cairo_stroker_limit (cairo_stroker_t *stroker,
                  const cairo_box_t *boxes,
                  int num_boxes)
{
    double dx, dy;
    cairo_fixed_t fdx, fdy;

    stroker->has_bounds = TRUE;
    _cairo_boxes_get_extents (boxes, num_boxes, &stroker->bounds);

    /* Extend the bounds in each direction to account for the maximum area
     * we might generate trapezoids, to capture line segments that are outside
     * of the bounds but which might generate rendering that's within bounds.
     */

    _cairo_stroke_style_max_distance_from_path (&stroker->style, stroker->ctm,
                                    &dx, &dy);

    fdx = _cairo_fixed_from_double (dx);
    fdy = _cairo_fixed_from_double (dy);

    stroker->bounds.p1.x -= fdx;
    stroker->bounds.p2.x += fdx;

    stroker->bounds.p1.y -= fdy;
    stroker->bounds.p2.y += fdy;
}

static void
_cairo_stroker_fini (cairo_stroker_t *stroker)
{
    _cairo_pen_fini (&stroker->pen);
}

static void
_translate_point (cairo_point_t *point, const cairo_point_t *offset)
{
    point->x += offset->x;
    point->y += offset->y;
}

static int
_cairo_stroker_join_is_clockwise (const cairo_stroke_face_t *in,
                          const cairo_stroke_face_t *out)
{
    cairo_slope_t in_slope, out_slope;

    _cairo_slope_init (&in_slope, &in->point, &in->cw);
    _cairo_slope_init (&out_slope, &out->point, &out->cw);

    return _cairo_slope_compare (&in_slope, &out_slope) < 0;
}

/**
 * _cairo_slope_compare_sgn
 *
 * Return -1, 0 or 1 depending on the relative slopes of
 * two lines.
 */
static int
_cairo_slope_compare_sgn (double dx1, double dy1, double dx2, double dy2)
{
    double  c = (dx1 * dy2 - dx2 * dy1);

    if (c > 0) return 1;
    if (c < 0) return -1;
    return 0;
}

static inline int
_range_step (int i, int step, int max)
{
    i += step;
    if (i < 0)
      i = max - 1;
    if (i >= max)
      i = 0;
    return i;
}

/*
 * Construct a fan around the midpoint using the vertices from pen between
 * inpt and outpt.
 */
static cairo_status_t
_tessellate_fan (cairo_stroker_t *stroker,
             const cairo_slope_t *in_vector,
             const cairo_slope_t *out_vector,
             const cairo_point_t *midpt,
             const cairo_point_t *inpt,
             const cairo_point_t *outpt,
             cairo_bool_t clockwise)
{
    cairo_point_t stack_points[64], *points = stack_points;
    int start, stop, step, i, npoints;
    cairo_status_t status;

    if (clockwise) {
      step  = -1;

      start = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
                                           in_vector);
      if (_cairo_slope_compare (&stroker->pen.vertices[start].slope_ccw,
                          in_vector) < 0)
          start = _range_step (start, -1, stroker->pen.num_vertices);

      stop  = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
                                           out_vector);
      if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_cw,
                          out_vector) > 0)
      {
          stop = _range_step (stop, 1, stroker->pen.num_vertices);
          if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_ccw,
                              in_vector) < 0)
          {
            goto BEVEL;
          }
      }

      npoints = start - stop;
    } else {
      step  = 1;

      start = _cairo_pen_find_active_cw_vertex_index (&stroker->pen,
                                          in_vector);
      if (_cairo_slope_compare (&stroker->pen.vertices[start].slope_cw,
                          in_vector) < 0)
          start = _range_step (start, 1, stroker->pen.num_vertices);

      stop  = _cairo_pen_find_active_cw_vertex_index (&stroker->pen,
                                          out_vector);
      if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_ccw,
                          out_vector) > 0)
      {
          stop = _range_step (stop, -1, stroker->pen.num_vertices);
          if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_cw,
                              in_vector) < 0)
          {
            goto BEVEL;
          }
      }

      npoints = stop - start;
    }
    stop = _range_step (stop, step, stroker->pen.num_vertices);

    if (npoints < 0)
      npoints += stroker->pen.num_vertices;
    npoints += 3;

    if (npoints <= 1)
      goto BEVEL;

    if (npoints > ARRAY_LENGTH (stack_points)) {
      points = _cairo_malloc_ab (npoints, sizeof (cairo_point_t));
      if (unlikely (points == NULL))
          return _cairo_error (CAIRO_STATUS_NO_MEMORY);
    }


    /* Construct the fan. */
    npoints = 0;
    points[npoints++] = *inpt;
    for (i = start;
       i != stop;
      i = _range_step (i, step, stroker->pen.num_vertices))
    {
      points[npoints] = *midpt;
      _translate_point (&points[npoints], &stroker->pen.vertices[i].point);
      npoints++;
    }
    points[npoints++] = *outpt;

    if (stroker->add_external_edge != NULL) {
      for (i = 0; i < npoints - 1; i++) {
          if (clockwise) {
            status = stroker->add_external_edge (stroker->closure,
                                         &points[i], &points[i+1]);
          } else {
            status = stroker->add_external_edge (stroker->closure,
                                         &points[i+1], &points[i]);
          }
          if (unlikely (status))
            break;
      }
    } else {
      status = stroker->add_triangle_fan (stroker->closure,
                                  midpt, points, npoints);
    }

    if (points != stack_points)
      free (points);

    return status;

BEVEL:
    /* Ensure a leak free connection... */
    if (stroker->add_external_edge != NULL) {
      if (clockwise)
          return stroker->add_external_edge (stroker->closure, inpt, outpt);
      else
          return stroker->add_external_edge (stroker->closure, outpt, inpt);
    } else {
      stack_points[0] = *midpt;
      stack_points[1] = *inpt;
      stack_points[2] = *outpt;
      return stroker->add_triangle (stroker->closure, stack_points);
    }
}

static cairo_status_t
_cairo_stroker_join (cairo_stroker_t *stroker,
                 const cairo_stroke_face_t *in,
                 const cairo_stroke_face_t *out)
{
    int      clockwise = _cairo_stroker_join_is_clockwise (out, in);
    const cairo_point_t *inpt, *outpt;
    cairo_point_t points[4];
    cairo_status_t status;

    if (in->cw.x  == out->cw.x  && in->cw.y  == out->cw.y &&
      in->ccw.x == out->ccw.x && in->ccw.y == out->ccw.y)
    {
      return CAIRO_STATUS_SUCCESS;
    }

    if (clockwise) {
      if (stroker->add_external_edge != NULL) {
          status = stroker->add_external_edge (stroker->closure,
                                     &out->cw, &in->point);
          if (unlikely (status))
            return status;

          status = stroker->add_external_edge (stroker->closure,
                                     &in->point, &in->cw);
          if (unlikely (status))
            return status;
      }

      inpt = &in->ccw;
      outpt = &out->ccw;
    } else {
      if (stroker->add_external_edge != NULL) {
          status = stroker->add_external_edge (stroker->closure,
                                     &in->ccw, &in->point);
          if (unlikely (status))
            return status;

          status = stroker->add_external_edge (stroker->closure,
                                     &in->point, &out->ccw);
          if (unlikely (status))
            return status;
      }

      inpt = &in->cw;
      outpt = &out->cw;
    }

    switch (stroker->style.line_join) {
    case CAIRO_LINE_JOIN_ROUND:
      /* construct a fan around the common midpoint */
      return _tessellate_fan (stroker,
                        &in->dev_vector,
                        &out->dev_vector,
                        &in->point, inpt, outpt,
                        clockwise);

    case CAIRO_LINE_JOIN_MITER:
    default: {
      /* dot product of incoming slope vector with outgoing slope vector */
      double      in_dot_out = -in->usr_vector.x * out->usr_vector.x +
                       -in->usr_vector.y * out->usr_vector.y;
      double      ml = stroker->style.miter_limit;

      /* Check the miter limit -- lines meeting at an acute angle
       * can generate long miters, the limit converts them to bevel
       *
       * Consider the miter join formed when two line segments
       * meet at an angle psi:
       *
       *       /.\
       *      /. .\
       *     /./ \.\
       *    /./psi\.\
       *
       * We can zoom in on the right half of that to see:
       *
       *        |\
       *        | \ psi/2
       *        |  \
       *        |   \
       *        |    \
       *        |     \
       *      miter    \
       *     length     \
       *        |        \
       *        |        .\
       *        |    .     \
       *        |.   line   \
       *         \    width  \
       *          \           \
       *
       *
       * The right triangle in that figure, (the line-width side is
       * shown faintly with three '.' characters), gives us the
       * following expression relating miter length, angle and line
       * width:
       *
       *    1 /sin (psi/2) = miter_length / line_width
       *
       * The right-hand side of this relationship is the same ratio
       * in which the miter limit (ml) is expressed. We want to know
       * when the miter length is within the miter limit. That is
       * when the following condition holds:
       *
       *    1/sin(psi/2) <= ml
       *    1 <= ml sin(psi/2)
       *    1 <= ml² sin²(psi/2)
       *    2 <= ml² 2 sin²(psi/2)
       *                      2·sin²(psi/2) = 1-cos(psi)
       *    2 <= ml² (1-cos(psi))
       *
       *                      in · out = |in| |out| cos (psi)
       *
       * in and out are both unit vectors, so:
       *
       *                      in · out = cos (psi)
       *
       *    2 <= ml² (1 - in · out)
       *
       */
      if (2 <= ml * ml * (1 - in_dot_out)) {
          double        x1, y1, x2, y2;
          double        mx, my;
          double        dx1, dx2, dy1, dy2;
          double        ix, iy;
          double        fdx1, fdy1, fdx2, fdy2;
          double        mdx, mdy;

          /*
           * we've got the points already transformed to device
           * space, but need to do some computation with them and
           * also need to transform the slope from user space to
           * device space
           */
          /* outer point of incoming line face */
          x1 = _cairo_fixed_to_double (inpt->x);
          y1 = _cairo_fixed_to_double (inpt->y);
          dx1 = in->usr_vector.x;
          dy1 = in->usr_vector.y;
          cairo_matrix_transform_distance (stroker->ctm, &dx1, &dy1);

          /* outer point of outgoing line face */
          x2 = _cairo_fixed_to_double (outpt->x);
          y2 = _cairo_fixed_to_double (outpt->y);
          dx2 = out->usr_vector.x;
          dy2 = out->usr_vector.y;
          cairo_matrix_transform_distance (stroker->ctm, &dx2, &dy2);

          /*
           * Compute the location of the outer corner of the miter.
           * That's pretty easy -- just the intersection of the two
           * outer edges.  We've got slopes and points on each
           * of those edges.  Compute my directly, then compute
           * mx by using the edge with the larger dy; that avoids
           * dividing by values close to zero.
           */
          my = (((x2 - x1) * dy1 * dy2 - y2 * dx2 * dy1 + y1 * dx1 * dy2) /
              (dx1 * dy2 - dx2 * dy1));
          if (fabs (dy1) >= fabs (dy2))
            mx = (my - y1) * dx1 / dy1 + x1;
          else
            mx = (my - y2) * dx2 / dy2 + x2;

          /*
           * When the two outer edges are nearly parallel, slight
           * perturbations in the position of the outer points of the lines
           * caused by representing them in fixed point form can cause the
           * intersection point of the miter to move a large amount. If
           * that moves the miter intersection from between the two faces,
           * then draw a bevel instead.
           */

          ix = _cairo_fixed_to_double (in->point.x);
          iy = _cairo_fixed_to_double (in->point.y);

          /* slope of one face */
          fdx1 = x1 - ix; fdy1 = y1 - iy;

          /* slope of the other face */
          fdx2 = x2 - ix; fdy2 = y2 - iy;

          /* slope from the intersection to the miter point */
          mdx = mx - ix; mdy = my - iy;

          /*
           * Make sure the miter point line lies between the two
           * faces by comparing the slopes
           */
          if (_cairo_slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
            _cairo_slope_compare_sgn (fdx2, fdy2, mdx, mdy))
          {
            if (stroker->add_external_edge != NULL) {
                points[0].x = _cairo_fixed_from_double (mx);
                points[0].y = _cairo_fixed_from_double (my);

                if (clockwise) {
                  status = stroker->add_external_edge (stroker->closure,
                                               inpt, &points[0]);
                  if (unlikely (status))
                      return status;

                  status = stroker->add_external_edge (stroker->closure,
                                               &points[0], outpt);
                  if (unlikely (status))
                      return status;
                } else {
                  status = stroker->add_external_edge (stroker->closure,
                                               outpt, &points[0]);
                  if (unlikely (status))
                      return status;

                  status = stroker->add_external_edge (stroker->closure,
                                               &points[0], inpt);
                  if (unlikely (status))
                      return status;
                }

                return CAIRO_STATUS_SUCCESS;
            } else {
                points[0] = in->point;
                points[1] = *inpt;
                points[2].x = _cairo_fixed_from_double (mx);
                points[2].y = _cairo_fixed_from_double (my);
                points[3] = *outpt;

                return stroker->add_convex_quad (stroker->closure, points);
            }
          }
      }
    }

    /* fall through ... */

    case CAIRO_LINE_JOIN_BEVEL:
      if (stroker->add_external_edge != NULL) {
          if (clockwise) {
            return stroker->add_external_edge (stroker->closure,
                                       inpt, outpt);
          } else {
            return stroker->add_external_edge (stroker->closure,
                                       outpt, inpt);
          }
      } else {
          points[0] = in->point;
          points[1] = *inpt;
          points[2] = *outpt;

          return stroker->add_triangle (stroker->closure, points);
      }
    }
}

static cairo_status_t
_cairo_stroker_add_cap (cairo_stroker_t *stroker,
                  const cairo_stroke_face_t *f)
{
    switch (stroker->style.line_cap) {
    case CAIRO_LINE_CAP_ROUND: {
      cairo_slope_t slope;

      slope.dx = -f->dev_vector.dx;
      slope.dy = -f->dev_vector.dy;

      return _tessellate_fan (stroker,
                        &f->dev_vector,
                        &slope,
                        &f->point, &f->cw, &f->ccw,
                        FALSE);

    }

    case CAIRO_LINE_CAP_SQUARE: {
      double dx, dy;
      cairo_slope_t     fvector;
      cairo_point_t     quad[4];

      dx = f->usr_vector.x;
      dy = f->usr_vector.y;
      dx *= stroker->style.line_width / 2.0;
      dy *= stroker->style.line_width / 2.0;
      cairo_matrix_transform_distance (stroker->ctm, &dx, &dy);
      fvector.dx = _cairo_fixed_from_double (dx);
      fvector.dy = _cairo_fixed_from_double (dy);

      quad[0] = f->ccw;
      quad[1].x = f->ccw.x + fvector.dx;
      quad[1].y = f->ccw.y + fvector.dy;
      quad[2].x = f->cw.x + fvector.dx;
      quad[2].y = f->cw.y + fvector.dy;
      quad[3] = f->cw;

      if (stroker->add_external_edge != NULL) {
          cairo_status_t status;

          status = stroker->add_external_edge (stroker->closure,
                                     &quad[0], &quad[1]);
          if (unlikely (status))
            return status;

          status = stroker->add_external_edge (stroker->closure,
                                     &quad[1], &quad[2]);
          if (unlikely (status))
            return status;

          status = stroker->add_external_edge (stroker->closure,
                                     &quad[2], &quad[3]);
          if (unlikely (status))
            return status;

          return CAIRO_STATUS_SUCCESS;
      } else {
          return stroker->add_convex_quad (stroker->closure, quad);
      }
    }

    case CAIRO_LINE_CAP_BUTT:
    default:
      if (stroker->add_external_edge != NULL) {
          return stroker->add_external_edge (stroker->closure,
                                     &f->ccw, &f->cw);
      } else {
          return CAIRO_STATUS_SUCCESS;
      }
    }
}

static cairo_status_t
_cairo_stroker_add_leading_cap (cairo_stroker_t     *stroker,
                        const cairo_stroke_face_t *face)
{
    cairo_stroke_face_t reversed;
    cairo_point_t t;

    reversed = *face;

    /* The initial cap needs an outward facing vector. Reverse everything */
    reversed.usr_vector.x = -reversed.usr_vector.x;
    reversed.usr_vector.y = -reversed.usr_vector.y;
    reversed.dev_vector.dx = -reversed.dev_vector.dx;
    reversed.dev_vector.dy = -reversed.dev_vector.dy;
    t = reversed.cw;
    reversed.cw = reversed.ccw;
    reversed.ccw = t;

    return _cairo_stroker_add_cap (stroker, &reversed);
}

static cairo_status_t
_cairo_stroker_add_trailing_cap (cairo_stroker_t     *stroker,
                         const cairo_stroke_face_t *face)
{
    return _cairo_stroker_add_cap (stroker, face);
}

static inline cairo_bool_t
_compute_normalized_device_slope (double *dx, double *dy,
                          const cairo_matrix_t *ctm_inverse,
                          double *mag_out)
{
    double dx0 = *dx, dy0 = *dy;
    double mag;

    cairo_matrix_transform_distance (ctm_inverse, &dx0, &dy0);

    if (dx0 == 0.0 && dy0 == 0.0) {
      if (mag_out)
          *mag_out = 0.0;
      return FALSE;
    }

    if (dx0 == 0.0) {
      *dx = 0.0;
      if (dy0 > 0.0) {
          mag = dy0;
          *dy = 1.0;
      } else {
          mag = -dy0;
          *dy = -1.0;
      }
    } else if (dy0 == 0.0) {
      *dy = 0.0;
      if (dx0 > 0.0) {
          mag = dx0;
          *dx = 1.0;
      } else {
          mag = -dx0;
          *dx = -1.0;
      }
    } else {
      mag = hypot (dx0, dy0);
      *dx = dx0 / mag;
      *dy = dy0 / mag;
    }

    if (mag_out)
      *mag_out = mag;

    return TRUE;
}

static void
_compute_face (const cairo_point_t *point, cairo_slope_t *dev_slope,
             double slope_dx, double slope_dy,
             cairo_stroker_t *stroker, cairo_stroke_face_t *face)
{
    double face_dx, face_dy;
    cairo_point_t offset_ccw, offset_cw;

    /*
     * rotate to get a line_width/2 vector along the face, note that
     * the vector must be rotated the right direction in device space,
     * but by 90° in user space. So, the rotation depends on
     * whether the ctm reflects or not, and that can be determined
     * by looking at the determinant of the matrix.
     */
    if (stroker->ctm_det_positive)
    {
      face_dx = - slope_dy * (stroker->style.line_width / 2.0);
      face_dy = slope_dx * (stroker->style.line_width / 2.0);
    }
    else
    {
      face_dx = slope_dy * (stroker->style.line_width / 2.0);
      face_dy = - slope_dx * (stroker->style.line_width / 2.0);
    }

    /* back to device space */
    cairo_matrix_transform_distance (stroker->ctm, &face_dx, &face_dy);

    offset_ccw.x = _cairo_fixed_from_double (face_dx);
    offset_ccw.y = _cairo_fixed_from_double (face_dy);
    offset_cw.x = -offset_ccw.x;
    offset_cw.y = -offset_ccw.y;

    face->ccw = *point;
    _translate_point (&face->ccw, &offset_ccw);

    face->point = *point;

    face->cw = *point;
    _translate_point (&face->cw, &offset_cw);

    face->usr_vector.x = slope_dx;
    face->usr_vector.y = slope_dy;

    face->dev_vector = *dev_slope;
}

static cairo_status_t
_cairo_stroker_add_caps (cairo_stroker_t *stroker)
{
    cairo_status_t status;

    /* check for a degenerative sub_path */
    if (stroker->has_initial_sub_path
      && ! stroker->has_first_face
      && ! stroker->has_current_face
      && stroker->style.line_cap == CAIRO_LINE_JOIN_ROUND)
    {
      /* pick an arbitrary slope to use */
      double dx = 1.0, dy = 0.0;
      cairo_slope_t slope = { CAIRO_FIXED_ONE, 0 };
      cairo_stroke_face_t face;

      _compute_normalized_device_slope (&dx, &dy,
                                stroker->ctm_inverse, NULL);

      /* arbitrarily choose first_point
       * first_point and current_point should be the same */
      _compute_face (&stroker->first_point, &slope, dx, dy, stroker, &face);

      status = _cairo_stroker_add_leading_cap (stroker, &face);
      if (unlikely (status))
          return status;

      status = _cairo_stroker_add_trailing_cap (stroker, &face);
      if (unlikely (status))
          return status;
    }

    if (stroker->has_first_face) {
      status = _cairo_stroker_add_leading_cap (stroker,
                                     &stroker->first_face);
      if (unlikely (status))
          return status;
    }

    if (stroker->has_current_face) {
      status = _cairo_stroker_add_trailing_cap (stroker,
                                      &stroker->current_face);
      if (unlikely (status))
          return status;
    }

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_stroker_add_sub_edge (cairo_stroker_t *stroker,
                       const cairo_point_t *p1,
                       const cairo_point_t *p2,
                       cairo_slope_t *dev_slope,
                       double slope_dx, double slope_dy,
                       cairo_stroke_face_t *start,
                       cairo_stroke_face_t *end)
{
    _compute_face (p1, dev_slope, slope_dx, slope_dy, stroker, start);
    *end = *start;

    if (p1->x == p2->x && p1->y == p2->y)
      return CAIRO_STATUS_SUCCESS;

    end->point = *p2;
    end->ccw.x += p2->x - p1->x;
    end->ccw.y += p2->y - p1->y;
    end->cw.x += p2->x - p1->x;
    end->cw.y += p2->y - p1->y;

    if (stroker->add_external_edge != NULL) {
      cairo_status_t status;

      status = stroker->add_external_edge (stroker->closure,
                                   &end->cw, &start->cw);
      if (unlikely (status))
          return status;

      status = stroker->add_external_edge (stroker->closure,
                                   &start->ccw, &end->ccw);
      if (unlikely (status))
          return status;

      return CAIRO_STATUS_SUCCESS;
    } else {
      cairo_point_t quad[4];

      quad[0] = start->cw;
      quad[1] = end->cw;
      quad[2] = end->ccw;
      quad[3] = start->ccw;

      return stroker->add_convex_quad (stroker->closure, quad);
    }
}

static cairo_status_t
_cairo_stroker_move_to (void *closure,
                  const cairo_point_t *point)
{
    cairo_stroker_t *stroker = closure;
    cairo_status_t status;

    /* reset the dash pattern for new sub paths */
    _cairo_stroker_dash_start (&stroker->dash);

    /* Cap the start and end of the previous sub path as needed */
    status = _cairo_stroker_add_caps (stroker);
    if (unlikely (status))
      return status;

    stroker->first_point = *point;
    stroker->current_point = *point;

    stroker->has_first_face = FALSE;
    stroker->has_current_face = FALSE;
    stroker->has_initial_sub_path = FALSE;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_stroker_line_to (void *closure,
                  const cairo_point_t *point)
{
    cairo_stroker_t *stroker = closure;
    cairo_stroke_face_t start, end;
    cairo_point_t *p1 = &stroker->current_point;
    cairo_slope_t dev_slope;
    double slope_dx, slope_dy;
    cairo_status_t status;

    stroker->has_initial_sub_path = TRUE;

    if (p1->x == point->x && p1->y == point->y)
      return CAIRO_STATUS_SUCCESS;

    _cairo_slope_init (&dev_slope, p1, point);
    slope_dx = _cairo_fixed_to_double (point->x - p1->x);
    slope_dy = _cairo_fixed_to_double (point->y - p1->y);
    _compute_normalized_device_slope (&slope_dx, &slope_dy,
                              stroker->ctm_inverse, NULL);

    status = _cairo_stroker_add_sub_edge (stroker,
                                p1, point,
                                &dev_slope,
                                slope_dx, slope_dy,
                                &start, &end);
    if (unlikely (status))
      return status;

    if (stroker->has_current_face) {
      /* Join with final face from previous segment */
      status = _cairo_stroker_join (stroker,
                              &stroker->current_face,
                              &start);
      if (unlikely (status))
          return status;
    } else if (! stroker->has_first_face) {
      /* Save sub path's first face in case needed for closing join */
      stroker->first_face = start;
      stroker->has_first_face = TRUE;
    }
    stroker->current_face = end;
    stroker->has_current_face = TRUE;

    stroker->current_point = *point;

    return CAIRO_STATUS_SUCCESS;
}

/*
 * Dashed lines.  Cap each dash end, join around turns when on
 */
static cairo_status_t
_cairo_stroker_line_to_dashed (void *closure,
                         const cairo_point_t *p2)
{
    cairo_stroker_t *stroker = closure;
    double mag, remain, step_length = 0;
    double slope_dx, slope_dy;
    double dx2, dy2;
    cairo_stroke_face_t sub_start, sub_end;
    cairo_point_t *p1 = &stroker->current_point;
    cairo_slope_t dev_slope;
    cairo_line_t segment;
    cairo_bool_t fully_in_bounds;
    cairo_status_t status;

    stroker->has_initial_sub_path = stroker->dash.dash_starts_on;

    if (p1->x == p2->x && p1->y == p2->y)
      return CAIRO_STATUS_SUCCESS;

    fully_in_bounds = TRUE;
    if (stroker->has_bounds &&
      (! _cairo_box_contains_point (&stroker->bounds, p1) ||
       ! _cairo_box_contains_point (&stroker->bounds, p2)))
    {
      fully_in_bounds = FALSE;
    }

    _cairo_slope_init (&dev_slope, p1, p2);

    slope_dx = _cairo_fixed_to_double (p2->x - p1->x);
    slope_dy = _cairo_fixed_to_double (p2->y - p1->y);

    if (! _compute_normalized_device_slope (&slope_dx, &slope_dy,
                                  stroker->ctm_inverse, &mag))
    {
      return CAIRO_STATUS_SUCCESS;
    }

    remain = mag;
    segment.p1 = *p1;
    while (remain) {
      step_length = MIN (stroker->dash.dash_remain, remain);
      remain -= step_length;
      dx2 = slope_dx * (mag - remain);
      dy2 = slope_dy * (mag - remain);
      cairo_matrix_transform_distance (stroker->ctm, &dx2, &dy2);
      segment.p2.x = _cairo_fixed_from_double (dx2) + p1->x;
      segment.p2.y = _cairo_fixed_from_double (dy2) + p1->y;

      if (stroker->dash.dash_on &&
          (fully_in_bounds ||
           (! stroker->has_first_face && stroker->dash.dash_starts_on) ||
           _cairo_box_intersects_line_segment (&stroker->bounds, &segment)))
      {
          status = _cairo_stroker_add_sub_edge (stroker,
                                      &segment.p1, &segment.p2,
                                      &dev_slope,
                                      slope_dx, slope_dy,
                                      &sub_start, &sub_end);
          if (unlikely (status))
            return status;

          if (stroker->has_current_face)
          {
            /* Join with final face from previous segment */
            status = _cairo_stroker_join (stroker,
                                    &stroker->current_face,
                                    &sub_start);
            if (unlikely (status))
                return status;

            stroker->has_current_face = FALSE;
          }
          else if (! stroker->has_first_face &&
                   stroker->dash.dash_starts_on)
          {
            /* Save sub path's first face in case needed for closing join */
            stroker->first_face = sub_start;
            stroker->has_first_face = TRUE;
          }
          else
          {
            /* Cap dash start if not connecting to a previous segment */
            status = _cairo_stroker_add_leading_cap (stroker, &sub_start);
            if (unlikely (status))
                return status;
          }

          if (remain) {
            /* Cap dash end if not at end of segment */
            status = _cairo_stroker_add_trailing_cap (stroker, &sub_end);
            if (unlikely (status))
                return status;
          } else {
            stroker->current_face = sub_end;
            stroker->has_current_face = TRUE;
          }
      } else {
          if (stroker->has_current_face) {
            /* Cap final face from previous segment */
            status = _cairo_stroker_add_trailing_cap (stroker,
                                            &stroker->current_face);
            if (unlikely (status))
                return status;

            stroker->has_current_face = FALSE;
          }
      }

      _cairo_stroker_dash_step (&stroker->dash, step_length);
      segment.p1 = segment.p2;
    }

    if (stroker->dash.dash_on && ! stroker->has_current_face) {
      /* This segment ends on a transition to dash_on, compute a new face
       * and add cap for the beginning of the next dash_on step.
       *
       * Note: this will create a degenerate cap if this is not the last line
       * in the path. Whether this behaviour is desirable or not is debatable.
       * On one side these degenerate caps can not be reproduced with regular
       * path stroking.
       * On the other hand, Acroread 7 also produces the degenerate caps.
       */
      _compute_face (p2, &dev_slope,
                   slope_dx, slope_dy,
                   stroker,
                   &stroker->current_face);

      status = _cairo_stroker_add_leading_cap (stroker,
                                     &stroker->current_face);
      if (unlikely (status))
          return status;

      stroker->has_current_face = TRUE;
    }

    stroker->current_point = *p2;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_stroker_curve_to (void *closure,
                   const cairo_point_t *b,
                   const cairo_point_t *c,
                   const cairo_point_t *d)
{
    cairo_stroker_t *stroker = closure;
    cairo_spline_t spline;
    cairo_line_join_t line_join_save;
    cairo_stroke_face_t face;
    double slope_dx, slope_dy;
    cairo_path_fixed_line_to_func_t *line_to;
    cairo_status_t status = CAIRO_STATUS_SUCCESS;

    line_to = stroker->dash.dashed ?
      _cairo_stroker_line_to_dashed :
      _cairo_stroker_line_to;

    if (! _cairo_spline_init (&spline,
                        line_to, stroker,
                        &stroker->current_point, b, c, d))
    {
      return line_to (closure, d);
    }

    /* If the line width is so small that the pen is reduced to a
       single point, then we have nothing to do. */
    if (stroker->pen.num_vertices <= 1)
      return CAIRO_STATUS_SUCCESS;

    /* Compute the initial face */
    if (! stroker->dash.dashed || stroker->dash.dash_on) {
      slope_dx = _cairo_fixed_to_double (spline.initial_slope.dx);
      slope_dy = _cairo_fixed_to_double (spline.initial_slope.dy);
      if (_compute_normalized_device_slope (&slope_dx, &slope_dy,
                                    stroker->ctm_inverse, NULL))
      {
          _compute_face (&stroker->current_point,
                     &spline.initial_slope,
                     slope_dx, slope_dy,
                     stroker, &face);
      }
      if (stroker->has_current_face) {
          status = _cairo_stroker_join (stroker,
                                &stroker->current_face, &face);
          if (unlikely (status))
            return status;
      } else if (! stroker->has_first_face) {
          stroker->first_face = face;
          stroker->has_first_face = TRUE;
      }

      stroker->current_face = face;
      stroker->has_current_face = TRUE;
    }

    /* Temporarily modify the stroker to use round joins to guarantee
     * smooth stroked curves. */
    line_join_save = stroker->style.line_join;
    stroker->style.line_join = CAIRO_LINE_JOIN_ROUND;

    status = _cairo_spline_decompose (&spline, stroker->tolerance);
    if (unlikely (status))
      return status;

    /* And join the final face */
    if (! stroker->dash.dashed || stroker->dash.dash_on) {
      slope_dx = _cairo_fixed_to_double (spline.final_slope.dx);
      slope_dy = _cairo_fixed_to_double (spline.final_slope.dy);
      if (_compute_normalized_device_slope (&slope_dx, &slope_dy,
                                    stroker->ctm_inverse, NULL))
      {
          _compute_face (&stroker->current_point,
                     &spline.final_slope,
                     slope_dx, slope_dy,
                     stroker, &face);
      }

      status = _cairo_stroker_join (stroker, &stroker->current_face, &face);
      if (unlikely (status))
          return status;

      stroker->current_face = face;
    }

    stroker->style.line_join = line_join_save;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_stroker_close_path (void *closure)
{
    cairo_stroker_t *stroker = closure;
    cairo_status_t status;

    if (stroker->dash.dashed)
      status = _cairo_stroker_line_to_dashed (stroker, &stroker->first_point);
    else
      status = _cairo_stroker_line_to (stroker, &stroker->first_point);
    if (unlikely (status))
      return status;

    if (stroker->has_first_face && stroker->has_current_face) {
      /* Join first and final faces of sub path */
      status = _cairo_stroker_join (stroker,
                              &stroker->current_face,
                              &stroker->first_face);
      if (unlikely (status))
          return status;
    } else {
      /* Cap the start and end of the sub path as needed */
      status = _cairo_stroker_add_caps (stroker);
      if (unlikely (status))
          return status;
    }

    stroker->has_initial_sub_path = FALSE;
    stroker->has_first_face = FALSE;
    stroker->has_current_face = FALSE;

    return CAIRO_STATUS_SUCCESS;
}

cairo_status_t
_cairo_path_fixed_stroke_to_shaper (cairo_path_fixed_t      *path,
                            const cairo_stroke_style_t      *stroke_style,
                            const cairo_matrix_t      *ctm,
                            const cairo_matrix_t      *ctm_inverse,
                            double         tolerance,
                            cairo_status_t (*add_triangle) (void *closure,
                                                    const cairo_point_t triangle[3]),
                            cairo_status_t (*add_triangle_fan) (void *closure,
                                                      const cairo_point_t *midpt,
                                                      const cairo_point_t *points,
                                                      int npoints),
                            cairo_status_t (*add_convex_quad) (void *closure,
                                                       const cairo_point_t quad[4]),
                            void *closure)
{
    cairo_stroker_t stroker;
    cairo_status_t status;

    status = _cairo_stroker_init (&stroker, stroke_style,
                            ctm, ctm_inverse, tolerance);
    if (unlikely (status))
      return status;

    stroker.add_triangle = add_triangle;
    stroker.add_triangle_fan = add_triangle_fan;
    stroker.add_convex_quad = add_convex_quad;
    stroker.closure = closure;

    status = _cairo_path_fixed_interpret (path,
                                CAIRO_DIRECTION_FORWARD,
                                _cairo_stroker_move_to,
                                stroker.dash.dashed ?
                                _cairo_stroker_line_to_dashed :
                                _cairo_stroker_line_to,
                                _cairo_stroker_curve_to,
                                _cairo_stroker_close_path,
                                &stroker);

    if (unlikely (status))
      goto BAIL;

    /* Cap the start and end of the final sub path as needed */
    status = _cairo_stroker_add_caps (&stroker);

BAIL:
    _cairo_stroker_fini (&stroker);

    return status;
}

cairo_status_t
_cairo_path_fixed_stroke_to_polygon (const cairo_path_fixed_t     *path,
                             const cairo_stroke_style_t     *stroke_style,
                             const cairo_matrix_t     *ctm,
                             const cairo_matrix_t     *ctm_inverse,
                             double        tolerance,
                             cairo_polygon_t *polygon)
{
    cairo_stroker_t stroker;
    cairo_status_t status;

    status = _cairo_stroker_init (&stroker, stroke_style,
                            ctm, ctm_inverse, tolerance);
    if (unlikely (status))
      return status;

    stroker.add_external_edge = _cairo_polygon_add_external_edge,
    stroker.closure = polygon;

    if (polygon->num_limits)
      _cairo_stroker_limit (&stroker, polygon->limits, polygon->num_limits);

    status = _cairo_path_fixed_interpret (path,
                                CAIRO_DIRECTION_FORWARD,
                                _cairo_stroker_move_to,
                                stroker.dash.dashed ?
                                _cairo_stroker_line_to_dashed :
                                _cairo_stroker_line_to,
                                _cairo_stroker_curve_to,
                                _cairo_stroker_close_path,
                                &stroker);

    if (unlikely (status))
      goto BAIL;

    /* Cap the start and end of the final sub path as needed */
    status = _cairo_stroker_add_caps (&stroker);

BAIL:
    _cairo_stroker_fini (&stroker);

    return status;
}

cairo_status_t
_cairo_path_fixed_stroke_to_traps (const cairo_path_fixed_t *path,
                           const cairo_stroke_style_t *stroke_style,
                           const cairo_matrix_t *ctm,
                           const cairo_matrix_t *ctm_inverse,
                           double          tolerance,
                           cairo_traps_t  *traps)
{
    cairo_status_t status;
    cairo_polygon_t polygon;

    /* Before we do anything else, we attempt the rectilinear
     * stroker. It's careful to generate trapezoids that align to
     * device-pixel boundaries when possible. Many backends can render
     * those much faster than non-aligned trapezoids, (by using clip
     * regions, etc.) */
    if (path->is_rectilinear) {
      status = _cairo_path_fixed_stroke_rectilinear_to_traps (path,
                                                stroke_style,
                                                ctm,
                                                traps);
      if (status != CAIRO_INT_STATUS_UNSUPPORTED)
          return status;
    }

    _cairo_polygon_init (&polygon);
    if (traps->num_limits)
      _cairo_polygon_limit (&polygon, traps->limits, traps->num_limits);

    status = _cairo_path_fixed_stroke_to_polygon (path,
                                      stroke_style,
                                      ctm,
                                      ctm_inverse,
                                      tolerance,
                                      &polygon);
    if (unlikely (status))
      goto BAIL;

    status = _cairo_polygon_status (&polygon);
    if (unlikely (status))
      goto BAIL;

    status = _cairo_bentley_ottmann_tessellate_polygon (traps, &polygon,
                                          CAIRO_FILL_RULE_WINDING);

BAIL:
    _cairo_polygon_fini (&polygon);

    return status;
}

01437 typedef struct _segment_t {
    cairo_point_t p1, p2;
    cairo_bool_t is_horizontal;
    cairo_bool_t has_join;
} segment_t;

01443 typedef struct _cairo_rectilinear_stroker {
    const cairo_stroke_style_t *stroke_style;
    const cairo_matrix_t *ctm;

    cairo_fixed_t half_line_width;
    cairo_bool_t do_traps;
    void *container;
    cairo_point_t current_point;
    cairo_point_t first_point;
    cairo_bool_t open_sub_path;

    cairo_stroker_dash_t dash;

    cairo_bool_t has_bounds;
    cairo_box_t bounds;

    int num_segments;
    int segments_size;
    segment_t *segments;
    segment_t segments_embedded[8]; /* common case is a single rectangle */
} cairo_rectilinear_stroker_t;

static void
_cairo_rectilinear_stroker_limit (cairo_rectilinear_stroker_t *stroker,
                          const cairo_box_t *boxes,
                          int num_boxes)
{
    stroker->has_bounds = TRUE;
    _cairo_boxes_get_extents (boxes, num_boxes, &stroker->bounds);

    stroker->bounds.p1.x -= stroker->half_line_width;
    stroker->bounds.p2.x += stroker->half_line_width;

    stroker->bounds.p1.y -= stroker->half_line_width;
    stroker->bounds.p2.y += stroker->half_line_width;
}

static cairo_bool_t
_cairo_rectilinear_stroker_init (cairo_rectilinear_stroker_t      *stroker,
                         const cairo_stroke_style_t   *stroke_style,
                         const cairo_matrix_t         *ctm,
                         cairo_bool_t                  do_traps,
                         void                   *container)
{
    /* This special-case rectilinear stroker only supports
     * miter-joined lines (not curves) and a translation-only matrix
     * (though it could probably be extended to support a matrix with
     * uniform, integer scaling).
     *
     * It also only supports horizontal and vertical line_to
     * elements. But we don't catch that here, but instead return
     * UNSUPPORTED from _cairo_rectilinear_stroker_line_to if any
     * non-rectilinear line_to is encountered.
     */
    if (stroke_style->line_join     != CAIRO_LINE_JOIN_MITER)
      return FALSE;

    /* If the miter limit turns right angles into bevels, then we
     * can't use this optimization. Remember, the ratio is
     * 1/sin(ɸ/2). So the cutoff is 1/sin(π/4.0) or ⎷2,
     * which we round for safety. */
    if (stroke_style->miter_limit < M_SQRT2)
      return FALSE;

    if (! (stroke_style->line_cap == CAIRO_LINE_CAP_BUTT ||
         stroke_style->line_cap == CAIRO_LINE_CAP_SQUARE))
    {
      return FALSE;
    }

    if (! _cairo_matrix_has_unity_scale (ctm))
      return FALSE;

    stroker->stroke_style = stroke_style;
    stroker->ctm = ctm;

    stroker->half_line_width =
      _cairo_fixed_from_double (stroke_style->line_width / 2.0);
    stroker->open_sub_path = FALSE;
    stroker->segments = stroker->segments_embedded;
    stroker->segments_size = ARRAY_LENGTH (stroker->segments_embedded);
    stroker->num_segments = 0;

    _cairo_stroker_dash_init (&stroker->dash, stroke_style);

    stroker->has_bounds = FALSE;

    stroker->do_traps = do_traps;
    stroker->container = container;

    return TRUE;
}

static void
_cairo_rectilinear_stroker_fini (cairo_rectilinear_stroker_t      *stroker)
{
    if (stroker->segments != stroker->segments_embedded)
      free (stroker->segments);
}

static cairo_status_t
_cairo_rectilinear_stroker_add_segment (cairo_rectilinear_stroker_t *stroker,
                              const cairo_point_t     *p1,
                              const cairo_point_t     *p2,
                              cairo_bool_t             is_horizontal,
                              cairo_bool_t             has_join)
{
    if (CAIRO_INJECT_FAULT ())
      return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    if (stroker->num_segments == stroker->segments_size) {
      int new_size = stroker->segments_size * 2;
      segment_t *new_segments;

      if (stroker->segments == stroker->segments_embedded) {
          new_segments = _cairo_malloc_ab (new_size, sizeof (segment_t));
          if (unlikely (new_segments == NULL))
            return _cairo_error (CAIRO_STATUS_NO_MEMORY);

          memcpy (new_segments, stroker->segments,
                stroker->num_segments * sizeof (segment_t));
      } else {
          new_segments = _cairo_realloc_ab (stroker->segments,
                                    new_size, sizeof (segment_t));
          if (unlikely (new_segments == NULL))
            return _cairo_error (CAIRO_STATUS_NO_MEMORY);
      }

      stroker->segments_size = new_size;
      stroker->segments = new_segments;
    }

    stroker->segments[stroker->num_segments].p1 = *p1;
    stroker->segments[stroker->num_segments].p2 = *p2;
    stroker->segments[stroker->num_segments].has_join = has_join;
    stroker->segments[stroker->num_segments].is_horizontal = is_horizontal;
    stroker->num_segments++;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_rectilinear_stroker_emit_segments (cairo_rectilinear_stroker_t *stroker)
{
    cairo_status_t status;
    cairo_line_cap_t line_cap = stroker->stroke_style->line_cap;
    cairo_fixed_t half_line_width = stroker->half_line_width;
    int i;

    for (i = 0; i < stroker->num_segments; i++) {
      cairo_point_t *a, *b;
      cairo_bool_t lengthen_initial, shorten_final, lengthen_final;

      a = &stroker->segments[i].p1;
      b = &stroker->segments[i].p2;

      /* For each segment we generate a single rectangular
       * trapezoid. This rectangle is based on a perpendicular
       * extension (by half the line width) of the segment endpoints
       * after some adjustments of the endpoints to account for caps
       * and joins.
       */

      /* We adjust the initial point of the segment to extend the
       * rectangle to include the previous cap or join, (this
       * adjustment applies to all segments except for the first
       * segment of open, butt-capped paths).
       */
      lengthen_initial = TRUE;
      if (i == 0 && stroker->open_sub_path && line_cap == CAIRO_LINE_CAP_BUTT)
          lengthen_initial = FALSE;

      /* The adjustment of the final point is trickier. For all but
       * the last segment we shorten the segment at the final
       * endpoint to not overlap with the subsequent join. For the
       * last segment we do the same shortening if the path is
       * closed. If the path is open and butt-capped we do no
       * adjustment, while if it's open and square-capped we do a
       * lengthening adjustment instead to include the cap.
       */
      shorten_final = TRUE;
      lengthen_final = FALSE;
      if (i == stroker->num_segments - 1 && stroker->open_sub_path) {
          shorten_final = FALSE;
          if (line_cap == CAIRO_LINE_CAP_SQUARE)
            lengthen_final = TRUE;
      }

      /* Perform the adjustments of the endpoints. */
      if (a->y == b->y) {
          if (a->x < b->x) {
            if (lengthen_initial)
                a->x -= half_line_width;
            if (shorten_final)
                b->x -= half_line_width;
            else if (lengthen_final)
                b->x += half_line_width;
          } else {
            if (lengthen_initial)
                a->x += half_line_width;
            if (shorten_final)
                b->x += half_line_width;
            else if (lengthen_final)
                b->x -= half_line_width;
          }

          if (a->x > b->x) {
            cairo_point_t *t;

            t = a;
            a = b;
            b = t;
          }
      } else {
          if (a->y < b->y) {
            if (lengthen_initial)
                a->y -= half_line_width;
            if (shorten_final)
                b->y -= half_line_width;
            else if (lengthen_final)
                b->y += half_line_width;
          } else {
            if (lengthen_initial)
                a->y += half_line_width;
            if (shorten_final)
                b->y += half_line_width;
            else if (lengthen_final)
                b->y -= half_line_width;
          }

          if (a->y > b->y) {
            cairo_point_t *t;

            t = a;
            a = b;
            b = t;
          }
      }

      /* Form the rectangle by expanding by half the line width in
       * either perpendicular direction. */
      if (a->y == b->y) {
          a->y -= half_line_width;
          b->y += half_line_width;
      } else {
          a->x -= half_line_width;
          b->x += half_line_width;
      }

      if (stroker->do_traps) {
          status = _cairo_traps_tessellate_rectangle (stroker->container, a, b);
      } else {
          cairo_box_t box;

          box.p1 = *a;
          box.p2 = *b;

          status = _cairo_boxes_add (stroker->container, &box);
      }
      if (unlikely (status))
          return status;
    }

    stroker->num_segments = 0;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_rectilinear_stroker_emit_segments_dashed (cairo_rectilinear_stroker_t *stroker)
{
    cairo_status_t status;
    cairo_line_cap_t line_cap = stroker->stroke_style->line_cap;
    cairo_fixed_t half_line_width = stroker->half_line_width;
    int i;

    for (i = 0; i < stroker->num_segments; i++) {
      cairo_point_t *a, *b;
      cairo_bool_t is_horizontal;

      a = &stroker->segments[i].p1;
      b = &stroker->segments[i].p2;

      is_horizontal = stroker->segments[i].is_horizontal;

      /* Handle the joins for a potentially degenerate segment. */
      if (line_cap == CAIRO_LINE_CAP_BUTT &&
          stroker->segments[i].has_join &&
          (i != stroker->num_segments - 1 ||
           (! stroker->open_sub_path && stroker->dash.dash_starts_on)))
      {
          cairo_point_t p1 = stroker->segments[i].p1;
          cairo_point_t p2 = stroker->segments[i].p2;
          cairo_slope_t out_slope;
          int j = (i + 1) % stroker->num_segments;

          _cairo_slope_init (&out_slope,
                         &stroker->segments[j].p1,
                         &stroker->segments[j].p2);

          if (is_horizontal) {
            if (p1.x <= p2.x) {
                p1.x = p2.x;
                p2.x += half_line_width;
            } else {
                p1.x = p2.x - half_line_width;
            }
            if (out_slope.dy >= 0)
                p1.y -= half_line_width;
            if (out_slope.dy <= 0)
                p2.y += half_line_width;
          } else {
            if (p1.y <= p2.y) {
                p1.y = p2.y;
                p2.y += half_line_width;
            } else {
                p1.y = p2.y - half_line_width;
            }
            if (out_slope.dx >= 0)
                p1.x -= half_line_width;
            if (out_slope.dx <= 0)
                p2.x += half_line_width;
          }

          if (stroker->do_traps) {
            status = _cairo_traps_tessellate_rectangle (stroker->container, &p1, &p2);
          } else {
            cairo_box_t box;

            box.p1 = p1;
            box.p2 = p2;

            status = _cairo_boxes_add (stroker->container, &box);
          }
          if (unlikely (status))
            return status;
      }

      /* Perform the adjustments of the endpoints. */
      if (is_horizontal) {
          if (line_cap == CAIRO_LINE_CAP_SQUARE) {
            if (a->x <= b->x) {
                a->x -= half_line_width;
                b->x += half_line_width;
            } else {
                a->x += half_line_width;
                b->x -= half_line_width;
            }
          }

          if (a->x > b->x) {
            cairo_point_t *t;

            t = a;
            a = b;
            b = t;
          }

          a->y -= half_line_width;
          b->y += half_line_width;
      } else {
          if (line_cap == CAIRO_LINE_CAP_SQUARE) {
            if (a->y <= b->y) {
                a->y -= half_line_width;
                b->y += half_line_width;
            } else {
                a->y += half_line_width;
                b->y -= half_line_width;
            }
          }

          if (a->y > b->y) {
            cairo_point_t *t;

            t = a;
            a = b;
            b = t;
          }

          a->x -= half_line_width;
          b->x += half_line_width;
      }

      if (a->x == b->x && a->y == b->y)
          continue;

      if (stroker->do_traps) {
          status = _cairo_traps_tessellate_rectangle (stroker->container, a, b);
      } else {
          cairo_box_t box;

          box.p1 = *a;
          box.p2 = *b;

          status = _cairo_boxes_add (stroker->container, &box);
      }
      if (unlikely (status))
          return status;
    }

    stroker->num_segments = 0;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_rectilinear_stroker_move_to (void        *closure,
                            const cairo_point_t *point)
{
    cairo_rectilinear_stroker_t *stroker = closure;
    cairo_status_t status;

    if (stroker->dash.dashed)
      status = _cairo_rectilinear_stroker_emit_segments_dashed (stroker);
    else
      status = _cairo_rectilinear_stroker_emit_segments (stroker);
    if (unlikely (status))
      return status;

    /* reset the dash pattern for new sub paths */
    _cairo_stroker_dash_start (&stroker->dash);

    stroker->current_point = *point;
    stroker->first_point = *point;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_rectilinear_stroker_line_to (void        *closure,
                            const cairo_point_t *b)
{
    cairo_rectilinear_stroker_t *stroker = closure;
    cairo_point_t *a = &stroker->current_point;
    cairo_status_t status;

    /* We only support horizontal or vertical elements. */
    assert (a->x == b->x || a->y == b->y);

    /* We don't draw anything for degenerate paths. */
    if (a->x == b->x && a->y == b->y)
      return CAIRO_STATUS_SUCCESS;

    status = _cairo_rectilinear_stroker_add_segment (stroker, a, b,
                                         a->y == b->y,
                                         TRUE);

    stroker->current_point = *b;
    stroker->open_sub_path = TRUE;

    return status;
}

static cairo_status_t
_cairo_rectilinear_stroker_line_to_dashed (void       *closure,
                                 const cairo_point_t  *point)
{
    cairo_rectilinear_stroker_t *stroker = closure;
    const cairo_point_t *a = &stroker->current_point;
    const cairo_point_t *b = point;
    cairo_bool_t fully_in_bounds;
    double sign, remain;
    cairo_fixed_t mag;
    cairo_status_t status;
    cairo_line_t segment;
    cairo_bool_t dash_on = FALSE;
    cairo_bool_t is_horizontal;

    /* We don't draw anything for degenerate paths. */
    if (a->x == b->x && a->y == b->y)
      return CAIRO_STATUS_SUCCESS;

    /* We only support horizontal or vertical elements. */
    assert (a->x == b->x || a->y == b->y);

    fully_in_bounds = TRUE;
    if (stroker->has_bounds &&
      (! _cairo_box_contains_point (&stroker->bounds, a) ||
       ! _cairo_box_contains_point (&stroker->bounds, b)))
    {
      fully_in_bounds = FALSE;
    }

    is_horizontal = a->y == b->y;
    if (is_horizontal)
      mag = b->x - a->x;
    else
      mag = b->y - a->y;
    if (mag < 0) {
      remain = _cairo_fixed_to_double (-mag);
      sign = 1.;
    } else {
      remain = _cairo_fixed_to_double (mag);
      sign = -1.;
    }

    segment.p2 = segment.p1 = *a;
    while (remain > 0.) {
      double step_length;

      step_length = MIN (stroker->dash.dash_remain, remain);
      remain -= step_length;

      mag = _cairo_fixed_from_double (sign*remain);
      if (is_horizontal)
          segment.p2.x = b->x + mag;
      else
          segment.p2.y = b->y + mag;

      if (stroker->dash.dash_on &&
          (fully_in_bounds ||
           _cairo_box_intersects_line_segment (&stroker->bounds, &segment)))
      {
          status = _cairo_rectilinear_stroker_add_segment (stroker,
                                               &segment.p1,
                                               &segment.p2,
                                               is_horizontal,
                                               remain <= 0.);
          if (unlikely (status))
            return status;

          dash_on = TRUE;
      }
      else
      {
          dash_on = FALSE;
      }

      _cairo_stroker_dash_step (&stroker->dash, step_length);
      segment.p1 = segment.p2;
    }

    if (stroker->dash.dash_on && ! dash_on &&
      (fully_in_bounds ||
       _cairo_box_intersects_line_segment (&stroker->bounds, &segment)))
    {

      /* This segment ends on a transition to dash_on, compute a new face
       * and add cap for the beginning of the next dash_on step.
       */

      status = _cairo_rectilinear_stroker_add_segment (stroker,
                                           &segment.p1,
                                           &segment.p1,
                                           is_horizontal,
                                           TRUE);
      if (unlikely (status))
          return status;
    }

    stroker->current_point = *point;
    stroker->open_sub_path = TRUE;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_rectilinear_stroker_close_path (void *closure)
{
    cairo_rectilinear_stroker_t *stroker = closure;
    cairo_status_t status;

    /* We don't draw anything for degenerate paths. */
    if (! stroker->open_sub_path)
      return CAIRO_STATUS_SUCCESS;

    if (stroker->dash.dashed) {
      status = _cairo_rectilinear_stroker_line_to_dashed (stroker,
                                              &stroker->first_point);
    } else {
      status = _cairo_rectilinear_stroker_line_to (stroker,
                                         &stroker->first_point);
    }
    if (unlikely (status))
      return status;

    stroker->open_sub_path = FALSE;

    if (stroker->dash.dashed)
      status = _cairo_rectilinear_stroker_emit_segments_dashed (stroker);
    else
      status = _cairo_rectilinear_stroker_emit_segments (stroker);
    if (unlikely (status))
      return status;

    return CAIRO_STATUS_SUCCESS;
}

cairo_int_status_t
_cairo_path_fixed_stroke_rectilinear_to_traps (const cairo_path_fixed_t *path,
                                     const cairo_stroke_style_t   *stroke_style,
                                     const cairo_matrix_t   *ctm,
                                     cairo_traps_t          *traps)
{
    cairo_rectilinear_stroker_t rectilinear_stroker;
    cairo_int_status_t status;

    assert (path->is_rectilinear);

    if (! _cairo_rectilinear_stroker_init (&rectilinear_stroker,
                                 stroke_style, ctm,
                                 TRUE, traps))
    {
      return CAIRO_INT_STATUS_UNSUPPORTED;
    }

    if (traps->num_limits) {
      _cairo_rectilinear_stroker_limit (&rectilinear_stroker,
                                traps->limits,
                                traps->num_limits);
    }

    status = _cairo_path_fixed_interpret (path,
                                CAIRO_DIRECTION_FORWARD,
                                _cairo_rectilinear_stroker_move_to,
                                rectilinear_stroker.dash.dashed ?
                                _cairo_rectilinear_stroker_line_to_dashed :
                                _cairo_rectilinear_stroker_line_to,
                                NULL,
                                _cairo_rectilinear_stroker_close_path,
                                &rectilinear_stroker);
    if (unlikely (status))
      goto BAIL;

    if (rectilinear_stroker.dash.dashed)
      status = _cairo_rectilinear_stroker_emit_segments_dashed (&rectilinear_stroker);
    else
      status = _cairo_rectilinear_stroker_emit_segments (&rectilinear_stroker);

    traps->is_rectilinear = 1;
    traps->is_rectangular = 1;
    /* As we incrementally tessellate, we do not eliminate self-intersections */
    traps->has_intersections = traps->num_traps > 1;
BAIL:
    _cairo_rectilinear_stroker_fini (&rectilinear_stroker);

    if (unlikely (status))
      _cairo_traps_clear (traps);

    return status;
}

cairo_int_status_t
_cairo_path_fixed_stroke_rectilinear_to_boxes (const cairo_path_fixed_t *path,
                                     const cairo_stroke_style_t   *stroke_style,
                                     const cairo_matrix_t   *ctm,
                                     cairo_boxes_t          *boxes)
{
    cairo_rectilinear_stroker_t rectilinear_stroker;
    cairo_int_status_t status;

    assert (path->is_rectilinear);

    if (! _cairo_rectilinear_stroker_init (&rectilinear_stroker,
                                 stroke_style, ctm,
                                 FALSE, boxes))
    {
      return CAIRO_INT_STATUS_UNSUPPORTED;
    }

    if (boxes->num_limits) {
      _cairo_rectilinear_stroker_limit (&rectilinear_stroker,
                                boxes->limits,
                                boxes->num_limits);
    }

    status = _cairo_path_fixed_interpret (path,
                                CAIRO_DIRECTION_FORWARD,
                                _cairo_rectilinear_stroker_move_to,
                                rectilinear_stroker.dash.dashed ?
                                _cairo_rectilinear_stroker_line_to_dashed :
                                _cairo_rectilinear_stroker_line_to,
                                NULL,
                                _cairo_rectilinear_stroker_close_path,
                                &rectilinear_stroker);
    if (unlikely (status))
      goto BAIL;

    if (rectilinear_stroker.dash.dashed)
      status = _cairo_rectilinear_stroker_emit_segments_dashed (&rectilinear_stroker);
    else
      status = _cairo_rectilinear_stroker_emit_segments (&rectilinear_stroker);
    if (unlikely (status))
      goto BAIL;

    /* As we incrementally tessellate, we do not eliminate self-intersections */
    status = _cairo_bentley_ottmann_tessellate_boxes (boxes,
                                          CAIRO_FILL_RULE_WINDING,
                                          boxes);
    if (unlikely (status))
      goto BAIL;

    _cairo_rectilinear_stroker_fini (&rectilinear_stroker);

    return CAIRO_STATUS_SUCCESS;

BAIL:
    _cairo_rectilinear_stroker_fini (&rectilinear_stroker);
    _cairo_boxes_clear (boxes);
    return status;
}

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