/work/workdir/UnpackedTarball/cairo/src/cairo-path-stroke-polygon.c

Source
/* -*- 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
 * Copyright © 2011 Intel Corporation
 *
 * 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 _DEFAULT_SOURCE /* for hypot() */
#include "cairoint.h"

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

#define DEBUG 0

struct stroker {
    cairo_stroke_style_t style;

#if DEBUG
    cairo_contour_t path;
#endif

    struct stroke_contour {
  /* Note that these are not strictly contours as they may intersect */
  cairo_contour_t contour;
    } cw, ccw;
    cairo_uint64_t contour_tolerance;
    cairo_polygon_t *polygon;

    const cairo_matrix_t *ctm;
    const cairo_matrix_t *ctm_inverse;
    double tolerance;
    double spline_cusp_tolerance;
    double half_line_width;
    cairo_bool_t ctm_det_positive;

    cairo_pen_t pen;

    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_bool_t has_bounds;
    cairo_box_t bounds;
};

static inline double
normalize_slope (double *dx, double *dy);

static void
compute_face (const cairo_point_t *point,
        const cairo_slope_t *dev_slope,
        struct stroker *stroker,
        cairo_stroke_face_t *face);

static cairo_uint64_t
point_distance_sq (const cairo_point_t *p1,
      const cairo_point_t *p2)
{
    int32_t dx = p1->x - p2->x;
    int32_t dy = p1->y - p2->y;
    return _cairo_int32x32_64_mul (dx, dx) + _cairo_int32x32_64_mul (dy, dy);
}

static cairo_bool_t
within_tolerance (const cairo_point_t *p1,
        const cairo_point_t *p2,
        cairo_uint64_t tolerance)
{
    return FALSE;
    return _cairo_int64_lt (point_distance_sq (p1, p2), tolerance);
}

static void
contour_add_point (struct stroker *stroker,
       struct stroke_contour *c,
       const cairo_point_t *point)
{
    if (! within_tolerance (point, _cairo_contour_last_point (&c->contour),
      stroker->contour_tolerance))
  _cairo_contour_add_point (&c->contour, point);
    //*_cairo_contour_last_point (&c->contour) = *point;
}

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

static int
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;
}

/*
 * Construct a fan around the midpoint using the vertices from pen between
 * inpt and outpt.
 */
static void
add_fan (struct stroker *stroker,
   const cairo_slope_t *in_vector,
   const cairo_slope_t *out_vector,
   const cairo_point_t *midpt,
   cairo_bool_t clockwise,
   struct stroke_contour *c)
{
    cairo_pen_t *pen = &stroker->pen;
    int start, stop;

    if (stroker->has_bounds &&
  ! _cairo_box_contains_point (&stroker->bounds, midpt))
  return;

    assert (stroker->pen.num_vertices);

    if (clockwise) {
  _cairo_pen_find_active_cw_vertices (pen,
              in_vector, out_vector,
              &start, &stop);
  while (start != stop) {
      cairo_point_t p = *midpt;
      translate_point (&p, &pen->vertices[start].point);
      contour_add_point (stroker, c, &p);

      if (++start == pen->num_vertices)
    start = 0;
  }
    } else {
  _cairo_pen_find_active_ccw_vertices (pen,
               in_vector, out_vector,
               &start, &stop);
  while (start != stop) {
      cairo_point_t p = *midpt;
      translate_point (&p, &pen->vertices[start].point);
      contour_add_point (stroker, c, &p);

      if (start-- == 0)
    start += pen->num_vertices;
  }
    }
}

static int
join_is_clockwise (const cairo_stroke_face_t *in,
       const cairo_stroke_face_t *out)
{
    return _cairo_slope_compare (&in->dev_vector, &out->dev_vector) < 0;
}

static void
inner_join (struct stroker *stroker,
      const cairo_stroke_face_t *in,
      const cairo_stroke_face_t *out,
      int clockwise)
{
#if 0
    cairo_point_t last;
    const cairo_point_t *p, *outpt;
    struct stroke_contour *inner;
    cairo_int64_t d_p, d_last;
    cairo_int64_t half_line_width;
    cairo_bool_t negate;

    /* XXX line segments shorter than line-width */

    if (clockwise) {
  inner = &stroker->ccw;
  outpt = &out->ccw;
  negate = 1;
    } else {
  inner = &stroker->cw;
  outpt = &out->cw;
  negate = 0;
    }

    half_line_width = CAIRO_FIXED_ONE*CAIRO_FIXED_ONE/2 * stroker->style.line_width * out->length + .5;

    /* On the inside, the previous end-point is always
     * closer to the new face by definition.
     */
    last = *_cairo_contour_last_point (&inner->contour);
    d_last = distance_from_face (out, &last, negate);
    _cairo_contour_remove_last_point (&inner->contour);

prev:
    if (inner->contour.chain.num_points == 0) {
  contour_add_point (stroker, inner, outpt);
  return;
    }
    p = _cairo_contour_last_point (&inner->contour);
    d_p = distance_from_face (out, p, negate);
    if (_cairo_int64_lt (d_p, half_line_width) &&
  !_cairo_int64_negative (distance_along_face (out, p)))
    {
  last = *p;
  d_last = d_p;
  _cairo_contour_remove_last_point (&inner->contour);
  goto prev;
    }

    compute_inner_joint (&last, d_last, p, d_p, half_line_width);
    contour_add_point (stroker, inner, &last);
#else
    const cairo_point_t *outpt;
    struct stroke_contour *inner;

    if (clockwise) {
  inner = &stroker->ccw;
  outpt = &out->ccw;
    } else {
  inner = &stroker->cw;
  outpt = &out->cw;
    }
    contour_add_point (stroker, inner, &in->point);
    contour_add_point (stroker, inner, outpt);
#endif
}

static void
inner_close (struct stroker *stroker,
       const cairo_stroke_face_t *in,
       cairo_stroke_face_t *out)
{
#if 0
    cairo_point_t last;
    const cairo_point_t *p, *outpt, *inpt;
    struct stroke_contour *inner;
    struct _cairo_contour_chain *chain;

    /* XXX line segments shorter than line-width */

    if (join_is_clockwise (in, out)) {
  inner = &stroker->ccw;
  outpt = &in->ccw;
  inpt = &out->ccw;
    } else {
  inner = &stroker->cw;
  outpt = &in->cw;
  inpt = &out->cw;
    }

    if (inner->contour.chain.num_points == 0) {
  contour_add_point (stroker, inner, &in->point);
  contour_add_point (stroker, inner, inpt);
  *_cairo_contour_first_point (&inner->contour) =
      *_cairo_contour_last_point (&inner->contour);
  return;
    }

    line_width = stroker->style.line_width/2;
    line_width *= CAIRO_FIXED_ONE;

    d_last = sign * distance_from_face (out, outpt);
    last = *outpt;

    for (chain = &inner->contour.chain; chain; chain = chain->next) {
  for (i = 0; i < chain->num_points; i++) {
      p = &chain->points[i];
      if ((d_p = sign * distance_from_face (in, p)) >= line_width &&
    distance_from_edge (stroker, inpt, &last, p) < line_width)
      {
    goto out;
      }

      if (p->x != last.x || p->y != last.y) {
    last = *p;
    d_last = d_p;
      }
  }
    }
out:

    if (d_p != d_last) {
  double dot = (line_width - d_last) / (d_p - d_last);
  last.x += dot * (p->x - last.x);
  last.y += dot * (p->y - last.y);
    }
    *_cairo_contour_last_point (&inner->contour) = last;

    for (chain = &inner->contour.chain; chain; chain = chain->next) {
  for (i = 0; i < chain->num_points; i++) {
      cairo_point_t *pp = &chain->points[i];
      if (pp == p)
    return;
      *pp = last;
  }
    }
#else
    const cairo_point_t *inpt;
    struct stroke_contour *inner;

    if (join_is_clockwise (in, out)) {
  inner = &stroker->ccw;
  inpt = &out->ccw;
    } else {
  inner = &stroker->cw;
  inpt = &out->cw;
    }

    contour_add_point (stroker, inner, &in->point);
    contour_add_point (stroker, inner, inpt);
    *_cairo_contour_first_point (&inner->contour) =
  *_cairo_contour_last_point (&inner->contour);
#endif
}

static void
outer_close (struct stroker *stroker,
       const cairo_stroke_face_t *in,
       const cairo_stroke_face_t *out)
{
    const cairo_point_t *inpt, *outpt;
    struct stroke_contour *outer;
    int clockwise;

    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;
    }

    clockwise = join_is_clockwise (in, out);
    if (clockwise) {
  inpt = &in->cw;
  outpt = &out->cw;
  outer = &stroker->cw;
    } else {
  inpt = &in->ccw;
  outpt = &out->ccw;
  outer = &stroker->ccw;
    }

    if (within_tolerance (inpt, outpt, stroker->contour_tolerance)) {
  *_cairo_contour_first_point (&outer->contour) =
      *_cairo_contour_last_point (&outer->contour);
  return;
    }

    switch (stroker->style.line_join) {
    case CAIRO_LINE_JOIN_ROUND:
  if ((in->dev_slope.x * out->dev_slope.x +
       in->dev_slope.y * out->dev_slope.y) < stroker->spline_cusp_tolerance)
  {
      /* construct a fan around the common midpoint */
      add_fan (stroker,
         &in->dev_vector, &out->dev_vector, &in->point,
         clockwise, outer);
  } /* else: bevel join */
  break;

    case CAIRO_LINE_JOIN_MITER:
    default: {
  /* dot product of incoming slope vector with outgoing slope vector */
  double  in_dot_out = in->dev_slope.x * out->dev_slope.x +
           in->dev_slope.y * out->dev_slope.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->dev_slope.x;
      dy1 = in->dev_slope.y;

      /* outer point of outgoing line face */
      x2 = _cairo_fixed_to_double (outpt->x);
      y2 = _cairo_fixed_to_double (outpt->y);
      dx2 = out->dev_slope.x;
      dy2 = out->dev_slope.y;

      /*
       * 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 (slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
    slope_compare_sgn (fdx2, fdy2, mdx, mdy))
      {
    cairo_point_t p;

    p.x = _cairo_fixed_from_double (mx);
    p.y = _cairo_fixed_from_double (my);

    *_cairo_contour_last_point (&outer->contour) = p;
    *_cairo_contour_first_point (&outer->contour) = p;
    return;
      }
  }
  break;
    }

    case CAIRO_LINE_JOIN_BEVEL:
  break;
    }
    contour_add_point (stroker, outer, outpt);
}

static void
outer_join (struct stroker *stroker,
      const cairo_stroke_face_t *in,
      const cairo_stroke_face_t *out,
      int clockwise)
{
    const cairo_point_t *inpt, *outpt;
    struct stroke_contour *outer;

    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;
    }
    if (clockwise) {
  inpt = &in->cw;
  outpt = &out->cw;
  outer = &stroker->cw;
    } else {
  inpt = &in->ccw;
  outpt = &out->ccw;
  outer = &stroker->ccw;
    }

    switch (stroker->style.line_join) {
    case CAIRO_LINE_JOIN_ROUND:
  if ((in->dev_slope.x * out->dev_slope.x +
       in->dev_slope.y * out->dev_slope.y) < stroker->spline_cusp_tolerance)
  {
      /* construct a fan around the common midpoint */
      add_fan (stroker,
         &in->dev_vector, &out->dev_vector, &in->point,
         clockwise, outer);
  } /* else: bevel join */
  break;

    case CAIRO_LINE_JOIN_MITER:
    default: {
  /* dot product of incoming slope vector with outgoing slope vector */
  double  in_dot_out = in->dev_slope.x * out->dev_slope.x +
           in->dev_slope.y * out->dev_slope.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->dev_slope.x;
      dy1 = in->dev_slope.y;

      /* outer point of outgoing line face */
      x2 = _cairo_fixed_to_double (outpt->x);
      y2 = _cairo_fixed_to_double (outpt->y);
      dx2 = out->dev_slope.x;
      dy2 = out->dev_slope.y;

      /*
       * 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 (slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
    slope_compare_sgn (fdx2, fdy2, mdx, mdy))
      {
    cairo_point_t p;

    p.x = _cairo_fixed_from_double (mx);
    p.y = _cairo_fixed_from_double (my);

    *_cairo_contour_last_point (&outer->contour) = p;
    return;
      }
  }
  break;
    }

    case CAIRO_LINE_JOIN_BEVEL:
  break;
    }
    contour_add_point (stroker,outer, outpt);
}

static void
add_cap (struct stroker *stroker,
   const cairo_stroke_face_t *f,
   struct stroke_contour *c)
{
    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;

  add_fan (stroker, &f->dev_vector, &slope, &f->point, FALSE, c);
  break;
    }

    case CAIRO_LINE_CAP_SQUARE: {
  cairo_slope_t fvector;
  cairo_point_t p;
  double dx, dy;

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

  p.x = f->ccw.x + fvector.dx;
  p.y = f->ccw.y + fvector.dy;
  contour_add_point (stroker, c, &p);

  p.x = f->cw.x + fvector.dx;
  p.y = f->cw.y + fvector.dy;
  contour_add_point (stroker, c, &p);
    }

    case CAIRO_LINE_CAP_BUTT:
    default:
  break;
    }
    contour_add_point (stroker, c, &f->cw);
}

static void
add_leading_cap (struct stroker *stroker,
     const cairo_stroke_face_t *face,
     struct stroke_contour *c)
{
    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;

    add_cap (stroker, &reversed, c);
}

static void
add_trailing_cap (struct stroker *stroker,
      const cairo_stroke_face_t *face,
      struct stroke_contour *c)
{
    add_cap (stroker, face, c);
}

static inline double
normalize_slope (double *dx, double *dy)
{
    double dx0 = *dx, dy0 = *dy;
    double mag;

    assert (dx0 != 0.0 || dy0 != 0.0);

    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;
    }

    return mag;
}

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

    slope_dx = _cairo_fixed_to_double (dev_slope->dx);
    slope_dy = _cairo_fixed_to_double (dev_slope->dy);
    face->length = normalize_slope (&slope_dx, &slope_dy);
    face->dev_slope.x = slope_dx;
    face->dev_slope.y = slope_dy;

    /*
     * 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 (! _cairo_matrix_is_identity (stroker->ctm_inverse)) {
  /* Normalize the matrix! */
  cairo_matrix_transform_distance (stroker->ctm_inverse,
           &slope_dx, &slope_dy);
  normalize_slope (&slope_dx, &slope_dy);

  if (stroker->ctm_det_positive) {
      face_dx = - slope_dy * stroker->half_line_width;
      face_dy = slope_dx * stroker->half_line_width;
  } else {
      face_dx = slope_dy * stroker->half_line_width;
      face_dy = - slope_dx * stroker->half_line_width;
  }

  /* back to device space */
  cairo_matrix_transform_distance (stroker->ctm, &face_dx, &face_dy);
    } else {
  face_dx = - slope_dy * stroker->half_line_width;
  face_dy = slope_dx * stroker->half_line_width;
    }

    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 void
add_caps (struct stroker *stroker)
{
    /* 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_CAP_ROUND)
    {
  /* pick an arbitrary slope to use */
  cairo_slope_t slope = { CAIRO_FIXED_ONE, 0 };
  cairo_stroke_face_t face;

  /* arbitrarily choose first_point */
  compute_face (&stroker->first_point, &slope, stroker, &face);

  add_leading_cap (stroker, &face, &stroker->ccw);
  add_trailing_cap (stroker, &face, &stroker->ccw);

  /* ensure the circle is complete */
  _cairo_contour_add_point (&stroker->ccw.contour,
          _cairo_contour_first_point (&stroker->ccw.contour));

  _cairo_polygon_add_contour (stroker->polygon, &stroker->ccw.contour);
  _cairo_contour_reset (&stroker->ccw.contour);
    } else {
  if (stroker->has_current_face)
      add_trailing_cap (stroker, &stroker->current_face, &stroker->ccw);

#if DEBUG
  {
      FILE *file = fopen ("contours.txt", "a");
      _cairo_debug_print_contour (file, &stroker->path);
      _cairo_debug_print_contour (file, &stroker->cw.contour);
      _cairo_debug_print_contour (file, &stroker->ccw.contour);
      fclose (file);
      _cairo_contour_reset (&stroker->path);
  }
#endif

  _cairo_polygon_add_contour (stroker->polygon, &stroker->ccw.contour);
  _cairo_contour_reset (&stroker->ccw.contour);

  if (stroker->has_first_face) {
      _cairo_contour_add_point (&stroker->ccw.contour,
              &stroker->first_face.cw);
      add_leading_cap (stroker, &stroker->first_face, &stroker->ccw);
#if DEBUG
      {
    FILE *file = fopen ("contours.txt", "a");
    _cairo_debug_print_contour (file, &stroker->ccw.contour);
    fclose (file);
      }
#endif

      _cairo_polygon_add_contour (stroker->polygon,
          &stroker->ccw.contour);
      _cairo_contour_reset (&stroker->ccw.contour);
  }

  _cairo_polygon_add_contour (stroker->polygon, &stroker->cw.contour);
  _cairo_contour_reset (&stroker->cw.contour);
    }
}

static cairo_status_t
close_path (void *closure);

static cairo_status_t
move_to (void *closure,
   const cairo_point_t *point)
{
    struct stroker *stroker = closure;

    /* Cap the start and end of the previous sub path as needed */
    add_caps (stroker);

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

    stroker->first_point = *point;

#if DEBUG
    _cairo_contour_add_point (&stroker->path, point);
#endif

    stroker->current_face.point = *point;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
line_to (void *closure,
   const cairo_point_t *point)
{
    struct stroker *stroker = closure;
    cairo_stroke_face_t start;
    cairo_point_t *p1 = &stroker->current_face.point;
    cairo_slope_t dev_slope;

    stroker->has_initial_sub_path = TRUE;

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

#if DEBUG
    _cairo_contour_add_point (&stroker->path, point);
#endif

    _cairo_slope_init (&dev_slope, p1, point);
    compute_face (p1, &dev_slope, stroker, &start);

    if (stroker->has_current_face) {
  int clockwise = _cairo_slope_compare (&stroker->current_face.dev_vector,
                &start.dev_vector);
  if (clockwise) {
      clockwise = clockwise < 0;
      /* Join with final face from previous segment */
      if (! within_tolerance (&stroker->current_face.ccw, &start.ccw,
            stroker->contour_tolerance) ||
    ! within_tolerance (&stroker->current_face.cw, &start.cw,
            stroker->contour_tolerance))
      {
    outer_join (stroker, &stroker->current_face, &start, clockwise);
    inner_join (stroker, &stroker->current_face, &start, clockwise);
      }
  }
    } 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->has_current_face = TRUE;

  contour_add_point (stroker, &stroker->cw, &start.cw);
  contour_add_point (stroker, &stroker->ccw, &start.ccw);
    }

    stroker->current_face = start;
    stroker->current_face.point = *point;
    stroker->current_face.ccw.x += dev_slope.dx;
    stroker->current_face.ccw.y += dev_slope.dy;
    stroker->current_face.cw.x += dev_slope.dx;
    stroker->current_face.cw.y += dev_slope.dy;

    contour_add_point (stroker, &stroker->cw, &stroker->current_face.cw);
    contour_add_point (stroker, &stroker->ccw, &stroker->current_face.ccw);

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
spline_to (void *closure,
     const cairo_point_t *point,
     const cairo_slope_t *tangent)
{
    struct stroker *stroker = closure;
    cairo_stroke_face_t face;

#if DEBUG
    _cairo_contour_add_point (&stroker->path, point);
#endif
    if ((tangent->dx | tangent->dy) == 0) {
  struct stroke_contour *outer;
  cairo_point_t t;
  int clockwise;

  face = stroker->current_face;

  face.usr_vector.x = -face.usr_vector.x;
  face.usr_vector.y = -face.usr_vector.y;
  face.dev_vector.dx = -face.dev_vector.dx;
  face.dev_vector.dy = -face.dev_vector.dy;

  t = face.cw;
  face.cw = face.ccw;
  face.ccw = t;

  clockwise = join_is_clockwise (&stroker->current_face, &face);
  if (clockwise) {
      outer = &stroker->cw;
  } else {
      outer = &stroker->ccw;
  }

  add_fan (stroker,
     &stroker->current_face.dev_vector,
     &face.dev_vector,
     &stroker->current_face.point,
     clockwise, outer);
    } else {
  compute_face (point, tangent, stroker, &face);

  if ((face.dev_slope.x * stroker->current_face.dev_slope.x +
       face.dev_slope.y * stroker->current_face.dev_slope.y) < stroker->spline_cusp_tolerance)
  {
      struct stroke_contour *outer;
      int clockwise = join_is_clockwise (&stroker->current_face, &face);

      stroker->current_face.cw.x += face.point.x - stroker->current_face.point.x;
      stroker->current_face.cw.y += face.point.y - stroker->current_face.point.y;
      contour_add_point (stroker, &stroker->cw, &stroker->current_face.cw);

      stroker->current_face.ccw.x += face.point.x - stroker->current_face.point.x;
      stroker->current_face.ccw.y += face.point.y - stroker->current_face.point.y;
      contour_add_point (stroker, &stroker->ccw, &stroker->current_face.ccw);

      if (clockwise) {
    outer = &stroker->cw;
      } else {
    outer = &stroker->ccw;
      }
      add_fan (stroker,
         &stroker->current_face.dev_vector,
         &face.dev_vector,
         &stroker->current_face.point,
         clockwise, outer);
  }

  contour_add_point (stroker, &stroker->cw, &face.cw);
  contour_add_point (stroker, &stroker->ccw, &face.ccw);
    }

    stroker->current_face = face;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
curve_to (void *closure,
    const cairo_point_t *b,
    const cairo_point_t *c,
    const cairo_point_t *d)
{
    struct stroker *stroker = closure;
    cairo_spline_t spline;
    cairo_stroke_face_t face;

    if (stroker->has_bounds &&
  ! _cairo_spline_intersects (&stroker->current_face.point, b, c, d,
            &stroker->bounds))
  return line_to (closure, d);

    if (! _cairo_spline_init (&spline, spline_to, stroker,
            &stroker->current_face.point, b, c, d))
  return line_to (closure, d);

    compute_face (&stroker->current_face.point, &spline.initial_slope,
      stroker, &face);

    if (stroker->has_current_face) {
  int clockwise = join_is_clockwise (&stroker->current_face, &face);
  /* Join with final face from previous segment */
  outer_join (stroker, &stroker->current_face, &face, clockwise);
  inner_join (stroker, &stroker->current_face, &face, clockwise);
    } else {
  if (! stroker->has_first_face) {
      /* Save sub path's first face in case needed for closing join */
      stroker->first_face = face;
      stroker->has_first_face = TRUE;
  }
  stroker->has_current_face = TRUE;

  contour_add_point (stroker, &stroker->cw, &face.cw);
  contour_add_point (stroker, &stroker->ccw, &face.ccw);
    }
    stroker->current_face = face;

    return _cairo_spline_decompose (&spline, stroker->tolerance);
}

static cairo_status_t
close_path (void *closure)
{
    struct stroker *stroker = closure;
    cairo_status_t status;

    status = 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 */
  outer_close (stroker, &stroker->current_face, &stroker->first_face);
  inner_close (stroker, &stroker->current_face, &stroker->first_face);
#if 0
  *_cairo_contour_first_point (&stroker->ccw.contour) =
      *_cairo_contour_last_point (&stroker->ccw.contour);

  *_cairo_contour_first_point (&stroker->cw.contour) =
      *_cairo_contour_last_point (&stroker->cw.contour);
#endif

  _cairo_polygon_add_contour (stroker->polygon, &stroker->cw.contour);
  _cairo_polygon_add_contour (stroker->polygon, &stroker->ccw.contour);

#if DEBUG
  {
      FILE *file = fopen ("contours.txt", "a");
      _cairo_debug_print_contour (file, &stroker->path);
      _cairo_debug_print_contour (file, &stroker->cw.contour);
      _cairo_debug_print_contour (file, &stroker->ccw.contour);
      fclose (file);

      _cairo_contour_reset (&stroker->path);
  }
#endif
  _cairo_contour_reset (&stroker->cw.contour);
  _cairo_contour_reset (&stroker->ccw.contour);
    } else {
  /* Cap the start and end of the sub path as needed */
  add_caps (stroker);
    }

    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_polygon (const cairo_path_fixed_t *path,
             const cairo_stroke_style_t *style,
             const cairo_matrix_t *ctm,
             const cairo_matrix_t *ctm_inverse,
             double    tolerance,
             cairo_polygon_t *polygon)
{
    struct stroker stroker;
    cairo_status_t status;

    if (style->num_dashes) {
  return _cairo_path_fixed_stroke_dashed_to_polygon (path,
                 style,
                 ctm,
                 ctm_inverse,
                 tolerance,
                 polygon);
    }

    stroker.has_bounds = polygon->num_limits;
    if (stroker.has_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.
   */
  double dx, dy;
  cairo_fixed_t fdx, fdy;
  int i;

  stroker.bounds = polygon->limits[0];
  for (i = 1; i < polygon->num_limits; i++)
       _cairo_box_add_box (&stroker.bounds, &polygon->limits[i]);

  _cairo_stroke_style_max_distance_from_path (style, path, 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;
    }

    stroker.style = *style;
    stroker.ctm = ctm;
    stroker.ctm_inverse = ctm_inverse;
    stroker.tolerance = tolerance;
    stroker.half_line_width = style->line_width / 2.;

    /* If `CAIRO_LINE_JOIN_ROUND` is selected and a joint's `arc height`
     * is greater than `tolerance` then two segments are joined with
     * round-join, otherwise bevel-join is used.
     *
     * (See https://gitlab.freedesktop.org/cairo/cairo/-/merge_requests/372#note_1698225
     *  for an illustration.)
     *
     * `Arc height` is the distance from the center of arc's chord to
     * the center of the arc. It is also the difference of arc's radius
     * and the "distance from a point where segments are joined to the
     * chord" (distance to the chord). Arc's radius is the half of a line
     * width and the "distance to the chord" is equal to "half of a line width"
     * times `cos(half the angle between segment vectors)`. So
     *
     *     arc_height = w/2 - w/2 * cos(phi/2),
     *
     * where `w/2` is the "half of a line width".
     *
     * Using the double angle cosine formula we can express the `cos(phi/2)`
     * with just `cos(phi)` which is also the dot product of segments'
     * unit vectors.
     *
     *     cos(phi/2) = sqrt ( (1 + cos(phi)) / 2 );
     *     cos(phi/2) is in [0; 1] range, cannot be negative;
     *
     *     cos(phi) = a . b  = (ax * bx + ay * by),
     *
     * where `a` and `b` are unit vectors of the segments to be joined.
     *
     * Since `arc height` should be greater than the `tolerance` to produce
     * a round-join we can write
     *
     *     w/2 * (1 - cos(phi/2))  >  tolerance;
     *     1 - tolerance / (w/2)  >  cos(phi/2);    [!]
     *
     * which can be rewritten with the above double angle formula to
     *
     *     cos(phi)  <  2 * ( 1 - tolerance / (w/2) )^2 - 1,
     *
     * [!] Note that `w/2` is in [tolerance; +inf] range, since `cos(phi/2)`
     * cannot be negative. The left part of the above inequality is the
     * dot product and the right part is the `spline_cusp_tolerance`:
     *
     *     (ax * bx + ay * by) < spline_cusp_tolerance.
     *
     * In the code below only the `spline_cusp_tolerance` is calculated.
     * The dot product is calculated later, in the condition expression
     * itself. "Half of a line width" must be scaled with CTM for tolerance
     * condition to be properly met. Also, since `arch height` cannot exceed
     * the "half of a line width" and since `cos(phi/2)` cannot be negative,
     * when `tolerance` is greater than the "half of a line width" the
     * bevel-join should be produced.
     */
    double scaled_hlw = hypot(stroker.half_line_width * ctm->xx,
            stroker.half_line_width * ctm->yx);

    if (scaled_hlw <= tolerance) {
  stroker.spline_cusp_tolerance = -1.0;
    } else {
  stroker.spline_cusp_tolerance = 1 - tolerance / scaled_hlw;
  stroker.spline_cusp_tolerance *= stroker.spline_cusp_tolerance;
  stroker.spline_cusp_tolerance *= 2;
  stroker.spline_cusp_tolerance -= 1;
    }

    stroker.ctm_det_positive =
  _cairo_matrix_compute_determinant (ctm) >= 0.0;

    stroker.pen.num_vertices = 0;
    if (path->has_curve_to ||
  style->line_join == CAIRO_LINE_JOIN_ROUND ||
  style->line_cap == CAIRO_LINE_CAP_ROUND) {
  status = _cairo_pen_init (&stroker.pen,
          stroker.half_line_width,
          tolerance, ctm);
  if (unlikely (status))
      return status;

  /* 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;
    }

    stroker.has_current_face = FALSE;
    stroker.has_first_face = FALSE;
    stroker.has_initial_sub_path = FALSE;

#if DEBUG
    remove ("contours.txt");
    remove ("polygons.txt");
    _cairo_contour_init (&stroker.path, 0);
#endif
    _cairo_contour_init (&stroker.cw.contour, 1);
    _cairo_contour_init (&stroker.ccw.contour, -1);
    tolerance *= CAIRO_FIXED_ONE;
    tolerance *= tolerance;
    stroker.contour_tolerance = tolerance;
    stroker.polygon = polygon;

    status = _cairo_path_fixed_interpret (path,
            move_to,
            line_to,
            curve_to,
            close_path,
            &stroker);
    /* Cap the start and end of the final sub path as needed */
    if (likely (status == CAIRO_STATUS_SUCCESS))
  add_caps (&stroker);

    _cairo_contour_fini (&stroker.cw.contour);
    _cairo_contour_fini (&stroker.ccw.contour);
    if (stroker.pen.num_vertices)
  _cairo_pen_fini (&stroker.pen);

#if DEBUG
    {
  FILE *file = fopen ("polygons.txt", "a");
  _cairo_debug_print_polygon (file, polygon);
  fclose (file);
    }
#endif

    return status;
}

Coverage Report

Created: 2026-03-31 11:00