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cairo-path-fixed.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
 * Copyright © 2005 Red Hat, Inc.
  *
 * 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>
 */

#include "cairoint.h"

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

static cairo_status_t
_cairo_path_fixed_add (cairo_path_fixed_t  *path,
                   cairo_path_op_t      op,
                   const cairo_point_t *points,
                   int            num_points);

static void
_cairo_path_fixed_add_buf (cairo_path_fixed_t *path,
                     cairo_path_buf_t   *buf);

static cairo_path_buf_t *
_cairo_path_buf_create (int size_ops, int size_points);

static void
_cairo_path_buf_destroy (cairo_path_buf_t *buf);

static void
_cairo_path_buf_add_op (cairo_path_buf_t *buf,
                  cairo_path_op_t   op);

static void
_cairo_path_buf_add_points (cairo_path_buf_t       *buf,
                      const cairo_point_t    *points,
                      int                       num_points);

#define cairo_path_head(path__) (&(path__)->buf.base)
#define cairo_path_tail(path__) cairo_path_buf_prev (cairo_path_head (path__))

#define cairo_path_buf_next(pos__) \
    cairo_list_entry ((pos__)->link.next, cairo_path_buf_t, link)
#define cairo_path_buf_prev(pos__) \
    cairo_list_entry ((pos__)->link.prev, cairo_path_buf_t, link)

#define cairo_path_foreach_buf_start(pos__, path__) \
    pos__ = cairo_path_head (path__); do
#define cairo_path_foreach_buf_end(pos__, path__) \
    while ((pos__ = cairo_path_buf_next (pos__)) !=  cairo_path_head (path__))

void
_cairo_path_fixed_init (cairo_path_fixed_t *path)
{
    VG (VALGRIND_MAKE_MEM_UNDEFINED (path, sizeof (cairo_path_fixed_t)));

    cairo_list_init (&path->buf.base.link);

    path->buf.base.num_ops = 0;
    path->buf.base.num_points = 0;
    path->buf.base.size_ops = ARRAY_LENGTH (path->buf.op);
    path->buf.base.size_points = ARRAY_LENGTH (path->buf.points);
    path->buf.base.op = path->buf.op;
    path->buf.base.points = path->buf.points;

    path->current_point.x = 0;
    path->current_point.y = 0;
    path->last_move_point = path->current_point;
    path->has_last_move_point = FALSE;
    path->has_current_point = FALSE;
    path->has_curve_to = FALSE;
    path->is_rectilinear = TRUE;
    path->maybe_fill_region = TRUE;
    path->is_empty_fill = TRUE;

    path->extents.p1.x = path->extents.p1.y = INT_MAX;
    path->extents.p2.x = path->extents.p2.y = INT_MIN;
}

cairo_status_t
_cairo_path_fixed_init_copy (cairo_path_fixed_t *path,
                       const cairo_path_fixed_t *other)
{
    cairo_path_buf_t *buf, *other_buf;
    unsigned int num_points, num_ops;

    VG (VALGRIND_MAKE_MEM_UNDEFINED (path, sizeof (cairo_path_fixed_t)));

    cairo_list_init (&path->buf.base.link);

    path->buf.base.op = path->buf.op;
    path->buf.base.points = path->buf.points;
    path->buf.base.size_ops = ARRAY_LENGTH (path->buf.op);
    path->buf.base.size_points = ARRAY_LENGTH (path->buf.points);

    path->current_point = other->current_point;
    path->last_move_point = other->last_move_point;
    path->has_last_move_point = other->has_last_move_point;
    path->has_current_point = other->has_current_point;
    path->has_curve_to = other->has_curve_to;
    path->is_rectilinear = other->is_rectilinear;
    path->maybe_fill_region = other->maybe_fill_region;
    path->is_empty_fill = other->is_empty_fill;

    path->extents = other->extents;

    path->buf.base.num_ops = other->buf.base.num_ops;
    path->buf.base.num_points = other->buf.base.num_points;
    memcpy (path->buf.op, other->buf.base.op,
          other->buf.base.num_ops * sizeof (other->buf.op[0]));
    memcpy (path->buf.points, other->buf.points,
          other->buf.base.num_points * sizeof (other->buf.points[0]));

    num_points = num_ops = 0;
    for (other_buf = cairo_path_buf_next (cairo_path_head (other));
       other_buf != cairo_path_head (other);
       other_buf = cairo_path_buf_next (other_buf))
    {
      num_ops    += other_buf->num_ops;
      num_points += other_buf->num_points;
    }

    if (num_ops) {
      buf = _cairo_path_buf_create (num_ops, num_points);
      if (unlikely (buf == NULL)) {
          _cairo_path_fixed_fini (path);
          return _cairo_error (CAIRO_STATUS_NO_MEMORY);
      }

      for (other_buf = cairo_path_buf_next (cairo_path_head (other));
           other_buf != cairo_path_head (other);
           other_buf = cairo_path_buf_next (other_buf))
      {
          memcpy (buf->op + buf->num_ops, other_buf->op,
                other_buf->num_ops * sizeof (buf->op[0]));
          buf->num_ops += other_buf->num_ops;

          memcpy (buf->points + buf->num_points, other_buf->points,
                other_buf->num_points * sizeof (buf->points[0]));
          buf->num_points += other_buf->num_points;
      }

      _cairo_path_fixed_add_buf (path, buf);
    }

    return CAIRO_STATUS_SUCCESS;
}

unsigned long
_cairo_path_fixed_hash (const cairo_path_fixed_t *path)
{
    unsigned long hash = _CAIRO_HASH_INIT_VALUE;
    const cairo_path_buf_t *buf;
    int num_points, num_ops;

    hash = _cairo_hash_bytes (hash, &path->extents, sizeof (path->extents));

    num_ops = num_points = 0;
    cairo_path_foreach_buf_start (buf, path) {
      hash = _cairo_hash_bytes (hash, buf->op,
                            buf->num_ops * sizeof (buf->op[0]));
      hash = _cairo_hash_bytes (hash, buf->points,
                            buf->num_points * sizeof (buf->points[0]));

      num_ops    += buf->num_ops;
      num_points += buf->num_points;
    } cairo_path_foreach_buf_end (buf, path);

    hash = _cairo_hash_bytes (hash, &num_ops, sizeof (num_ops));
    hash = _cairo_hash_bytes (hash, &num_points, sizeof (num_points));

    return hash;
}

unsigned long
_cairo_path_fixed_size (const cairo_path_fixed_t *path)
{
    const cairo_path_buf_t *buf;
    int num_points, num_ops;

    num_ops = num_points = 0;
    cairo_path_foreach_buf_start (buf, path) {
      num_ops    += buf->num_ops;
      num_points += buf->num_points;
    } cairo_path_foreach_buf_end (buf, path);

    return num_ops * sizeof (buf->op[0]) +
         num_points * sizeof (buf->points[0]);
}

cairo_bool_t
_cairo_path_fixed_equal (const cairo_path_fixed_t *a,
                   const cairo_path_fixed_t *b)
{
    const cairo_path_buf_t *buf_a, *buf_b;
    const cairo_path_op_t *ops_a, *ops_b;
    const cairo_point_t *points_a, *points_b;
    int num_points_a, num_ops_a;
    int num_points_b, num_ops_b;

    if (a == b)
      return TRUE;

    /* use the flags to quickly differentiate based on contents */
    if (a->is_empty_fill != b->is_empty_fill ||
      a->has_curve_to != b->has_curve_to ||
      a->maybe_fill_region != b->maybe_fill_region ||
      a->is_rectilinear != b->is_rectilinear)
    {
      return FALSE;
    }

    if (a->extents.p1.x != b->extents.p1.x ||
      a->extents.p1.y != b->extents.p1.y ||
      a->extents.p2.x != b->extents.p2.x ||
      a->extents.p2.y != b->extents.p2.y)
    {
      return FALSE;
    }

    num_ops_a = num_points_a = 0;
    cairo_path_foreach_buf_start (buf_a, a) {
      num_ops_a    += buf_a->num_ops;
      num_points_a += buf_a->num_points;
    } cairo_path_foreach_buf_end (buf_a, a);

    num_ops_b = num_points_b = 0;
    cairo_path_foreach_buf_start (buf_b, b) {
      num_ops_b    += buf_b->num_ops;
      num_points_b += buf_b->num_points;
    } cairo_path_foreach_buf_end (buf_b, b);

    if (num_ops_a == 0 && num_ops_b == 0)
      return TRUE;

    if (num_ops_a != num_ops_b || num_points_a != num_points_b)
      return FALSE;

    buf_a = cairo_path_head (a);
    num_points_a = buf_a->num_points;
    num_ops_a = buf_a->num_ops;
    ops_a = buf_a->op;
    points_a = buf_a->points;

    buf_b = cairo_path_head (b);
    num_points_b = buf_b->num_points;
    num_ops_b = buf_b->num_ops;
    ops_b = buf_b->op;
    points_b = buf_b->points;

    while (TRUE) {
      int num_ops = MIN (num_ops_a, num_ops_b);
      int num_points = MIN (num_points_a, num_points_b);

      if (memcmp (ops_a, ops_b, num_ops * sizeof (cairo_path_op_t)))
          return FALSE;
      if (memcmp (points_a, points_b, num_points * sizeof (cairo_point_t)))
          return FALSE;

      num_ops_a -= num_ops;
      ops_a += num_ops;
      num_points_a -= num_points;
      points_a += num_points;
      if (num_ops_a == 0 || num_points_a == 0) {
          if (num_ops_a || num_points_a)
            return FALSE;

          buf_a = cairo_path_buf_next (buf_a);
          if (buf_a == cairo_path_head (a))
            break;

          num_points_a = buf_a->num_points;
          num_ops_a = buf_a->num_ops;
          ops_a = buf_a->op;
          points_a = buf_a->points;
      }

      num_ops_b -= num_ops;
      ops_b += num_ops;
      num_points_b -= num_points;
      points_b += num_points;
      if (num_ops_b == 0 || num_points_b == 0) {
          if (num_ops_b || num_points_b)
            return FALSE;

          buf_b = cairo_path_buf_next (buf_b);
          if (buf_b == cairo_path_head (b))
            break;

          num_points_b = buf_b->num_points;
          num_ops_b = buf_b->num_ops;
          ops_b = buf_b->op;
          points_b = buf_b->points;
      }
    }

    return TRUE;
}

cairo_path_fixed_t *
_cairo_path_fixed_create (void)
{
    cairo_path_fixed_t  *path;

    path = malloc (sizeof (cairo_path_fixed_t));
    if (!path) {
      _cairo_error_throw (CAIRO_STATUS_NO_MEMORY);
      return NULL;
    }

    _cairo_path_fixed_init (path);
    return path;
}

void
_cairo_path_fixed_fini (cairo_path_fixed_t *path)
{
    cairo_path_buf_t *buf;

    buf = cairo_path_buf_next (cairo_path_head (path));
    while (buf != cairo_path_head (path)) {
      cairo_path_buf_t *this = buf;
      buf = cairo_path_buf_next (buf);
      _cairo_path_buf_destroy (this);
    }

    VG (VALGRIND_MAKE_MEM_NOACCESS (path, sizeof (cairo_path_fixed_t)));
}

void
_cairo_path_fixed_destroy (cairo_path_fixed_t *path)
{
    _cairo_path_fixed_fini (path);
    free (path);
}

static cairo_path_op_t
_cairo_path_last_op (cairo_path_fixed_t *path)
{
    cairo_path_buf_t *buf;

    buf = cairo_path_tail (path);
    if (buf->num_ops == 0)
      return -1;

    return buf->op[buf->num_ops - 1];
}

static inline void
_cairo_path_fixed_extents_add (cairo_path_fixed_t *path,
                         const cairo_point_t *point)
{
    if (point->x < path->extents.p1.x)
      path->extents.p1.x = point->x;
    if (point->y < path->extents.p1.y)
      path->extents.p1.y = point->y;

    if (point->x > path->extents.p2.x)
      path->extents.p2.x = point->x;
    if (point->y > path->extents.p2.y)
      path->extents.p2.y = point->y;
}

cairo_status_t
_cairo_path_fixed_move_to (cairo_path_fixed_t  *path,
                     cairo_fixed_t  x,
                     cairo_fixed_t  y)
{
    cairo_status_t status;
    cairo_point_t point;

    point.x = x;
    point.y = y;

    /* If the previous op was also a MOVE_TO, then just change its
     * point rather than adding a new op. */
    if (_cairo_path_last_op (path) == CAIRO_PATH_OP_MOVE_TO) {
      cairo_path_buf_t *buf;

      buf = cairo_path_tail (path);
      buf->points[buf->num_points - 1] = point;
    } else {
      status = _cairo_path_fixed_add (path, CAIRO_PATH_OP_MOVE_TO, &point, 1);
      if (unlikely (status))
          return status;

      if (path->has_current_point && path->is_rectilinear) {
          /* a move-to is first an implicit close */
          path->is_rectilinear = path->current_point.x == path->last_move_point.x ||
                           path->current_point.y == path->last_move_point.y;
          path->maybe_fill_region &= path->is_rectilinear;
      }
      if (path->maybe_fill_region) {
          path->maybe_fill_region =
            _cairo_fixed_is_integer (path->last_move_point.x) &&
            _cairo_fixed_is_integer (path->last_move_point.y);
      }
    }

    path->current_point = point;
    path->last_move_point = point;
    path->has_last_move_point = TRUE;
    path->has_current_point = TRUE;

    return CAIRO_STATUS_SUCCESS;
}

void
_cairo_path_fixed_new_sub_path (cairo_path_fixed_t *path)
{
    path->has_current_point = FALSE;
}

cairo_status_t
_cairo_path_fixed_rel_move_to (cairo_path_fixed_t *path,
                         cairo_fixed_t       dx,
                         cairo_fixed_t       dy)
{
    if (unlikely (! path->has_current_point))
      return _cairo_error (CAIRO_STATUS_NO_CURRENT_POINT);

    return _cairo_path_fixed_move_to (path,
                              path->current_point.x + dx,
                              path->current_point.y + dy);

}

cairo_status_t
_cairo_path_fixed_line_to (cairo_path_fixed_t *path,
                     cairo_fixed_t  x,
                     cairo_fixed_t  y)
{
    cairo_status_t status;
    cairo_point_t point;

    point.x = x;
    point.y = y;

    /* When there is not yet a current point, the line_to operation
     * becomes a move_to instead. Note: We have to do this by
     * explicitly calling into _cairo_path_fixed_move_to to ensure
     * that the last_move_point state is updated properly.
     */
    if (! path->has_current_point)
      return _cairo_path_fixed_move_to (path, point.x, point.y);

    /* If the previous op was but the initial MOVE_TO and this segment
     * is degenerate, then we can simply skip this point. Note that
     * a move-to followed by a degenerate line-to is a valid path for
     * stroking, but at all other times is simply a degenerate segment.
     */
    if (_cairo_path_last_op (path) != CAIRO_PATH_OP_MOVE_TO) {
      if (x == path->current_point.x && y == path->current_point.y)
          return CAIRO_STATUS_SUCCESS;
    }

    /* If the previous op was also a LINE_TO with the same gradient,
     * then just change its end-point rather than adding a new op.
     */
    if (_cairo_path_last_op (path) == CAIRO_PATH_OP_LINE_TO) {
      cairo_path_buf_t *buf;
      const cairo_point_t *p;

      buf = cairo_path_tail (path);
      if (likely (buf->num_points >= 2)) {
          p = &buf->points[buf->num_points-2];
      } else {
          cairo_path_buf_t *prev_buf = cairo_path_buf_prev (buf);
          p = &prev_buf->points[prev_buf->num_points - (2 - buf->num_points)];
      }

      if (p->x == path->current_point.x && p->y == path->current_point.y) {
          /* previous line element was degenerate, replace */
          buf->points[buf->num_points - 1] = point;
          goto FLAGS;
      } else {
          cairo_slope_t prev, self;

          _cairo_slope_init (&prev, p, &path->current_point);
          _cairo_slope_init (&self, &path->current_point, &point);
          if (_cairo_slope_equal (&prev, &self) &&
            /* cannot trim anti-parallel segments whilst stroking */
            ! _cairo_slope_backwards (&prev, &self))
          {
            buf->points[buf->num_points - 1] = point;
            goto FLAGS;
          }
      }
    }

    status = _cairo_path_fixed_add (path, CAIRO_PATH_OP_LINE_TO, &point, 1);
    if (unlikely (status))
      return status;

  FLAGS:
    if (path->is_rectilinear) {
      path->is_rectilinear = path->current_point.x == x ||
                         path->current_point.y == y;
      path->maybe_fill_region &= path->is_rectilinear;
    }
    if (path->maybe_fill_region) {
      path->maybe_fill_region = _cairo_fixed_is_integer (x) &&
                          _cairo_fixed_is_integer (y);
    }
    if (path->is_empty_fill) {
      path->is_empty_fill = path->current_point.x == x &&
                        path->current_point.y == y;
    }

    path->current_point = point;
    if (path->has_last_move_point) {
      _cairo_path_fixed_extents_add (path, &path->last_move_point);
      path->has_last_move_point = FALSE;
    }
    _cairo_path_fixed_extents_add (path, &point);
    return CAIRO_STATUS_SUCCESS;
}

cairo_status_t
_cairo_path_fixed_rel_line_to (cairo_path_fixed_t *path,
                         cairo_fixed_t       dx,
                         cairo_fixed_t       dy)
{
    if (unlikely (! path->has_current_point))
      return _cairo_error (CAIRO_STATUS_NO_CURRENT_POINT);

    return _cairo_path_fixed_line_to (path,
                              path->current_point.x + dx,
                              path->current_point.y + dy);
}

cairo_status_t
_cairo_path_fixed_curve_to (cairo_path_fixed_t  *path,
                      cairo_fixed_t x0, cairo_fixed_t y0,
                      cairo_fixed_t x1, cairo_fixed_t y1,
                      cairo_fixed_t x2, cairo_fixed_t y2)
{
    cairo_status_t status;
    cairo_point_t point[3];

    /* make sure subpaths are started properly */
    if (! path->has_current_point) {
      status = _cairo_path_fixed_move_to (path, x0, y0);
      if (unlikely (status))
          return status;
    }

    point[0].x = x0; point[0].y = y0;
    point[1].x = x1; point[1].y = y1;
    point[2].x = x2; point[2].y = y2;
    status = _cairo_path_fixed_add (path, CAIRO_PATH_OP_CURVE_TO, point, 3);
    if (unlikely (status))
      return status;

    path->current_point = point[2];
    path->has_current_point = TRUE;
    path->is_empty_fill = FALSE;
    path->has_curve_to = TRUE;
    path->is_rectilinear = FALSE;
    path->maybe_fill_region = FALSE;

    /* coarse bounds */
    if (path->has_last_move_point) {
      _cairo_path_fixed_extents_add (path, &path->last_move_point);
      path->has_last_move_point = FALSE;
    }
    _cairo_path_fixed_extents_add (path, &point[0]);
    _cairo_path_fixed_extents_add (path, &point[1]);
    _cairo_path_fixed_extents_add (path, &point[2]);

    return CAIRO_STATUS_SUCCESS;
}

cairo_status_t
_cairo_path_fixed_rel_curve_to (cairo_path_fixed_t *path,
                        cairo_fixed_t dx0, cairo_fixed_t dy0,
                        cairo_fixed_t dx1, cairo_fixed_t dy1,
                        cairo_fixed_t dx2, cairo_fixed_t dy2)
{
    if (unlikely (! path->has_current_point))
      return _cairo_error (CAIRO_STATUS_NO_CURRENT_POINT);

    return _cairo_path_fixed_curve_to (path,
                               path->current_point.x + dx0,
                               path->current_point.y + dy0,

                               path->current_point.x + dx1,
                               path->current_point.y + dy1,

                               path->current_point.x + dx2,
                               path->current_point.y + dy2);
}

cairo_status_t
_cairo_path_fixed_close_path (cairo_path_fixed_t *path)
{
    cairo_status_t status;

    if (! path->has_current_point)
      return CAIRO_STATUS_SUCCESS;

    /* If the previous op was also a LINE_TO back to the start, discard it */
    if (_cairo_path_last_op (path) == CAIRO_PATH_OP_LINE_TO) {
      if (path->current_point.x == path->last_move_point.x &&
          path->current_point.y == path->last_move_point.y)
      {
          cairo_path_buf_t *buf;
          cairo_point_t *p;

          buf = cairo_path_tail (path);
          if (likely (buf->num_points >= 2)) {
            p = &buf->points[buf->num_points-2];
          } else {
            cairo_path_buf_t *prev_buf = cairo_path_buf_prev (buf);
            p = &prev_buf->points[prev_buf->num_points - (2 - buf->num_points)];
          }

          path->current_point = *p;
          buf->num_ops--;
          buf->num_points--;
      }
    }

    status = _cairo_path_fixed_add (path, CAIRO_PATH_OP_CLOSE_PATH, NULL, 0);
    if (unlikely (status))
      return status;

    return _cairo_path_fixed_move_to (path,
                              path->last_move_point.x,
                              path->last_move_point.y);
}

cairo_bool_t
_cairo_path_fixed_get_current_point (cairo_path_fixed_t *path,
                             cairo_fixed_t      *x,
                             cairo_fixed_t      *y)
{
    if (! path->has_current_point)
      return FALSE;

    *x = path->current_point.x;
    *y = path->current_point.y;

    return TRUE;
}

static cairo_status_t
_cairo_path_fixed_add (cairo_path_fixed_t   *path,
                   cairo_path_op_t       op,
                   const cairo_point_t  *points,
                   int             num_points)
{
    cairo_path_buf_t *buf = cairo_path_tail (path);

    if (buf->num_ops + 1 > buf->size_ops ||
      buf->num_points + num_points > buf->size_points)
    {
      buf = _cairo_path_buf_create (buf->num_ops * 2, buf->num_points * 2);
      if (unlikely (buf == NULL))
          return _cairo_error (CAIRO_STATUS_NO_MEMORY);

      _cairo_path_fixed_add_buf (path, buf);
    }

    if (WATCH_PATH) {
      const char *op_str[] = {
          "move-to",
          "line-to",
          "curve-to",
          "close-path",
      };
      char buf[1024];
      int len = 0;
      int i;

      len += snprintf (buf + len, sizeof (buf), "[");
      for (i = 0; i < num_points; i++) {
          if (i != 0)
            len += snprintf (buf + len, sizeof (buf), " ");
          len += snprintf (buf + len, sizeof (buf), "(%f, %f)",
                       _cairo_fixed_to_double (points[i].x),
                       _cairo_fixed_to_double (points[i].y));
      }
      len += snprintf (buf + len, sizeof (buf), "]");

      fprintf (stderr,
             "_cairo_path_fixed_add (%s, %s)\n",
             op_str[(int) op], buf);
    }

    _cairo_path_buf_add_op (buf, op);
    _cairo_path_buf_add_points (buf, points, num_points);

    return CAIRO_STATUS_SUCCESS;
}

static void
_cairo_path_fixed_add_buf (cairo_path_fixed_t *path,
                     cairo_path_buf_t   *buf)
{
    cairo_list_add_tail (&buf->link, &cairo_path_head (path)->link);
}

COMPILE_TIME_ASSERT (sizeof (cairo_path_op_t) == 1);
static cairo_path_buf_t *
_cairo_path_buf_create (int size_ops, int size_points)
{
    cairo_path_buf_t *buf;

    /* adjust size_ops to ensure that buf->points is naturally aligned */
    size_ops += sizeof (double) - ((sizeof (cairo_path_buf_t) + size_ops) % sizeof (double));
    buf = _cairo_malloc_ab_plus_c (size_points, sizeof (cairo_point_t), size_ops + sizeof (cairo_path_buf_t));
    if (buf) {
      buf->num_ops = 0;
      buf->num_points = 0;
      buf->size_ops = size_ops;
      buf->size_points = size_points;

      buf->op = (cairo_path_op_t *) (buf + 1);
      buf->points = (cairo_point_t *) (buf->op + size_ops);
    }

    return buf;
}

static void
_cairo_path_buf_destroy (cairo_path_buf_t *buf)
{
    free (buf);
}

static void
_cairo_path_buf_add_op (cairo_path_buf_t *buf,
                  cairo_path_op_t     op)
{
    buf->op[buf->num_ops++] = op;
}

static void
_cairo_path_buf_add_points (cairo_path_buf_t       *buf,
                      const cairo_point_t    *points,
                      int                       num_points)
{
    memcpy (buf->points + buf->num_points,
          points,
          sizeof (points[0]) * num_points);
    buf->num_points += num_points;
}

cairo_status_t
_cairo_path_fixed_interpret (const cairo_path_fixed_t       *path,
                       cairo_direction_t               dir,
                       cairo_path_fixed_move_to_func_t      *move_to,
                       cairo_path_fixed_line_to_func_t      *line_to,
                       cairo_path_fixed_curve_to_func_t     *curve_to,
                       cairo_path_fixed_close_path_func_t   *close_path,
                       void                     *closure)
{
    const uint8_t num_args[] = {
      1, /* cairo_path_move_to */
      1, /* cairo_path_op_line_to */
      3, /* cairo_path_op_curve_to */
      0, /* cairo_path_op_close_path */
    };
    cairo_status_t status;
    const cairo_path_buf_t *buf, *first;
    cairo_bool_t forward = (dir == CAIRO_DIRECTION_FORWARD);
    int step = forward ? 1 : -1;

    buf = first = forward ? cairo_path_head (path) : cairo_path_tail (path);
    do {
      cairo_point_t *points;
      int start, stop, i;

      if (forward) {
          start = 0;
          stop = buf->num_ops;
          points = buf->points;
      } else {
          start = buf->num_ops - 1;
          stop = -1;
          points = buf->points + buf->num_points;
      }

      for (i = start; i != stop; i += step) {
          cairo_path_op_t op = buf->op[i];

          if (! forward)
            points -= num_args[(int) op];

          switch (op) {
          case CAIRO_PATH_OP_MOVE_TO:
            status = (*move_to) (closure, &points[0]);
            break;
          case CAIRO_PATH_OP_LINE_TO:
            status = (*line_to) (closure, &points[0]);
            break;
          case CAIRO_PATH_OP_CURVE_TO:
            status = (*curve_to) (closure, &points[0], &points[1], &points[2]);
            break;
          default:
            ASSERT_NOT_REACHED;
          case CAIRO_PATH_OP_CLOSE_PATH:
            status = (*close_path) (closure);
            break;
          }
          if (unlikely (status))
            return status;

          if (forward)
            points += num_args[(int) op];
      }
    } while ((buf = forward ? cairo_path_buf_next (buf) : cairo_path_buf_prev (buf)) != first);

    return CAIRO_STATUS_SUCCESS;
}

00849 typedef struct _cairo_path_fixed_append_closure {
    cairo_point_t     offset;
    cairo_path_fixed_t      *path;
} cairo_path_fixed_append_closure_t;

static cairo_status_t
_append_move_to (void          *abstract_closure,
             const cairo_point_t  *point)
{
    cairo_path_fixed_append_closure_t     *closure = abstract_closure;

    return _cairo_path_fixed_move_to (closure->path,
                              point->x + closure->offset.x,
                              point->y + closure->offset.y);
}

static cairo_status_t
_append_line_to (void          *abstract_closure,
             const cairo_point_t *point)
{
    cairo_path_fixed_append_closure_t     *closure = abstract_closure;

    return _cairo_path_fixed_line_to (closure->path,
                              point->x + closure->offset.x,
                              point->y + closure->offset.y);
}

static cairo_status_t
_append_curve_to (void    *abstract_closure,
              const cairo_point_t *p0,
              const cairo_point_t *p1,
              const cairo_point_t *p2)
{
    cairo_path_fixed_append_closure_t     *closure = abstract_closure;

    return _cairo_path_fixed_curve_to (closure->path,
                               p0->x + closure->offset.x,
                               p0->y + closure->offset.y,
                               p1->x + closure->offset.x,
                               p1->y + closure->offset.y,
                               p2->x + closure->offset.x,
                               p2->y + closure->offset.y);
}

static cairo_status_t
_append_close_path (void *abstract_closure)
{
    cairo_path_fixed_append_closure_t     *closure = abstract_closure;

    return _cairo_path_fixed_close_path (closure->path);
}

cairo_status_t
_cairo_path_fixed_append (cairo_path_fixed_t              *path,
                    const cairo_path_fixed_t        *other,
                    cairo_direction_t                dir,
                    cairo_fixed_t                    tx,
                    cairo_fixed_t                    ty)
{
    cairo_path_fixed_append_closure_t closure;

    closure.path = path;
    closure.offset.x = tx;
    closure.offset.y = ty;

    return _cairo_path_fixed_interpret (other, dir,
                              _append_move_to,
                              _append_line_to,
                              _append_curve_to,
                              _append_close_path,
                              &closure);
}

static void
_cairo_path_fixed_offset_and_scale (cairo_path_fixed_t *path,
                            cairo_fixed_t offx,
                            cairo_fixed_t offy,
                            cairo_fixed_t scalex,
                            cairo_fixed_t scaley)
{
    cairo_path_buf_t *buf;
    unsigned int i;

    if (path->maybe_fill_region) {
      path->maybe_fill_region = _cairo_fixed_is_integer (offx) &&
                                _cairo_fixed_is_integer (offy) &&
                            _cairo_fixed_is_integer (scalex) &&
                            _cairo_fixed_is_integer (scaley);
    }

    cairo_path_foreach_buf_start (buf, path) {
       for (i = 0; i < buf->num_points; i++) {
           if (scalex != CAIRO_FIXED_ONE)
             buf->points[i].x = _cairo_fixed_mul (buf->points[i].x, scalex);
           buf->points[i].x += offx;

           if (scaley != CAIRO_FIXED_ONE)
             buf->points[i].y = _cairo_fixed_mul (buf->points[i].y, scaley);
           buf->points[i].y += offy;
       }
    } cairo_path_foreach_buf_end (buf, path);

    path->extents.p1.x = _cairo_fixed_mul (scalex, path->extents.p1.x) + offx;
    path->extents.p2.x = _cairo_fixed_mul (scalex, path->extents.p2.x) + offx;

    path->extents.p1.y = _cairo_fixed_mul (scaley, path->extents.p1.y) + offy;
    path->extents.p2.y = _cairo_fixed_mul (scaley, path->extents.p2.y) + offy;
}

void
_cairo_path_fixed_translate (cairo_path_fixed_t *path,
                       cairo_fixed_t offx,
                       cairo_fixed_t offy)
{
    cairo_path_buf_t *buf;
    unsigned int i;

    if (offx == 0 && offy == 0)
      return;

    if (path->maybe_fill_region &&
      ! (_cairo_fixed_is_integer (offx) && _cairo_fixed_is_integer (offy)))
    {
      path->maybe_fill_region = FALSE;
    }

    path->last_move_point.x += offx;
    path->last_move_point.y += offy;
    path->current_point.x += offx;
    path->current_point.y += offy;

    cairo_path_foreach_buf_start (buf, path) {
       for (i = 0; i < buf->num_points; i++) {
           buf->points[i].x += offx;
           buf->points[i].y += offy;
       }
    } cairo_path_foreach_buf_end (buf, path);

    path->extents.p1.x += offx;
    path->extents.p1.y += offy;
    path->extents.p2.x += offx;
    path->extents.p2.y += offy;
}

/**
 * _cairo_path_fixed_transform:
 * @path: a #cairo_path_fixed_t to be transformed
 * @matrix: a #cairo_matrix_t
 *
 * Transform the fixed-point path according to the given matrix.
 * There is a fast path for the case where @matrix has no rotation
 * or shear.
 **/
void
_cairo_path_fixed_transform (cairo_path_fixed_t *path,
                       const cairo_matrix_t     *matrix)
{
    cairo_path_buf_t *buf;
    unsigned int i;
    double dx, dy;

    /* XXX current_point, last_move_to */

    if (matrix->yx == 0.0 && matrix->xy == 0.0) {
      /* Fast path for the common case of scale+transform */
       if (matrix->xx == 1. && matrix->yy == 1.) {
           _cairo_path_fixed_translate (path,
                                _cairo_fixed_from_double (matrix->x0),
                                _cairo_fixed_from_double (matrix->y0));
       } else {
           _cairo_path_fixed_offset_and_scale (path,
                                     _cairo_fixed_from_double (matrix->x0),
                                     _cairo_fixed_from_double (matrix->y0),
                                     _cairo_fixed_from_double (matrix->xx),
                                     _cairo_fixed_from_double (matrix->yy));
       }
      return;
    }

    path->extents.p1.x = path->extents.p1.y = INT_MAX;
    path->extents.p2.x = path->extents.p2.y = INT_MIN;
    path->maybe_fill_region = FALSE;
    cairo_path_foreach_buf_start (buf, path) {
       for (i = 0; i < buf->num_points; i++) {
          dx = _cairo_fixed_to_double (buf->points[i].x);
          dy = _cairo_fixed_to_double (buf->points[i].y);

          cairo_matrix_transform_point (matrix, &dx, &dy);

          buf->points[i].x = _cairo_fixed_from_double (dx);
          buf->points[i].y = _cairo_fixed_from_double (dy);

          /* XXX need to eliminate surplus move-to's? */
          _cairo_path_fixed_extents_add (path, &buf->points[i]);
       }
    } cairo_path_foreach_buf_end (buf, path);
}

cairo_bool_t
_cairo_path_fixed_is_equal (const cairo_path_fixed_t *path,
                      const cairo_path_fixed_t *other)
{
    const cairo_path_buf_t *path_buf, *other_buf;

    if (path->current_point.x != other->current_point.x ||
      path->current_point.y != other->current_point.y ||
      path->has_current_point != other->has_current_point ||
      path->has_curve_to != other->has_curve_to ||
      path->is_rectilinear != other->is_rectilinear ||
      path->maybe_fill_region != other->maybe_fill_region ||
      path->last_move_point.x != other->last_move_point.x ||
      path->last_move_point.y != other->last_move_point.y)
    {
      return FALSE;
    }

    other_buf = cairo_path_head (other);
    cairo_path_foreach_buf_start (path_buf, path) {
      if (path_buf->num_ops != other_buf->num_ops ||
          path_buf->num_points != other_buf->num_points ||
          memcmp (path_buf->op, other_buf->op,
                sizeof (cairo_path_op_t) * path_buf->num_ops) != 0 ||
          memcmp (path_buf->points, other_buf->points,
                sizeof (cairo_point_t) * path_buf->num_points) != 0)
      {
          return FALSE;
      }
      other_buf = cairo_path_buf_next (other_buf);
    } cairo_path_foreach_buf_end (path_buf, path);

    return TRUE;
}

/* Closure for path flattening */
01083 typedef struct cairo_path_flattener {
    double tolerance;
    cairo_point_t current_point;
    cairo_path_fixed_move_to_func_t *move_to;
    cairo_path_fixed_line_to_func_t *line_to;
    cairo_path_fixed_close_path_func_t    *close_path;
    void *closure;
} cpf_t;

static cairo_status_t
_cpf_move_to (void *closure,
            const cairo_point_t *point)
{
    cpf_t *cpf = closure;

    cpf->current_point = *point;

    return cpf->move_to (cpf->closure, point);
}

static cairo_status_t
_cpf_line_to (void *closure,
            const cairo_point_t *point)
{
    cpf_t *cpf = closure;

    cpf->current_point = *point;

    return cpf->line_to (cpf->closure, point);
}

static cairo_status_t
_cpf_curve_to (void           *closure,
             const cairo_point_t    *p1,
             const cairo_point_t    *p2,
             const cairo_point_t    *p3)
{
    cpf_t *cpf = closure;
    cairo_spline_t spline;

    cairo_point_t *p0 = &cpf->current_point;

    if (! _cairo_spline_init (&spline,
                        cpf->line_to,
                        cpf->closure,
                        p0, p1, p2, p3))
    {
      return _cpf_line_to (closure, p3);
    }

    cpf->current_point = *p3;

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

static cairo_status_t
_cpf_close_path (void *closure)
{
    cpf_t *cpf = closure;

    return cpf->close_path (cpf->closure);
}

cairo_status_t
_cairo_path_fixed_interpret_flat (const cairo_path_fixed_t        *path,
                          cairo_direction_t                 dir,
                          cairo_path_fixed_move_to_func_t   *move_to,
                          cairo_path_fixed_line_to_func_t   *line_to,
                          cairo_path_fixed_close_path_func_t      *close_path,
                          void                              *closure,
                          double                      tolerance)
{
    cpf_t flattener;

    if (! path->has_curve_to) {
      return _cairo_path_fixed_interpret (path, dir,
                                  move_to,
                                  line_to,
                                  NULL,
                                  close_path,
                                  closure);
    }

    flattener.tolerance = tolerance;
    flattener.move_to = move_to;
    flattener.line_to = line_to;
    flattener.close_path = close_path;
    flattener.closure = closure;
    return _cairo_path_fixed_interpret (path, dir,
                              _cpf_move_to,
                              _cpf_line_to,
                              _cpf_curve_to,
                              _cpf_close_path,
                              &flattener);
}

static inline void
_canonical_box (cairo_box_t *box,
            const cairo_point_t *p1,
            const cairo_point_t *p2)
{
    if (p1->x <= p2->x) {
      box->p1.x = p1->x;
      box->p2.x = p2->x;
    } else {
      box->p1.x = p2->x;
      box->p2.x = p1->x;
    }

    if (p1->y <= p2->y) {
      box->p1.y = p1->y;
      box->p2.y = p2->y;
    } else {
      box->p1.y = p2->y;
      box->p2.y = p1->y;
    }
}

/*
 * Check whether the given path contains a single rectangle.
 */
cairo_bool_t
_cairo_path_fixed_is_box (const cairo_path_fixed_t *path,
                    cairo_box_t *box)
{
    const cairo_path_buf_t *buf = cairo_path_head (path);

    if (! path->is_rectilinear)
      return FALSE;

    /* Do we have the right number of ops? */
    if (buf->num_ops < 4 || buf->num_ops > 6)
      return FALSE;

    /* Check whether the ops are those that would be used for a rectangle */
    if (buf->op[0] != CAIRO_PATH_OP_MOVE_TO ||
      buf->op[1] != CAIRO_PATH_OP_LINE_TO ||
      buf->op[2] != CAIRO_PATH_OP_LINE_TO ||
      buf->op[3] != CAIRO_PATH_OP_LINE_TO)
    {
      return FALSE;
    }

    /* we accept an implicit close for filled paths */
    if (buf->num_ops > 4) {
      /* Now, there are choices. The rectangle might end with a LINE_TO
       * (to the original point), but this isn't required. If it
       * doesn't, then it must end with a CLOSE_PATH. */
      if (buf->op[4] == CAIRO_PATH_OP_LINE_TO) {
          if (buf->points[4].x != buf->points[0].x ||
            buf->points[4].y != buf->points[0].y)
            return FALSE;
      } else if (buf->op[4] != CAIRO_PATH_OP_CLOSE_PATH) {
          return FALSE;
      }

      if (buf->num_ops == 6) {
          /* A trailing CLOSE_PATH or MOVE_TO is ok */
          if (buf->op[5] != CAIRO_PATH_OP_MOVE_TO &&
            buf->op[5] != CAIRO_PATH_OP_CLOSE_PATH)
            return FALSE;
      }
    }

    /* Ok, we may have a box, if the points line up */
    if (buf->points[0].y == buf->points[1].y &&
      buf->points[1].x == buf->points[2].x &&
      buf->points[2].y == buf->points[3].y &&
      buf->points[3].x == buf->points[0].x)
    {
      _canonical_box (box, &buf->points[0], &buf->points[2]);
      return TRUE;
    }

    if (buf->points[0].x == buf->points[1].x &&
      buf->points[1].y == buf->points[2].y &&
      buf->points[2].x == buf->points[3].x &&
      buf->points[3].y == buf->points[0].y)
    {
      _canonical_box (box, &buf->points[0], &buf->points[2]);
      return TRUE;
    }

    return FALSE;
}

/*
 * Check whether the given path contains a single rectangle
 * that is logically equivalent to:
 * <informalexample><programlisting>
 *   cairo_move_to (cr, x, y);
 *   cairo_rel_line_to (cr, width, 0);
 *   cairo_rel_line_to (cr, 0, height);
 *   cairo_rel_line_to (cr, -width, 0);
 *   cairo_close_path (cr);
 * </programlisting></informalexample>
 */
cairo_bool_t
_cairo_path_fixed_is_rectangle (const cairo_path_fixed_t *path,
                        cairo_box_t        *box)
{
    const cairo_path_buf_t *buf;

    if (! _cairo_path_fixed_is_box (path, box))
      return FALSE;

    buf = cairo_path_head (path);
    if (buf->points[0].y == buf->points[1].y)
      return TRUE;

    return FALSE;
}

void
_cairo_path_fixed_iter_init (cairo_path_fixed_iter_t *iter,
                       const cairo_path_fixed_t *path)
{
    iter->first = iter->buf = cairo_path_head (path);
    iter->n_op = 0;
    iter->n_point = 0;
}

static cairo_bool_t
_cairo_path_fixed_iter_next_op (cairo_path_fixed_iter_t *iter)
{
    if (++iter->n_op >= iter->buf->num_ops) {
      iter->buf = cairo_path_buf_next (iter->buf);
      if (iter->buf == iter->first) {
          iter->buf = NULL;
          return FALSE;
      }

      iter->n_op = 0;
      iter->n_point = 0;
    }

    return TRUE;
}

cairo_bool_t
_cairo_path_fixed_iter_is_fill_box (cairo_path_fixed_iter_t *_iter,
                            cairo_box_t *box)
{
    cairo_point_t points[5];
    cairo_path_fixed_iter_t iter;

    if (_iter->buf == NULL)
      return FALSE;

    iter = *_iter;

    if (iter.n_op == iter.buf->num_ops &&
      ! _cairo_path_fixed_iter_next_op (&iter))
    {
      return FALSE;
    }

    /* Check whether the ops are those that would be used for a rectangle */
    if (iter.buf->op[iter.n_op] != CAIRO_PATH_OP_MOVE_TO)
      return FALSE;
    points[0] = iter.buf->points[iter.n_point++];
    if (! _cairo_path_fixed_iter_next_op (&iter))
      return FALSE;

    if (iter.buf->op[iter.n_op] != CAIRO_PATH_OP_LINE_TO)
      return FALSE;
    points[1] = iter.buf->points[iter.n_point++];
    if (! _cairo_path_fixed_iter_next_op (&iter))
      return FALSE;

    if (iter.buf->op[iter.n_op] != CAIRO_PATH_OP_LINE_TO)
      return FALSE;
    points[2] = iter.buf->points[iter.n_point++];
    if (! _cairo_path_fixed_iter_next_op (&iter))
      return FALSE;

    if (iter.buf->op[iter.n_op] != CAIRO_PATH_OP_LINE_TO)
      return FALSE;
    points[3] = iter.buf->points[iter.n_point++];
    if (! _cairo_path_fixed_iter_next_op (&iter))
      return FALSE;

    /* Now, there are choices. The rectangle might end with a LINE_TO
     * (to the original point), but this isn't required. If it
     * doesn't, then it must end with a CLOSE_PATH (which may be implicit). */
    if (iter.buf->op[iter.n_op] == CAIRO_PATH_OP_LINE_TO)
    {
      points[4] = iter.buf->points[iter.n_point++];
      if (points[4].x != points[0].x || points[4].y != points[0].y)
          return FALSE;
    }
    else if (! (iter.buf->op[iter.n_op] == CAIRO_PATH_OP_CLOSE_PATH ||
            iter.buf->op[iter.n_op] == CAIRO_PATH_OP_MOVE_TO))
    {
      return FALSE;
    }
    if (! _cairo_path_fixed_iter_next_op (&iter))
      return FALSE;

    /* Ok, we may have a box, if the points line up */
    if (points[0].y == points[1].y &&
      points[1].x == points[2].x &&
      points[2].y == points[3].y &&
      points[3].x == points[0].x)
    {
      box->p1 = points[0];
      box->p2 = points[2];
      *_iter = iter;
      return TRUE;
    }

    if (points[0].x == points[1].x &&
      points[1].y == points[2].y &&
      points[2].x == points[3].x &&
      points[3].y == points[0].y)
    {
      box->p1 = points[1];
      box->p2 = points[3];
      *_iter = iter;
      return TRUE;
    }

    return FALSE;
}

cairo_bool_t
_cairo_path_fixed_iter_at_end (const cairo_path_fixed_iter_t *iter)
{
    if (iter->buf == NULL)
      return TRUE;

    if (iter->n_op == iter->buf->num_ops)
      return TRUE;

    if (iter->buf->op[iter->n_op] == CAIRO_PATH_OP_MOVE_TO &&
      iter->buf->num_ops == iter->n_op + 1)
    {
      return TRUE;
    }

    return FALSE;
}

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