/* -*- 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;

}

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 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:

  /* construct a fan around the common midpoint */

  if ((in->dev_slope.x * out->dev_slope.x +

       in->dev_slope.y * out->dev_slope.y) < stroker->spline_cusp_tolerance)

  {

      add_fan (stroker,

         &in->dev_vector, &out->dev_vector, &in->point,

         clockwise, outer);

      break;

  }

  /* else fall through */

    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:

  /* construct a fan around the common midpoint */

  add_fan (stroker,

     &in->dev_vector, &out->dev_vector, &in->point,

     clockwise, outer);

  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;