beta-0.89.2

[luatex.git] / source / libs / cairo / cairo-src / src / cairo-pattern.c

/* -*- Mode: c; c-basic-offset: 4; indent-tabs-mode: t; tab-width: 8; -*- */
/* cairo - a vector graphics library with display and print output
 *
 * Copyright © 2004 David Reveman
 * Copyright © 2005 Red Hat, Inc.
 *
 * Permission to use, copy, modify, distribute, and sell this software
 * and its documentation for any purpose is hereby granted without
 * fee, provided that the above copyright notice appear in all copies
 * and that both that copyright notice and this permission notice
 * appear in supporting documentation, and that the name of David
 * Reveman not be used in advertising or publicity pertaining to
 * distribution of the software without specific, written prior
 * permission. David Reveman makes no representations about the
 * suitability of this software for any purpose.  It is provided "as
 * is" without express or implied warranty.
 *
 * DAVID REVEMAN DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS
 * SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
 * FITNESS, IN NO EVENT SHALL DAVID REVEMAN BE LIABLE FOR ANY SPECIAL,
 * INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
 * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR
 * IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 *
 * Authors: David Reveman <davidr@novell.com>
 *          Keith Packard <keithp@keithp.com>
 *          Carl Worth <cworth@cworth.org>
 */

#include "cairoint.h"

#include "cairo-array-private.h"
#include "cairo-error-private.h"
#include "cairo-freed-pool-private.h"
#include "cairo-image-surface-private.h"
#include "cairo-list-inline.h"
#include "cairo-path-private.h"
#include "cairo-pattern-private.h"
#include "cairo-recording-surface-inline.h"
#include "cairo-surface-snapshot-inline.h"

#include <float.h>

#define PIXMAN_MAX_INT ((pixman_fixed_1 >> 1) - pixman_fixed_e) /* need to ensure deltas also fit */

/**
 * SECTION:cairo-pattern
 * @Title: cairo_pattern_t
 * @Short_Description: Sources for drawing
 * @See_Also: #cairo_t, #cairo_surface_t
 *
 * #cairo_pattern_t is the paint with which cairo draws.
 * The primary use of patterns is as the source for all cairo drawing
 * operations, although they can also be used as masks, that is, as the
 * brush too.
 *
 * A cairo pattern is created by using one of the many constructors,
 * of the form
 * <function>cairo_pattern_create_<emphasis>type</emphasis>()</function>
 * or implicitly through
 * <function>cairo_set_source_<emphasis>type</emphasis>()</function>
 * functions.
 **/

static freed_pool_t freed_pattern_pool[5];

static const cairo_solid_pattern_t _cairo_pattern_nil = {
    {
      CAIRO_REFERENCE_COUNT_INVALID,    /* ref_count */
      CAIRO_STATUS_NO_MEMORY,           /* status */
      { 0, 0, 0, NULL },                /* user_data */
      { NULL, NULL },                   /* observers */

      CAIRO_PATTERN_TYPE_SOLID,         /* type */
      CAIRO_FILTER_DEFAULT,             /* filter */
      CAIRO_EXTEND_GRADIENT_DEFAULT,    /* extend */
      FALSE,                            /* has component alpha */
      { 1., 0., 0., 1., 0., 0., },      /* matrix */
      1.0                               /* opacity */
    }
};

static const cairo_solid_pattern_t _cairo_pattern_nil_null_pointer = {
    {
      CAIRO_REFERENCE_COUNT_INVALID,    /* ref_count */
      CAIRO_STATUS_NULL_POINTER,        /* status */
      { 0, 0, 0, NULL },                /* user_data */
      { NULL, NULL },                   /* observers */

      CAIRO_PATTERN_TYPE_SOLID,         /* type */
      CAIRO_FILTER_DEFAULT,             /* filter */
      CAIRO_EXTEND_GRADIENT_DEFAULT,    /* extend */
      FALSE,                            /* has component alpha */
      { 1., 0., 0., 1., 0., 0., },      /* matrix */
      1.0                               /* opacity */
    }
};

const cairo_solid_pattern_t _cairo_pattern_black = {
    {
      CAIRO_REFERENCE_COUNT_INVALID,    /* ref_count */
      CAIRO_STATUS_SUCCESS,             /* status */
      { 0, 0, 0, NULL },                /* user_data */
      { NULL, NULL },                   /* observers */

      CAIRO_PATTERN_TYPE_SOLID,         /* type */
      CAIRO_FILTER_NEAREST,             /* filter */
      CAIRO_EXTEND_REPEAT,              /* extend */
      FALSE,                            /* has component alpha */
      { 1., 0., 0., 1., 0., 0., },      /* matrix */
      1.0                               /* opacity */
    },
    { 0., 0., 0., 1., 0, 0, 0, 0xffff },/* color (double rgba, short rgba) */
};

const cairo_solid_pattern_t _cairo_pattern_clear = {
    {
      CAIRO_REFERENCE_COUNT_INVALID,    /* ref_count */
      CAIRO_STATUS_SUCCESS,             /* status */
      { 0, 0, 0, NULL },                /* user_data */
      { NULL, NULL },                   /* observers */

      CAIRO_PATTERN_TYPE_SOLID,         /* type */
      CAIRO_FILTER_NEAREST,             /* filter */
      CAIRO_EXTEND_REPEAT,              /* extend */
      FALSE,                            /* has component alpha */
      { 1., 0., 0., 1., 0., 0., },      /* matrix */
      1.0                               /* opacity */
    },
    { 0., 0., 0., 0., 0, 0, 0, 0 },/* color (double rgba, short rgba) */
};

const cairo_solid_pattern_t _cairo_pattern_white = {
    {
      CAIRO_REFERENCE_COUNT_INVALID,    /* ref_count */
      CAIRO_STATUS_SUCCESS,             /* status */
      { 0, 0, 0, NULL },                /* user_data */
      { NULL, NULL },                   /* observers */

      CAIRO_PATTERN_TYPE_SOLID,         /* type */
      CAIRO_FILTER_NEAREST,             /* filter */
      CAIRO_EXTEND_REPEAT,              /* extend */
      FALSE,                            /* has component alpha */
      { 1., 0., 0., 1., 0., 0., },      /* matrix */
      1.0                               /* opacity */
    },
    { 1., 1., 1., 1., 0xffff, 0xffff, 0xffff, 0xffff },/* color (double rgba, short rgba) */
};

static void
_cairo_pattern_notify_observers (cairo_pattern_t *pattern,
                                 unsigned int flags)
{
    cairo_pattern_observer_t *pos;

    cairo_list_foreach_entry (pos, cairo_pattern_observer_t, &pattern->observers, link)
        pos->notify (pos, pattern, flags);
}

/**
 * _cairo_pattern_set_error:
 * @pattern: a pattern
 * @status: a status value indicating an error
 *
 * Atomically sets pattern->status to @status and calls _cairo_error;
 * Does nothing if status is %CAIRO_STATUS_SUCCESS.
 *
 * All assignments of an error status to pattern->status should happen
 * through _cairo_pattern_set_error(). Note that due to the nature of
 * the atomic operation, it is not safe to call this function on the nil
 * objects.
 *
 * The purpose of this function is to allow the user to set a
 * breakpoint in _cairo_error() to generate a stack trace for when the
 * user causes cairo to detect an error.
 **/
static cairo_status_t
_cairo_pattern_set_error (cairo_pattern_t *pattern,
                          cairo_status_t status)
{
    if (status == CAIRO_STATUS_SUCCESS)
        return status;

    /* Don't overwrite an existing error. This preserves the first
     * error, which is the most significant. */
    _cairo_status_set_error (&pattern->status, status);

    return _cairo_error (status);
}

void
_cairo_pattern_init (cairo_pattern_t *pattern, cairo_pattern_type_t type)
{
#if HAVE_VALGRIND
    switch (type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_solid_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_SURFACE:
        VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_surface_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_LINEAR:
        VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_linear_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_RADIAL:
        VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_radial_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_MESH:
        VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_mesh_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        break;
    }
#endif

    pattern->type      = type;
    pattern->status    = CAIRO_STATUS_SUCCESS;

    /* Set the reference count to zero for on-stack patterns.
     * Callers needs to explicitly increment the count for heap allocations. */
    CAIRO_REFERENCE_COUNT_INIT (&pattern->ref_count, 0);

    _cairo_user_data_array_init (&pattern->user_data);

    if (type == CAIRO_PATTERN_TYPE_SURFACE ||
        type == CAIRO_PATTERN_TYPE_RASTER_SOURCE)
        pattern->extend = CAIRO_EXTEND_SURFACE_DEFAULT;
    else
        pattern->extend = CAIRO_EXTEND_GRADIENT_DEFAULT;

    pattern->filter    = CAIRO_FILTER_DEFAULT;
    pattern->opacity   = 1.0;

    pattern->has_component_alpha = FALSE;

    cairo_matrix_init_identity (&pattern->matrix);

    cairo_list_init (&pattern->observers);
}

static cairo_status_t
_cairo_gradient_pattern_init_copy (cairo_gradient_pattern_t       *pattern,
                                   const cairo_gradient_pattern_t *other)
{
    if (CAIRO_INJECT_FAULT ())
        return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    if (other->base.type == CAIRO_PATTERN_TYPE_LINEAR)
    {
        cairo_linear_pattern_t *dst = (cairo_linear_pattern_t *) pattern;
        cairo_linear_pattern_t *src = (cairo_linear_pattern_t *) other;

        *dst = *src;
    }
    else
    {
        cairo_radial_pattern_t *dst = (cairo_radial_pattern_t *) pattern;
        cairo_radial_pattern_t *src = (cairo_radial_pattern_t *) other;

        *dst = *src;
    }

    if (other->stops == other->stops_embedded)
        pattern->stops = pattern->stops_embedded;
    else if (other->stops)
    {
        pattern->stops = _cairo_malloc_ab (other->stops_size,
                                           sizeof (cairo_gradient_stop_t));
        if (unlikely (pattern->stops == NULL)) {
            pattern->stops_size = 0;
            pattern->n_stops = 0;
            return _cairo_pattern_set_error (&pattern->base, CAIRO_STATUS_NO_MEMORY);
        }

        memcpy (pattern->stops, other->stops,
                other->n_stops * sizeof (cairo_gradient_stop_t));
    }

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_mesh_pattern_init_copy (cairo_mesh_pattern_t       *pattern,
                               const cairo_mesh_pattern_t *other)
{
    *pattern = *other;

    _cairo_array_init (&pattern->patches,  sizeof (cairo_mesh_patch_t));
    return _cairo_array_append_multiple (&pattern->patches,
                                         _cairo_array_index_const (&other->patches, 0),
                                         _cairo_array_num_elements (&other->patches));
}

cairo_status_t
_cairo_pattern_init_copy (cairo_pattern_t       *pattern,
                          const cairo_pattern_t *other)
{
    cairo_status_t status;

    if (other->status)
        return _cairo_pattern_set_error (pattern, other->status);

    switch (other->type) {
    case CAIRO_PATTERN_TYPE_SOLID: {
        cairo_solid_pattern_t *dst = (cairo_solid_pattern_t *) pattern;
        cairo_solid_pattern_t *src = (cairo_solid_pattern_t *) other;

        VG (VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_solid_pattern_t)));

        *dst = *src;
    } break;
    case CAIRO_PATTERN_TYPE_SURFACE: {
        cairo_surface_pattern_t *dst = (cairo_surface_pattern_t *) pattern;
        cairo_surface_pattern_t *src = (cairo_surface_pattern_t *) other;

        VG (VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_surface_pattern_t)));

        *dst = *src;
        cairo_surface_reference (dst->surface);
    } break;
    case CAIRO_PATTERN_TYPE_LINEAR:
    case CAIRO_PATTERN_TYPE_RADIAL: {
        cairo_gradient_pattern_t *dst = (cairo_gradient_pattern_t *) pattern;
        cairo_gradient_pattern_t *src = (cairo_gradient_pattern_t *) other;

        if (other->type == CAIRO_PATTERN_TYPE_LINEAR) {
            VG (VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_linear_pattern_t)));
        } else {
            VG (VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_radial_pattern_t)));
        }

        status = _cairo_gradient_pattern_init_copy (dst, src);
        if (unlikely (status))
            return status;

    } break;
    case CAIRO_PATTERN_TYPE_MESH: {
        cairo_mesh_pattern_t *dst = (cairo_mesh_pattern_t *) pattern;
        cairo_mesh_pattern_t *src = (cairo_mesh_pattern_t *) other;

        VG (VALGRIND_MAKE_MEM_UNDEFINED (pattern, sizeof (cairo_mesh_pattern_t)));

        status = _cairo_mesh_pattern_init_copy (dst, src);
        if (unlikely (status))
            return status;

    } break;

    case CAIRO_PATTERN_TYPE_RASTER_SOURCE: {
        status = _cairo_raster_source_pattern_init_copy (pattern, other);
        if (unlikely (status))
            return status;
    } break;
    }

    /* The reference count and user_data array are unique to the copy. */
    CAIRO_REFERENCE_COUNT_INIT (&pattern->ref_count, 0);
    _cairo_user_data_array_init (&pattern->user_data);

    return CAIRO_STATUS_SUCCESS;
}

void
_cairo_pattern_init_static_copy (cairo_pattern_t        *pattern,
                                 const cairo_pattern_t *other)
{
    int size;

    assert (other->status == CAIRO_STATUS_SUCCESS);

    switch (other->type) {
    default:
        ASSERT_NOT_REACHED;
    case CAIRO_PATTERN_TYPE_SOLID:
        size = sizeof (cairo_solid_pattern_t);
        break;
    case CAIRO_PATTERN_TYPE_SURFACE:
        size = sizeof (cairo_surface_pattern_t);
        break;
    case CAIRO_PATTERN_TYPE_LINEAR:
        size = sizeof (cairo_linear_pattern_t);
        break;
    case CAIRO_PATTERN_TYPE_RADIAL:
        size = sizeof (cairo_radial_pattern_t);
        break;
    case CAIRO_PATTERN_TYPE_MESH:
        size = sizeof (cairo_mesh_pattern_t);
        break;
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        size = sizeof (cairo_raster_source_pattern_t);
        break;
    }

    memcpy (pattern, other, size);

    CAIRO_REFERENCE_COUNT_INIT (&pattern->ref_count, 0);
    _cairo_user_data_array_init (&pattern->user_data);
}

cairo_status_t
_cairo_pattern_init_snapshot (cairo_pattern_t       *pattern,
                              const cairo_pattern_t *other)
{
    cairo_status_t status;

    /* We don't bother doing any fancy copy-on-write implementation
     * for the pattern's data. It's generally quite tiny. */
    status = _cairo_pattern_init_copy (pattern, other);
    if (unlikely (status))
        return status;

    /* But we do let the surface snapshot stuff be as fancy as it
     * would like to be. */
    if (pattern->type == CAIRO_PATTERN_TYPE_SURFACE) {
        cairo_surface_pattern_t *surface_pattern =
            (cairo_surface_pattern_t *) pattern;
        cairo_surface_t *surface = surface_pattern->surface;

        surface_pattern->surface = _cairo_surface_snapshot (surface);

        cairo_surface_destroy (surface);

        status = surface_pattern->surface->status;
    } else if (pattern->type == CAIRO_PATTERN_TYPE_RASTER_SOURCE)
        status = _cairo_raster_source_pattern_snapshot (pattern);

    return status;
}

void
_cairo_pattern_fini (cairo_pattern_t *pattern)
{
    _cairo_user_data_array_fini (&pattern->user_data);

    switch (pattern->type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        break;
    case CAIRO_PATTERN_TYPE_SURFACE: {
        cairo_surface_pattern_t *surface_pattern =
            (cairo_surface_pattern_t *) pattern;

        cairo_surface_destroy (surface_pattern->surface);
    } break;
    case CAIRO_PATTERN_TYPE_LINEAR:
    case CAIRO_PATTERN_TYPE_RADIAL: {
        cairo_gradient_pattern_t *gradient =
            (cairo_gradient_pattern_t *) pattern;

        if (gradient->stops && gradient->stops != gradient->stops_embedded)
            free (gradient->stops);
    } break;
    case CAIRO_PATTERN_TYPE_MESH: {
        cairo_mesh_pattern_t *mesh =
            (cairo_mesh_pattern_t *) pattern;

        _cairo_array_fini (&mesh->patches);
    } break;
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        _cairo_raster_source_pattern_finish (pattern);
        break;
    }

#if HAVE_VALGRIND
    switch (pattern->type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        VALGRIND_MAKE_MEM_NOACCESS (pattern, sizeof (cairo_solid_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_SURFACE:
        VALGRIND_MAKE_MEM_NOACCESS (pattern, sizeof (cairo_surface_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_LINEAR:
        VALGRIND_MAKE_MEM_NOACCESS (pattern, sizeof (cairo_linear_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_RADIAL:
        VALGRIND_MAKE_MEM_NOACCESS (pattern, sizeof (cairo_radial_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_MESH:
        VALGRIND_MAKE_MEM_NOACCESS (pattern, sizeof (cairo_mesh_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        break;
    }
#endif
}

cairo_status_t
_cairo_pattern_create_copy (cairo_pattern_t       **pattern_out,
                            const cairo_pattern_t  *other)
{
    cairo_pattern_t *pattern;
    cairo_status_t status;

    if (other->status)
        return other->status;

    switch (other->type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        pattern = malloc (sizeof (cairo_solid_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_SURFACE:
        pattern = malloc (sizeof (cairo_surface_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_LINEAR:
        pattern = malloc (sizeof (cairo_linear_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_RADIAL:
        pattern = malloc (sizeof (cairo_radial_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_MESH:
        pattern = malloc (sizeof (cairo_mesh_pattern_t));
        break;
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        pattern = malloc (sizeof (cairo_raster_source_pattern_t));
        break;
    default:
        ASSERT_NOT_REACHED;
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
    }
    if (unlikely (pattern == NULL))
        return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    status = _cairo_pattern_init_copy (pattern, other);
    if (unlikely (status)) {
        free (pattern);
        return status;
    }

    CAIRO_REFERENCE_COUNT_INIT (&pattern->ref_count, 1);
    *pattern_out = pattern;
    return CAIRO_STATUS_SUCCESS;
}

void
_cairo_pattern_init_solid (cairo_solid_pattern_t *pattern,
                           const cairo_color_t   *color)
{
    _cairo_pattern_init (&pattern->base, CAIRO_PATTERN_TYPE_SOLID);
    pattern->color = *color;
}

void
_cairo_pattern_init_for_surface (cairo_surface_pattern_t *pattern,
                                 cairo_surface_t         *surface)
{
    if (surface->status) {
        /* Force to solid to simplify the pattern_fini process. */
        _cairo_pattern_init (&pattern->base, CAIRO_PATTERN_TYPE_SOLID);
        _cairo_pattern_set_error (&pattern->base, surface->status);
        return;
    }

    _cairo_pattern_init (&pattern->base, CAIRO_PATTERN_TYPE_SURFACE);

    pattern->surface = cairo_surface_reference (surface);
}

static void
_cairo_pattern_init_gradient (cairo_gradient_pattern_t *pattern,
                              cairo_pattern_type_t     type)
{
    _cairo_pattern_init (&pattern->base, type);

    pattern->n_stops    = 0;
    pattern->stops_size = 0;
    pattern->stops      = NULL;
}

static void
_cairo_pattern_init_linear (cairo_linear_pattern_t *pattern,
                            double x0, double y0, double x1, double y1)
{
    _cairo_pattern_init_gradient (&pattern->base, CAIRO_PATTERN_TYPE_LINEAR);

    pattern->pd1.x = x0;
    pattern->pd1.y = y0;
    pattern->pd2.x = x1;
    pattern->pd2.y = y1;
}

static void
_cairo_pattern_init_radial (cairo_radial_pattern_t *pattern,
                            double cx0, double cy0, double radius0,
                            double cx1, double cy1, double radius1)
{
    _cairo_pattern_init_gradient (&pattern->base, CAIRO_PATTERN_TYPE_RADIAL);

    pattern->cd1.center.x = cx0;
    pattern->cd1.center.y = cy0;
    pattern->cd1.radius   = fabs (radius0);
    pattern->cd2.center.x = cx1;
    pattern->cd2.center.y = cy1;
    pattern->cd2.radius   = fabs (radius1);
}

cairo_pattern_t *
_cairo_pattern_create_solid (const cairo_color_t *color)
{
    cairo_solid_pattern_t *pattern;

    pattern =
        _freed_pool_get (&freed_pattern_pool[CAIRO_PATTERN_TYPE_SOLID]);
    if (unlikely (pattern == NULL)) {
        /* None cached, need to create a new pattern. */
        pattern = malloc (sizeof (cairo_solid_pattern_t));
        if (unlikely (pattern == NULL)) {
            _cairo_error_throw (CAIRO_STATUS_NO_MEMORY);
            return (cairo_pattern_t *) &_cairo_pattern_nil;
        }
    }

    _cairo_pattern_init_solid (pattern, color);
    CAIRO_REFERENCE_COUNT_INIT (&pattern->base.ref_count, 1);

    return &pattern->base;
}

cairo_pattern_t *
_cairo_pattern_create_in_error (cairo_status_t status)
{
    cairo_pattern_t *pattern;

    if (status == CAIRO_STATUS_NO_MEMORY)
        return (cairo_pattern_t *)&_cairo_pattern_nil.base;

    CAIRO_MUTEX_INITIALIZE ();

    pattern = _cairo_pattern_create_solid (CAIRO_COLOR_BLACK);
    if (pattern->status == CAIRO_STATUS_SUCCESS)
        status = _cairo_pattern_set_error (pattern, status);

    return pattern;
}

/**
 * cairo_pattern_create_rgb:
 * @red: red component of the color
 * @green: green component of the color
 * @blue: blue component of the color
 *
 * Creates a new #cairo_pattern_t corresponding to an opaque color.  The
 * color components are floating point numbers in the range 0 to 1.
 * If the values passed in are outside that range, they will be
 * clamped.
 *
 * Return value: the newly created #cairo_pattern_t if successful, or
 * an error pattern in case of no memory.  The caller owns the
 * returned object and should call cairo_pattern_destroy() when
 * finished with it.
 *
 * This function will always return a valid pointer, but if an error
 * occurred the pattern status will be set to an error.  To inspect
 * the status of a pattern use cairo_pattern_status().
 *
 * Since: 1.0
 **/
cairo_pattern_t *
cairo_pattern_create_rgb (double red, double green, double blue)
{
    return cairo_pattern_create_rgba (red, green, blue, 1.0);
}
slim_hidden_def (cairo_pattern_create_rgb);

/**
 * cairo_pattern_create_rgba:
 * @red: red component of the color
 * @green: green component of the color
 * @blue: blue component of the color
 * @alpha: alpha component of the color
 *
 * Creates a new #cairo_pattern_t corresponding to a translucent color.
 * The color components are floating point numbers in the range 0 to
 * 1.  If the values passed in are outside that range, they will be
 * clamped.
 *
 * Return value: the newly created #cairo_pattern_t if successful, or
 * an error pattern in case of no memory.  The caller owns the
 * returned object and should call cairo_pattern_destroy() when
 * finished with it.
 *
 * This function will always return a valid pointer, but if an error
 * occurred the pattern status will be set to an error.  To inspect
 * the status of a pattern use cairo_pattern_status().
 *
 * Since: 1.0
 **/
cairo_pattern_t *
cairo_pattern_create_rgba (double red, double green, double blue,
                           double alpha)
{
    cairo_color_t color;

    red   = _cairo_restrict_value (red,   0.0, 1.0);
    green = _cairo_restrict_value (green, 0.0, 1.0);
    blue  = _cairo_restrict_value (blue,  0.0, 1.0);
    alpha = _cairo_restrict_value (alpha, 0.0, 1.0);

    _cairo_color_init_rgba (&color, red, green, blue, alpha);

    CAIRO_MUTEX_INITIALIZE ();

    return _cairo_pattern_create_solid (&color);
}
slim_hidden_def (cairo_pattern_create_rgba);

/**
 * cairo_pattern_create_for_surface:
 * @surface: the surface
 *
 * Create a new #cairo_pattern_t for the given surface.
 *
 * Return value: the newly created #cairo_pattern_t if successful, or
 * an error pattern in case of no memory.  The caller owns the
 * returned object and should call cairo_pattern_destroy() when
 * finished with it.
 *
 * This function will always return a valid pointer, but if an error
 * occurred the pattern status will be set to an error.  To inspect
 * the status of a pattern use cairo_pattern_status().
 *
 * Since: 1.0
 **/
cairo_pattern_t *
cairo_pattern_create_for_surface (cairo_surface_t *surface)
{
    cairo_surface_pattern_t *pattern;

    if (surface == NULL) {
        _cairo_error_throw (CAIRO_STATUS_NULL_POINTER);
        return (cairo_pattern_t*) &_cairo_pattern_nil_null_pointer;
    }

    if (surface->status)
        return _cairo_pattern_create_in_error (surface->status);

    pattern =
        _freed_pool_get (&freed_pattern_pool[CAIRO_PATTERN_TYPE_SURFACE]);
    if (unlikely (pattern == NULL)) {
        pattern = malloc (sizeof (cairo_surface_pattern_t));
        if (unlikely (pattern == NULL)) {
            _cairo_error_throw (CAIRO_STATUS_NO_MEMORY);
            return (cairo_pattern_t *)&_cairo_pattern_nil.base;
        }
    }

    CAIRO_MUTEX_INITIALIZE ();

    _cairo_pattern_init_for_surface (pattern, surface);
    CAIRO_REFERENCE_COUNT_INIT (&pattern->base.ref_count, 1);

    return &pattern->base;
}
slim_hidden_def (cairo_pattern_create_for_surface);

/**
 * cairo_pattern_create_linear:
 * @x0: x coordinate of the start point
 * @y0: y coordinate of the start point
 * @x1: x coordinate of the end point
 * @y1: y coordinate of the end point
 *
 * Create a new linear gradient #cairo_pattern_t along the line defined
 * by (x0, y0) and (x1, y1).  Before using the gradient pattern, a
 * number of color stops should be defined using
 * cairo_pattern_add_color_stop_rgb() or
 * cairo_pattern_add_color_stop_rgba().
 *
 * Note: The coordinates here are in pattern space. For a new pattern,
 * pattern space is identical to user space, but the relationship
 * between the spaces can be changed with cairo_pattern_set_matrix().
 *
 * Return value: the newly created #cairo_pattern_t if successful, or
 * an error pattern in case of no memory.  The caller owns the
 * returned object and should call cairo_pattern_destroy() when
 * finished with it.
 *
 * This function will always return a valid pointer, but if an error
 * occurred the pattern status will be set to an error.  To inspect
 * the status of a pattern use cairo_pattern_status().
 *
 * Since: 1.0
 **/
cairo_pattern_t *
cairo_pattern_create_linear (double x0, double y0, double x1, double y1)
{
    cairo_linear_pattern_t *pattern;

    pattern =
        _freed_pool_get (&freed_pattern_pool[CAIRO_PATTERN_TYPE_LINEAR]);
    if (unlikely (pattern == NULL)) {
        pattern = malloc (sizeof (cairo_linear_pattern_t));
        if (unlikely (pattern == NULL)) {
            _cairo_error_throw (CAIRO_STATUS_NO_MEMORY);
            return (cairo_pattern_t *) &_cairo_pattern_nil.base;
        }
    }

    CAIRO_MUTEX_INITIALIZE ();

    _cairo_pattern_init_linear (pattern, x0, y0, x1, y1);
    CAIRO_REFERENCE_COUNT_INIT (&pattern->base.base.ref_count, 1);

    return &pattern->base.base;
}

/**
 * cairo_pattern_create_radial:
 * @cx0: x coordinate for the center of the start circle
 * @cy0: y coordinate for the center of the start circle
 * @radius0: radius of the start circle
 * @cx1: x coordinate for the center of the end circle
 * @cy1: y coordinate for the center of the end circle
 * @radius1: radius of the end circle
 *
 * Creates a new radial gradient #cairo_pattern_t between the two
 * circles defined by (cx0, cy0, radius0) and (cx1, cy1, radius1).  Before using the
 * gradient pattern, a number of color stops should be defined using
 * cairo_pattern_add_color_stop_rgb() or
 * cairo_pattern_add_color_stop_rgba().
 *
 * Note: The coordinates here are in pattern space. For a new pattern,
 * pattern space is identical to user space, but the relationship
 * between the spaces can be changed with cairo_pattern_set_matrix().
 *
 * Return value: the newly created #cairo_pattern_t if successful, or
 * an error pattern in case of no memory.  The caller owns the
 * returned object and should call cairo_pattern_destroy() when
 * finished with it.
 *
 * This function will always return a valid pointer, but if an error
 * occurred the pattern status will be set to an error.  To inspect
 * the status of a pattern use cairo_pattern_status().
 *
 * Since: 1.0
 **/
cairo_pattern_t *
cairo_pattern_create_radial (double cx0, double cy0, double radius0,
                             double cx1, double cy1, double radius1)
{
    cairo_radial_pattern_t *pattern;

    pattern =
        _freed_pool_get (&freed_pattern_pool[CAIRO_PATTERN_TYPE_RADIAL]);
    if (unlikely (pattern == NULL)) {
        pattern = malloc (sizeof (cairo_radial_pattern_t));
        if (unlikely (pattern == NULL)) {
            _cairo_error_throw (CAIRO_STATUS_NO_MEMORY);
            return (cairo_pattern_t *) &_cairo_pattern_nil.base;
        }
    }

    CAIRO_MUTEX_INITIALIZE ();

    _cairo_pattern_init_radial (pattern, cx0, cy0, radius0, cx1, cy1, radius1);
    CAIRO_REFERENCE_COUNT_INIT (&pattern->base.base.ref_count, 1);

    return &pattern->base.base;
}

/* This order is specified in the diagram in the documentation for
 * cairo_pattern_create_mesh() */
static const int mesh_path_point_i[12] = { 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 2, 1 };
static const int mesh_path_point_j[12] = { 0, 1, 2, 3, 3, 3, 3, 2, 1, 0, 0, 0 };
static const int mesh_control_point_i[4] = { 1, 1, 2, 2 };
static const int mesh_control_point_j[4] = { 1, 2, 2, 1 };

/**
 * cairo_pattern_create_mesh:
 *
 * Create a new mesh pattern.
 *
 * Mesh patterns are tensor-product patch meshes (type 7 shadings in
 * PDF). Mesh patterns may also be used to create other types of
 * shadings that are special cases of tensor-product patch meshes such
 * as Coons patch meshes (type 6 shading in PDF) and Gouraud-shaded
 * triangle meshes (type 4 and 5 shadings in PDF).
 *
 * Mesh patterns consist of one or more tensor-product patches, which
 * should be defined before using the mesh pattern. Using a mesh
 * pattern with a partially defined patch as source or mask will put
 * the context in an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * A tensor-product patch is defined by 4 Bézier curves (side 0, 1, 2,
 * 3) and by 4 additional control points (P0, P1, P2, P3) that provide
 * further control over the patch and complete the definition of the
 * tensor-product patch. The corner C0 is the first point of the
 * patch.
 *
 * Degenerate sides are permitted so straight lines may be used. A
 * zero length line on one side may be used to create 3 sided patches.
 *
 * <informalexample><screen>
 *       C1     Side 1       C2
 *        +---------------+
 *        |               |
 *        |  P1       P2  |
 *        |               |
 * Side 0 |               | Side 2
 *        |               |
 *        |               |
 *        |  P0       P3  |
 *        |               |
 *        +---------------+
 *      C0     Side 3        C3
 * </screen></informalexample>
 *
 * Each patch is constructed by first calling
 * cairo_mesh_pattern_begin_patch(), then cairo_mesh_pattern_move_to()
 * to specify the first point in the patch (C0). Then the sides are
 * specified with calls to cairo_mesh_pattern_curve_to() and
 * cairo_mesh_pattern_line_to().
 *
 * The four additional control points (P0, P1, P2, P3) in a patch can
 * be specified with cairo_mesh_pattern_set_control_point().
 *
 * At each corner of the patch (C0, C1, C2, C3) a color may be
 * specified with cairo_mesh_pattern_set_corner_color_rgb() or
 * cairo_mesh_pattern_set_corner_color_rgba(). Any corner whose color
 * is not explicitly specified defaults to transparent black.
 *
 * A Coons patch is a special case of the tensor-product patch where
 * the control points are implicitly defined by the sides of the
 * patch. The default value for any control point not specified is the
 * implicit value for a Coons patch, i.e. if no control points are
 * specified the patch is a Coons patch.
 *
 * A triangle is a special case of the tensor-product patch where the
 * control points are implicitly defined by the sides of the patch,
 * all the sides are lines and one of them has length 0, i.e. if the
 * patch is specified using just 3 lines, it is a triangle. If the
 * corners connected by the 0-length side have the same color, the
 * patch is a Gouraud-shaded triangle.
 *
 * Patches may be oriented differently to the above diagram. For
 * example the first point could be at the top left. The diagram only
 * shows the relationship between the sides, corners and control
 * points. Regardless of where the first point is located, when
 * specifying colors, corner 0 will always be the first point, corner
 * 1 the point between side 0 and side 1 etc.
 *
 * Calling cairo_mesh_pattern_end_patch() completes the current
 * patch. If less than 4 sides have been defined, the first missing
 * side is defined as a line from the current point to the first point
 * of the patch (C0) and the other sides are degenerate lines from C0
 * to C0. The corners between the added sides will all be coincident
 * with C0 of the patch and their color will be set to be the same as
 * the color of C0.
 *
 * Additional patches may be added with additional calls to
 * cairo_mesh_pattern_begin_patch()/cairo_mesh_pattern_end_patch().
 *
 * <informalexample><programlisting>
 * cairo_pattern_t *pattern = cairo_pattern_create_mesh ();
 *
 * /&ast; Add a Coons patch &ast;/
 * cairo_mesh_pattern_begin_patch (pattern);
 * cairo_mesh_pattern_move_to (pattern, 0, 0);
 * cairo_mesh_pattern_curve_to (pattern, 30, -30,  60,  30, 100, 0);
 * cairo_mesh_pattern_curve_to (pattern, 60,  30, 130,  60, 100, 100);
 * cairo_mesh_pattern_curve_to (pattern, 60,  70,  30, 130,   0, 100);
 * cairo_mesh_pattern_curve_to (pattern, 30,  70, -30,  30,   0, 0);
 * cairo_mesh_pattern_set_corner_color_rgb (pattern, 0, 1, 0, 0);
 * cairo_mesh_pattern_set_corner_color_rgb (pattern, 1, 0, 1, 0);
 * cairo_mesh_pattern_set_corner_color_rgb (pattern, 2, 0, 0, 1);
 * cairo_mesh_pattern_set_corner_color_rgb (pattern, 3, 1, 1, 0);
 * cairo_mesh_pattern_end_patch (pattern);
 *
 * /&ast; Add a Gouraud-shaded triangle &ast;/
 * cairo_mesh_pattern_begin_patch (pattern)
 * cairo_mesh_pattern_move_to (pattern, 100, 100);
 * cairo_mesh_pattern_line_to (pattern, 130, 130);
 * cairo_mesh_pattern_line_to (pattern, 130,  70);
 * cairo_mesh_pattern_set_corner_color_rgb (pattern, 0, 1, 0, 0);
 * cairo_mesh_pattern_set_corner_color_rgb (pattern, 1, 0, 1, 0);
 * cairo_mesh_pattern_set_corner_color_rgb (pattern, 2, 0, 0, 1);
 * cairo_mesh_pattern_end_patch (pattern)
 * </programlisting></informalexample>
 *
 * When two patches overlap, the last one that has been added is drawn
 * over the first one.
 *
 * When a patch folds over itself, points are sorted depending on
 * their parameter coordinates inside the patch. The v coordinate
 * ranges from 0 to 1 when moving from side 3 to side 1; the u
 * coordinate ranges from 0 to 1 when going from side 0 to side
 * 2. Points with higher v coordinate hide points with lower v
 * coordinate. When two points have the same v coordinate, the one
 * with higher u coordinate is above. This means that points nearer to
 * side 1 are above points nearer to side 3; when this is not
 * sufficient to decide which point is above (for example when both
 * points belong to side 1 or side 3) points nearer to side 2 are
 * above points nearer to side 0.
 *
 * For a complete definition of tensor-product patches, see the PDF
 * specification (ISO32000), which describes the parametrization in
 * detail.
 *
 * Note: The coordinates are always in pattern space. For a new
 * pattern, pattern space is identical to user space, but the
 * relationship between the spaces can be changed with
 * cairo_pattern_set_matrix().
 *
 * Return value: the newly created #cairo_pattern_t if successful, or
 * an error pattern in case of no memory. The caller owns the returned
 * object and should call cairo_pattern_destroy() when finished with
 * it.
 *
 * This function will always return a valid pointer, but if an error
 * occurred the pattern status will be set to an error. To inspect the
 * status of a pattern use cairo_pattern_status().
 *
 * Since: 1.12
 **/
cairo_pattern_t *
cairo_pattern_create_mesh (void)
{
    cairo_mesh_pattern_t *pattern;

    pattern =
        _freed_pool_get (&freed_pattern_pool[CAIRO_PATTERN_TYPE_MESH]);
    if (unlikely (pattern == NULL)) {
        pattern = malloc (sizeof (cairo_mesh_pattern_t));
        if (unlikely (pattern == NULL)) {
            _cairo_error_throw (CAIRO_STATUS_NO_MEMORY);
            return (cairo_pattern_t *) &_cairo_pattern_nil.base;
        }
    }

    CAIRO_MUTEX_INITIALIZE ();

    _cairo_pattern_init (&pattern->base, CAIRO_PATTERN_TYPE_MESH);
    _cairo_array_init (&pattern->patches, sizeof (cairo_mesh_patch_t));
    pattern->current_patch = NULL;
    CAIRO_REFERENCE_COUNT_INIT (&pattern->base.ref_count, 1);

    return &pattern->base;
}

/**
 * cairo_pattern_reference:
 * @pattern: a #cairo_pattern_t
 *
 * Increases the reference count on @pattern by one. This prevents
 * @pattern from being destroyed until a matching call to
 * cairo_pattern_destroy() is made.
 *
 * The number of references to a #cairo_pattern_t can be get using
 * cairo_pattern_get_reference_count().
 *
 * Return value: the referenced #cairo_pattern_t.
 *
 * Since: 1.0
 **/
cairo_pattern_t *
cairo_pattern_reference (cairo_pattern_t *pattern)
{
    if (pattern == NULL ||
            CAIRO_REFERENCE_COUNT_IS_INVALID (&pattern->ref_count))
        return pattern;

    assert (CAIRO_REFERENCE_COUNT_HAS_REFERENCE (&pattern->ref_count));

    _cairo_reference_count_inc (&pattern->ref_count);

    return pattern;
}
slim_hidden_def (cairo_pattern_reference);

/**
 * cairo_pattern_get_type:
 * @pattern: a #cairo_pattern_t
 *
 * This function returns the type a pattern.
 * See #cairo_pattern_type_t for available types.
 *
 * Return value: The type of @pattern.
 *
 * Since: 1.2
 **/
cairo_pattern_type_t
cairo_pattern_get_type (cairo_pattern_t *pattern)
{
    return pattern->type;
}

/**
 * cairo_pattern_status:
 * @pattern: a #cairo_pattern_t
 *
 * Checks whether an error has previously occurred for this
 * pattern.
 *
 * Return value: %CAIRO_STATUS_SUCCESS, %CAIRO_STATUS_NO_MEMORY,
 * %CAIRO_STATUS_INVALID_MATRIX, %CAIRO_STATUS_PATTERN_TYPE_MISMATCH,
 * or %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.0
 **/
cairo_status_t
cairo_pattern_status (cairo_pattern_t *pattern)
{
    return pattern->status;
}

/**
 * cairo_pattern_destroy:
 * @pattern: a #cairo_pattern_t
 *
 * Decreases the reference count on @pattern by one. If the result is
 * zero, then @pattern and all associated resources are freed.  See
 * cairo_pattern_reference().
 *
 * Since: 1.0
 **/
void
cairo_pattern_destroy (cairo_pattern_t *pattern)
{
    cairo_pattern_type_t type;

    if (pattern == NULL ||
            CAIRO_REFERENCE_COUNT_IS_INVALID (&pattern->ref_count))
        return;

    assert (CAIRO_REFERENCE_COUNT_HAS_REFERENCE (&pattern->ref_count));

    if (! _cairo_reference_count_dec_and_test (&pattern->ref_count))
        return;

    type = pattern->type;
    _cairo_pattern_fini (pattern);

    /* maintain a small cache of freed patterns */
    if (type < ARRAY_LENGTH (freed_pattern_pool))
        _freed_pool_put (&freed_pattern_pool[type], pattern);
    else
        free (pattern);
}
slim_hidden_def (cairo_pattern_destroy);

/**
 * cairo_pattern_get_reference_count:
 * @pattern: a #cairo_pattern_t
 *
 * Returns the current reference count of @pattern.
 *
 * Return value: the current reference count of @pattern.  If the
 * object is a nil object, 0 will be returned.
 *
 * Since: 1.4
 **/
unsigned int
cairo_pattern_get_reference_count (cairo_pattern_t *pattern)
{
    if (pattern == NULL ||
            CAIRO_REFERENCE_COUNT_IS_INVALID (&pattern->ref_count))
        return 0;

    return CAIRO_REFERENCE_COUNT_GET_VALUE (&pattern->ref_count);
}

/**
 * cairo_pattern_get_user_data:
 * @pattern: a #cairo_pattern_t
 * @key: the address of the #cairo_user_data_key_t the user data was
 * attached to
 *
 * Return user data previously attached to @pattern using the
 * specified key.  If no user data has been attached with the given
 * key this function returns %NULL.
 *
 * Return value: the user data previously attached or %NULL.
 *
 * Since: 1.4
 **/
void *
cairo_pattern_get_user_data (cairo_pattern_t             *pattern,
                             const cairo_user_data_key_t *key)
{
    return _cairo_user_data_array_get_data (&pattern->user_data,
                                            key);
}

/**
 * cairo_pattern_set_user_data:
 * @pattern: a #cairo_pattern_t
 * @key: the address of a #cairo_user_data_key_t to attach the user data to
 * @user_data: the user data to attach to the #cairo_pattern_t
 * @destroy: a #cairo_destroy_func_t which will be called when the
 * #cairo_t is destroyed or when new user data is attached using the
 * same key.
 *
 * Attach user data to @pattern.  To remove user data from a surface,
 * call this function with the key that was used to set it and %NULL
 * for @data.
 *
 * Return value: %CAIRO_STATUS_SUCCESS or %CAIRO_STATUS_NO_MEMORY if a
 * slot could not be allocated for the user data.
 *
 * Since: 1.4
 **/
cairo_status_t
cairo_pattern_set_user_data (cairo_pattern_t             *pattern,
                             const cairo_user_data_key_t *key,
                             void                        *user_data,
                             cairo_destroy_func_t         destroy)
{
    if (CAIRO_REFERENCE_COUNT_IS_INVALID (&pattern->ref_count))
        return pattern->status;

    return _cairo_user_data_array_set_data (&pattern->user_data,
                                            key, user_data, destroy);
}

/**
 * cairo_mesh_pattern_begin_patch:
 * @pattern: a #cairo_pattern_t
 *
 * Begin a patch in a mesh pattern.
 *
 * After calling this function, the patch shape should be defined with
 * cairo_mesh_pattern_move_to(), cairo_mesh_pattern_line_to() and
 * cairo_mesh_pattern_curve_to().
 *
 * After defining the patch, cairo_mesh_pattern_end_patch() must be
 * called before using @pattern as a source or mask.
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @pattern already has a
 * current patch, it will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_begin_patch (cairo_pattern_t *pattern)
{
    cairo_mesh_pattern_t *mesh;
    cairo_status_t status;
    cairo_mesh_patch_t *current_patch;
    int i;

    if (unlikely (pattern->status))
        return;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    mesh = (cairo_mesh_pattern_t *) pattern;
    if (unlikely (mesh->current_patch)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    status = _cairo_array_allocate (&mesh->patches, 1, (void **) &current_patch);
    if (unlikely (status)) {
        _cairo_pattern_set_error (pattern, status);
        return;
    }

    mesh->current_patch = current_patch;
    mesh->current_side = -2; /* no current point */

    for (i = 0; i < 4; i++)
        mesh->has_control_point[i] = FALSE;

    for (i = 0; i < 4; i++)
        mesh->has_color[i] = FALSE;
}


static void
_calc_control_point (cairo_mesh_patch_t *patch, int control_point)
{
    /* The Coons patch is a special case of the Tensor Product patch
     * where the four control points are:
     *
     * P11 = S(1/3, 1/3)
     * P12 = S(1/3, 2/3)
     * P21 = S(2/3, 1/3)
     * P22 = S(2/3, 2/3)
     *
     * where S is the gradient surface.
     *
     * When one or more control points has not been specified
     * calculated the Coons patch control points are substituted. If
     * no control points are specified the gradient will be a Coons
     * patch.
     *
     * The equations below are defined in the ISO32000 standard.
     */
    cairo_point_double_t *p[3][3];
    int cp_i, cp_j, i, j;

    cp_i = mesh_control_point_i[control_point];
    cp_j = mesh_control_point_j[control_point];

    for (i = 0; i < 3; i++)
        for (j = 0; j < 3; j++)
            p[i][j] = &patch->points[cp_i ^ i][cp_j ^ j];

    p[0][0]->x = (- 4 * p[1][1]->x
                  + 6 * (p[1][0]->x + p[0][1]->x)
                  - 2 * (p[1][2]->x + p[2][1]->x)
                  + 3 * (p[2][0]->x + p[0][2]->x)
                  - 1 * p[2][2]->x) * (1. / 9);

    p[0][0]->y = (- 4 * p[1][1]->y
                  + 6 * (p[1][0]->y + p[0][1]->y)
                  - 2 * (p[1][2]->y + p[2][1]->y)
                  + 3 * (p[2][0]->y + p[0][2]->y)
                  - 1 * p[2][2]->y) * (1. / 9);
}

/**
 * cairo_mesh_pattern_end_patch:
 * @pattern: a #cairo_pattern_t
 *
 * Indicates the end of the current patch in a mesh pattern.
 *
 * If the current patch has less than 4 sides, it is closed with a
 * straight line from the current point to the first point of the
 * patch as if cairo_mesh_pattern_line_to() was used.
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @pattern has no current
 * patch or the current patch has no current point, @pattern will be
 * put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_end_patch (cairo_pattern_t *pattern)
{
    cairo_mesh_pattern_t *mesh;
    cairo_mesh_patch_t *current_patch;
    int i;

    if (unlikely (pattern->status))
        return;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    mesh = (cairo_mesh_pattern_t *) pattern;
    current_patch = mesh->current_patch;
    if (unlikely (!current_patch)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    if (unlikely (mesh->current_side == -2)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    while (mesh->current_side < 3) {
        int corner_num;

        cairo_mesh_pattern_line_to (pattern,
                                    current_patch->points[0][0].x,
                                    current_patch->points[0][0].y);

        corner_num = mesh->current_side + 1;
        if (corner_num < 4 && ! mesh->has_color[corner_num]) {
            current_patch->colors[corner_num] = current_patch->colors[0];
            mesh->has_color[corner_num] = TRUE;
        }
    }

    for (i = 0; i < 4; i++) {
        if (! mesh->has_control_point[i])
            _calc_control_point (current_patch, i);
    }

    for (i = 0; i < 4; i++) {
        if (! mesh->has_color[i])
            current_patch->colors[i] = *CAIRO_COLOR_TRANSPARENT;
    }

    mesh->current_patch = NULL;
}

/**
 * cairo_mesh_pattern_curve_to:
 * @pattern: a #cairo_pattern_t
 * @x1: the X coordinate of the first control point
 * @y1: the Y coordinate of the first control point
 * @x2: the X coordinate of the second control point
 * @y2: the Y coordinate of the second control point
 * @x3: the X coordinate of the end of the curve
 * @y3: the Y coordinate of the end of the curve
 *
 * Adds a cubic Bézier spline to the current patch from the current
 * point to position (@x3, @y3) in pattern-space coordinates, using
 * (@x1, @y1) and (@x2, @y2) as the control points.
 *
 * If the current patch has no current point before the call to
 * cairo_mesh_pattern_curve_to(), this function will behave as if
 * preceded by a call to cairo_mesh_pattern_move_to(@pattern, @x1,
 * @y1).
 *
 * After this call the current point will be (@x3, @y3).
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @pattern has no current
 * patch or the current patch already has 4 sides, @pattern will be
 * put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_curve_to (cairo_pattern_t *pattern,
                             double x1, double y1,
                             double x2, double y2,
                             double x3, double y3)
{
    cairo_mesh_pattern_t *mesh;
    int current_point, i, j;

    if (unlikely (pattern->status))
        return;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    mesh = (cairo_mesh_pattern_t *) pattern;
    if (unlikely (!mesh->current_patch)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    if (unlikely (mesh->current_side == 3)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    if (mesh->current_side == -2)
        cairo_mesh_pattern_move_to (pattern, x1, y1);

    assert (mesh->current_side >= -1);
    assert (pattern->status == CAIRO_STATUS_SUCCESS);

    mesh->current_side++;

    current_point = 3 * mesh->current_side;

    current_point++;
    i = mesh_path_point_i[current_point];
    j = mesh_path_point_j[current_point];
    mesh->current_patch->points[i][j].x = x1;
    mesh->current_patch->points[i][j].y = y1;

    current_point++;
    i = mesh_path_point_i[current_point];
    j = mesh_path_point_j[current_point];
    mesh->current_patch->points[i][j].x = x2;
    mesh->current_patch->points[i][j].y = y2;

    current_point++;
    if (current_point < 12) {
        i = mesh_path_point_i[current_point];
        j = mesh_path_point_j[current_point];
        mesh->current_patch->points[i][j].x = x3;
        mesh->current_patch->points[i][j].y = y3;
    }
}
slim_hidden_def (cairo_mesh_pattern_curve_to);

/**
 * cairo_mesh_pattern_line_to:
 * @pattern: a #cairo_pattern_t
 * @x: the X coordinate of the end of the new line
 * @y: the Y coordinate of the end of the new line
 *
 * Adds a line to the current patch from the current point to position
 * (@x, @y) in pattern-space coordinates.
 *
 * If there is no current point before the call to
 * cairo_mesh_pattern_line_to() this function will behave as
 * cairo_mesh_pattern_move_to(@pattern, @x, @y).
 *
 * After this call the current point will be (@x, @y).
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @pattern has no current
 * patch or the current patch already has 4 sides, @pattern will be
 * put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_line_to (cairo_pattern_t *pattern,
                            double x, double y)
{
    cairo_mesh_pattern_t *mesh;
    cairo_point_double_t last_point;
    int last_point_idx, i, j;

    if (unlikely (pattern->status))
        return;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    mesh = (cairo_mesh_pattern_t *) pattern;
    if (unlikely (!mesh->current_patch)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    if (unlikely (mesh->current_side == 3)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    if (mesh->current_side == -2) {
        cairo_mesh_pattern_move_to (pattern, x, y);
        return;
    }

    last_point_idx = 3 * (mesh->current_side + 1);
    i = mesh_path_point_i[last_point_idx];
    j = mesh_path_point_j[last_point_idx];

    last_point = mesh->current_patch->points[i][j];

    cairo_mesh_pattern_curve_to (pattern,
                                 (2 * last_point.x + x) * (1. / 3),
                                 (2 * last_point.y + y) * (1. / 3),
                                 (last_point.x + 2 * x) * (1. / 3),
                                 (last_point.y + 2 * y) * (1. / 3),
                                 x, y);
}
slim_hidden_def (cairo_mesh_pattern_line_to);

/**
 * cairo_mesh_pattern_move_to:
 * @pattern: a #cairo_pattern_t
 * @x: the X coordinate of the new position
 * @y: the Y coordinate of the new position
 *
 * Define the first point of the current patch in a mesh pattern.
 *
 * After this call the current point will be (@x, @y).
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @pattern has no current
 * patch or the current patch already has at least one side, @pattern
 * will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_move_to (cairo_pattern_t *pattern,
                            double x, double y)
{
    cairo_mesh_pattern_t *mesh;

    if (unlikely (pattern->status))
        return;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    mesh = (cairo_mesh_pattern_t *) pattern;
    if (unlikely (!mesh->current_patch)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    if (unlikely (mesh->current_side >= 0)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    mesh->current_side = -1;
    mesh->current_patch->points[0][0].x = x;
    mesh->current_patch->points[0][0].y = y;
}
slim_hidden_def (cairo_mesh_pattern_move_to);

/**
 * cairo_mesh_pattern_set_control_point:
 * @pattern: a #cairo_pattern_t
 * @point_num: the control point to set the position for
 * @x: the X coordinate of the control point
 * @y: the Y coordinate of the control point
 *
 * Set an internal control point of the current patch.
 *
 * Valid values for @point_num are from 0 to 3 and identify the
 * control points as explained in cairo_pattern_create_mesh().
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @point_num is not valid,
 * @pattern will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_INDEX.  If @pattern has no current patch,
 * @pattern will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_set_control_point (cairo_pattern_t *pattern,
                                      unsigned int     point_num,
                                      double           x,
                                      double           y)
{
    cairo_mesh_pattern_t *mesh;
    int i, j;

    if (unlikely (pattern->status))
        return;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    if (unlikely (point_num > 3)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_INDEX);
        return;
    }

    mesh = (cairo_mesh_pattern_t *) pattern;
    if (unlikely (!mesh->current_patch)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    i = mesh_control_point_i[point_num];
    j = mesh_control_point_j[point_num];

    mesh->current_patch->points[i][j].x = x;
    mesh->current_patch->points[i][j].y = y;
    mesh->has_control_point[point_num] = TRUE;
}

/* make room for at least one more color stop */
static cairo_status_t
_cairo_pattern_gradient_grow (cairo_gradient_pattern_t *pattern)
{
    cairo_gradient_stop_t *new_stops;
    int old_size = pattern->stops_size;
    int embedded_size = ARRAY_LENGTH (pattern->stops_embedded);
    int new_size = 2 * MAX (old_size, 4);

    /* we have a local buffer at pattern->stops_embedded.  try to fulfill the request
     * from there. */
    if (old_size < embedded_size) {
        pattern->stops = pattern->stops_embedded;
        pattern->stops_size = embedded_size;
        return CAIRO_STATUS_SUCCESS;
    }

    if (CAIRO_INJECT_FAULT ())
        return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    assert (pattern->n_stops <= pattern->stops_size);

    if (pattern->stops == pattern->stops_embedded) {
        new_stops = _cairo_malloc_ab (new_size, sizeof (cairo_gradient_stop_t));
        if (new_stops)
            memcpy (new_stops, pattern->stops, old_size * sizeof (cairo_gradient_stop_t));
    } else {
        new_stops = _cairo_realloc_ab (pattern->stops,
                                       new_size,
                                       sizeof (cairo_gradient_stop_t));
    }

    if (unlikely (new_stops == NULL))
        return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    pattern->stops = new_stops;
    pattern->stops_size = new_size;

    return CAIRO_STATUS_SUCCESS;
}

static void
_cairo_mesh_pattern_set_corner_color (cairo_mesh_pattern_t *mesh,
                                      unsigned int     corner_num,
                                      double red, double green, double blue,
                                      double alpha)
{
    cairo_color_t *color;

    assert (mesh->current_patch);
    assert (corner_num <= 3);

    color = &mesh->current_patch->colors[corner_num];
    color->red   = red;
    color->green = green;
    color->blue  = blue;
    color->alpha = alpha;

    color->red_short   = _cairo_color_double_to_short (red);
    color->green_short = _cairo_color_double_to_short (green);
    color->blue_short  = _cairo_color_double_to_short (blue);
    color->alpha_short = _cairo_color_double_to_short (alpha);

    mesh->has_color[corner_num] = TRUE;
}

/**
 * cairo_mesh_pattern_set_corner_color_rgb:
 * @pattern: a #cairo_pattern_t
 * @corner_num: the corner to set the color for
 * @red: red component of color
 * @green: green component of color
 * @blue: blue component of color
 *
 * Sets the color of a corner of the current patch in a mesh pattern.
 *
 * The color is specified in the same way as in cairo_set_source_rgb().
 *
 * Valid values for @corner_num are from 0 to 3 and identify the
 * corners as explained in cairo_pattern_create_mesh().
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @corner_num is not valid,
 * @pattern will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_INDEX.  If @pattern has no current patch,
 * @pattern will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_set_corner_color_rgb (cairo_pattern_t *pattern,
                                         unsigned int     corner_num,
                                         double red, double green, double blue)
{
    cairo_mesh_pattern_set_corner_color_rgba (pattern, corner_num, red, green, blue, 1.0);
}

/**
 * cairo_mesh_pattern_set_corner_color_rgba:
 * @pattern: a #cairo_pattern_t
 * @corner_num: the corner to set the color for
 * @red: red component of color
 * @green: green component of color
 * @blue: blue component of color
 * @alpha: alpha component of color
 *
 * Sets the color of a corner of the current patch in a mesh pattern.
 *
 * The color is specified in the same way as in cairo_set_source_rgba().
 *
 * Valid values for @corner_num are from 0 to 3 and identify the
 * corners as explained in cairo_pattern_create_mesh().
 *
 * Note: If @pattern is not a mesh pattern then @pattern will be put
 * into an error status with a status of
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH. If @corner_num is not valid,
 * @pattern will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_INDEX.  If @pattern has no current patch,
 * @pattern will be put into an error status with a status of
 * %CAIRO_STATUS_INVALID_MESH_CONSTRUCTION.
 *
 * Since: 1.12
 **/
void
cairo_mesh_pattern_set_corner_color_rgba (cairo_pattern_t *pattern,
                                          unsigned int     corner_num,
                                          double red, double green, double blue,
                                          double alpha)
{
    cairo_mesh_pattern_t *mesh;

    if (unlikely (pattern->status))
        return;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    if (unlikely (corner_num > 3)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_INDEX);
        return;
    }

    mesh = (cairo_mesh_pattern_t *) pattern;
    if (unlikely (!mesh->current_patch)) {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_INVALID_MESH_CONSTRUCTION);
        return;
    }

    red    = _cairo_restrict_value (red,    0.0, 1.0);
    green  = _cairo_restrict_value (green,  0.0, 1.0);
    blue   = _cairo_restrict_value (blue,   0.0, 1.0);
    alpha  = _cairo_restrict_value (alpha,  0.0, 1.0);

    _cairo_mesh_pattern_set_corner_color (mesh, corner_num, red, green, blue, alpha);
}
slim_hidden_def (cairo_mesh_pattern_set_corner_color_rgba);

static void
_cairo_pattern_add_color_stop (cairo_gradient_pattern_t *pattern,
                               double                    offset,
                               double                    red,
                               double                    green,
                               double                    blue,
                               double                    alpha)
{
    cairo_gradient_stop_t *stops;
    unsigned int           i;

    if (pattern->n_stops >= pattern->stops_size) {
        cairo_status_t status = _cairo_pattern_gradient_grow (pattern);
        if (unlikely (status)) {
            status = _cairo_pattern_set_error (&pattern->base, status);
            return;
        }
    }

    stops = pattern->stops;

    for (i = 0; i < pattern->n_stops; i++)
    {
        if (offset < stops[i].offset)
        {
            memmove (&stops[i + 1], &stops[i],
                     sizeof (cairo_gradient_stop_t) * (pattern->n_stops - i));

            break;
        }
    }

    stops[i].offset = offset;

    stops[i].color.red   = red;
    stops[i].color.green = green;
    stops[i].color.blue  = blue;
    stops[i].color.alpha = alpha;

    stops[i].color.red_short   = _cairo_color_double_to_short (red);
    stops[i].color.green_short = _cairo_color_double_to_short (green);
    stops[i].color.blue_short  = _cairo_color_double_to_short (blue);
    stops[i].color.alpha_short = _cairo_color_double_to_short (alpha);

    pattern->n_stops++;
}

/**
 * cairo_pattern_add_color_stop_rgb:
 * @pattern: a #cairo_pattern_t
 * @offset: an offset in the range [0.0 .. 1.0]
 * @red: red component of color
 * @green: green component of color
 * @blue: blue component of color
 *
 * Adds an opaque color stop to a gradient pattern. The offset
 * specifies the location along the gradient's control vector. For
 * example, a linear gradient's control vector is from (x0,y0) to
 * (x1,y1) while a radial gradient's control vector is from any point
 * on the start circle to the corresponding point on the end circle.
 *
 * The color is specified in the same way as in cairo_set_source_rgb().
 *
 * If two (or more) stops are specified with identical offset values,
 * they will be sorted according to the order in which the stops are
 * added, (stops added earlier will compare less than stops added
 * later). This can be useful for reliably making sharp color
 * transitions instead of the typical blend.
 *
 *
 * Note: If the pattern is not a gradient pattern, (eg. a linear or
 * radial pattern), then the pattern will be put into an error status
 * with a status of %CAIRO_STATUS_PATTERN_TYPE_MISMATCH.
 *
 * Since: 1.0
 **/
void
cairo_pattern_add_color_stop_rgb (cairo_pattern_t *pattern,
                                  double           offset,
                                  double           red,
                                  double           green,
                                  double           blue)
{
    cairo_pattern_add_color_stop_rgba (pattern, offset, red, green, blue, 1.0);
}

/**
 * cairo_pattern_add_color_stop_rgba:
 * @pattern: a #cairo_pattern_t
 * @offset: an offset in the range [0.0 .. 1.0]
 * @red: red component of color
 * @green: green component of color
 * @blue: blue component of color
 * @alpha: alpha component of color
 *
 * Adds a translucent color stop to a gradient pattern. The offset
 * specifies the location along the gradient's control vector. For
 * example, a linear gradient's control vector is from (x0,y0) to
 * (x1,y1) while a radial gradient's control vector is from any point
 * on the start circle to the corresponding point on the end circle.
 *
 * The color is specified in the same way as in cairo_set_source_rgba().
 *
 * If two (or more) stops are specified with identical offset values,
 * they will be sorted according to the order in which the stops are
 * added, (stops added earlier will compare less than stops added
 * later). This can be useful for reliably making sharp color
 * transitions instead of the typical blend.
 *
 * Note: If the pattern is not a gradient pattern, (eg. a linear or
 * radial pattern), then the pattern will be put into an error status
 * with a status of %CAIRO_STATUS_PATTERN_TYPE_MISMATCH.
 *
 * Since: 1.0
 **/
void
cairo_pattern_add_color_stop_rgba (cairo_pattern_t *pattern,
                                   double          offset,
                                   double          red,
                                   double          green,
                                   double          blue,
                                   double          alpha)
{
    if (pattern->status)
        return;

    if (pattern->type != CAIRO_PATTERN_TYPE_LINEAR &&
        pattern->type != CAIRO_PATTERN_TYPE_RADIAL)
    {
        _cairo_pattern_set_error (pattern, CAIRO_STATUS_PATTERN_TYPE_MISMATCH);
        return;
    }

    offset = _cairo_restrict_value (offset, 0.0, 1.0);
    red    = _cairo_restrict_value (red,    0.0, 1.0);
    green  = _cairo_restrict_value (green,  0.0, 1.0);
    blue   = _cairo_restrict_value (blue,   0.0, 1.0);
    alpha  = _cairo_restrict_value (alpha,  0.0, 1.0);

    _cairo_pattern_add_color_stop ((cairo_gradient_pattern_t *) pattern,
                                   offset, red, green, blue, alpha);
}
slim_hidden_def (cairo_pattern_add_color_stop_rgba);

/**
 * cairo_pattern_set_matrix:
 * @pattern: a #cairo_pattern_t
 * @matrix: a #cairo_matrix_t
 *
 * Sets the pattern's transformation matrix to @matrix. This matrix is
 * a transformation from user space to pattern space.
 *
 * When a pattern is first created it always has the identity matrix
 * for its transformation matrix, which means that pattern space is
 * initially identical to user space.
 *
 * Important: Please note that the direction of this transformation
 * matrix is from user space to pattern space. This means that if you
 * imagine the flow from a pattern to user space (and on to device
 * space), then coordinates in that flow will be transformed by the
 * inverse of the pattern matrix.
 *
 * For example, if you want to make a pattern appear twice as large as
 * it does by default the correct code to use is:
 *
 * <informalexample><programlisting>
 * cairo_matrix_init_scale (&amp;matrix, 0.5, 0.5);
 * cairo_pattern_set_matrix (pattern, &amp;matrix);
 * </programlisting></informalexample>
 *
 * Meanwhile, using values of 2.0 rather than 0.5 in the code above
 * would cause the pattern to appear at half of its default size.
 *
 * Also, please note the discussion of the user-space locking
 * semantics of cairo_set_source().
 *
 * Since: 1.0
 **/
void
cairo_pattern_set_matrix (cairo_pattern_t      *pattern,
                          const cairo_matrix_t *matrix)
{
    cairo_matrix_t inverse;
    cairo_status_t status;

    if (pattern->status)
        return;

    if (memcmp (&pattern->matrix, matrix, sizeof (cairo_matrix_t)) == 0)
        return;

    pattern->matrix = *matrix;
    _cairo_pattern_notify_observers (pattern, CAIRO_PATTERN_NOTIFY_MATRIX);

    inverse = *matrix;
    status = cairo_matrix_invert (&inverse);
    if (unlikely (status))
        status = _cairo_pattern_set_error (pattern, status);
}
slim_hidden_def (cairo_pattern_set_matrix);

/**
 * cairo_pattern_get_matrix:
 * @pattern: a #cairo_pattern_t
 * @matrix: return value for the matrix
 *
 * Stores the pattern's transformation matrix into @matrix.
 *
 * Since: 1.0
 **/
void
cairo_pattern_get_matrix (cairo_pattern_t *pattern, cairo_matrix_t *matrix)
{
    *matrix = pattern->matrix;
}

/**
 * cairo_pattern_set_filter:
 * @pattern: a #cairo_pattern_t
 * @filter: a #cairo_filter_t describing the filter to use for resizing
 * the pattern
 *
 * Sets the filter to be used for resizing when using this pattern.
 * See #cairo_filter_t for details on each filter.
 *
 * * Note that you might want to control filtering even when you do not
 * have an explicit #cairo_pattern_t object, (for example when using
 * cairo_set_source_surface()). In these cases, it is convenient to
 * use cairo_get_source() to get access to the pattern that cairo
 * creates implicitly. For example:
 *
 * <informalexample><programlisting>
 * cairo_set_source_surface (cr, image, x, y);
 * cairo_pattern_set_filter (cairo_get_source (cr), CAIRO_FILTER_NEAREST);
 * </programlisting></informalexample>
 *
 * Since: 1.0
 **/
void
cairo_pattern_set_filter (cairo_pattern_t *pattern, cairo_filter_t filter)
{
    if (pattern->status)
        return;

    pattern->filter = filter;
    _cairo_pattern_notify_observers (pattern, CAIRO_PATTERN_NOTIFY_FILTER);
}

/**
 * cairo_pattern_get_filter:
 * @pattern: a #cairo_pattern_t
 *
 * Gets the current filter for a pattern.  See #cairo_filter_t
 * for details on each filter.
 *
 * Return value: the current filter used for resizing the pattern.
 *
 * Since: 1.0
 **/
cairo_filter_t
cairo_pattern_get_filter (cairo_pattern_t *pattern)
{
    return pattern->filter;
}

/**
 * cairo_pattern_set_extend:
 * @pattern: a #cairo_pattern_t
 * @extend: a #cairo_extend_t describing how the area outside of the
 * pattern will be drawn
 *
 * Sets the mode to be used for drawing outside the area of a pattern.
 * See #cairo_extend_t for details on the semantics of each extend
 * strategy.
 *
 * The default extend mode is %CAIRO_EXTEND_NONE for surface patterns
 * and %CAIRO_EXTEND_PAD for gradient patterns.
 *
 * Since: 1.0
 **/
void
cairo_pattern_set_extend (cairo_pattern_t *pattern, cairo_extend_t extend)
{
    if (pattern->status)
        return;

    pattern->extend = extend;
    _cairo_pattern_notify_observers (pattern, CAIRO_PATTERN_NOTIFY_EXTEND);
}

/**
 * cairo_pattern_get_extend:
 * @pattern: a #cairo_pattern_t
 *
 * Gets the current extend mode for a pattern.  See #cairo_extend_t
 * for details on the semantics of each extend strategy.
 *
 * Return value: the current extend strategy used for drawing the
 * pattern.
 *
 * Since: 1.0
 **/
cairo_extend_t
cairo_pattern_get_extend (cairo_pattern_t *pattern)
{
    return pattern->extend;
}
slim_hidden_def (cairo_pattern_get_extend);

void
_cairo_pattern_pretransform (cairo_pattern_t    *pattern,
                             const cairo_matrix_t  *ctm)
{
    if (pattern->status)
        return;

    cairo_matrix_multiply (&pattern->matrix, &pattern->matrix, ctm);
}

void
_cairo_pattern_transform (cairo_pattern_t       *pattern,
                          const cairo_matrix_t  *ctm_inverse)
{
    if (pattern->status)
        return;

    cairo_matrix_multiply (&pattern->matrix, ctm_inverse, &pattern->matrix);
}

static cairo_bool_t
_linear_pattern_is_degenerate (const cairo_linear_pattern_t *linear)
{
    return fabs (linear->pd1.x - linear->pd2.x) < DBL_EPSILON &&
           fabs (linear->pd1.y - linear->pd2.y) < DBL_EPSILON;
}

static cairo_bool_t
_radial_pattern_is_degenerate (const cairo_radial_pattern_t *radial)
{
    /* A radial pattern is considered degenerate if it can be
     * represented as a solid or clear pattern.  This corresponds to
     * one of the two cases:
     *
     * 1) The radii are both very small:
     *      |dr| < DBL_EPSILON && min (r0, r1) < DBL_EPSILON
     *
     * 2) The two circles have about the same radius and are very
     *    close to each other (approximately a cylinder gradient that
     *    doesn't move with the parameter):
     *      |dr| < DBL_EPSILON && max (|dx|, |dy|) < 2 * DBL_EPSILON
     *
     * These checks are consistent with the assumptions used in
     * _cairo_radial_pattern_box_to_parameter ().
     */

    return fabs (radial->cd1.radius - radial->cd2.radius) < DBL_EPSILON &&
        (MIN (radial->cd1.radius, radial->cd2.radius) < DBL_EPSILON ||
         MAX (fabs (radial->cd1.center.x - radial->cd2.center.x),
              fabs (radial->cd1.center.y - radial->cd2.center.y)) < 2 * DBL_EPSILON);
}

static void
_cairo_linear_pattern_box_to_parameter (const cairo_linear_pattern_t *linear,
                                        double x0, double y0,
                                        double x1, double y1,
                                        double range[2])
{
    double t0, tdx, tdy;
    double p1x, p1y, pdx, pdy, invsqnorm;

    assert (! _linear_pattern_is_degenerate (linear));

    /*
     * Linear gradients are othrogonal to the line passing through
     * their extremes. Because of convexity, the parameter range can
     * be computed as the convex hull (one the real line) of the
     * parameter values of the 4 corners of the box.
     *
     * The parameter value t for a point (x,y) can be computed as:
     *
     *   t = (p2 - p1) . (x,y) / |p2 - p1|^2
     *
     * t0  is the t value for the top left corner
     * tdx is the difference between left and right corners
     * tdy is the difference between top and bottom corners
     */

    p1x = linear->pd1.x;
    p1y = linear->pd1.y;
    pdx = linear->pd2.x - p1x;
    pdy = linear->pd2.y - p1y;
    invsqnorm = 1.0 / (pdx * pdx + pdy * pdy);
    pdx *= invsqnorm;
    pdy *= invsqnorm;

    t0 = (x0 - p1x) * pdx + (y0 - p1y) * pdy;
    tdx = (x1 - x0) * pdx;
    tdy = (y1 - y0) * pdy;

    /*
     * Because of the linearity of the t value, tdx can simply be
     * added the t0 to move along the top edge. After this, range[0]
     * and range[1] represent the parameter range for the top edge, so
     * extending it to include the whole box simply requires adding
     * tdy to the correct extreme.
     */

    range[0] = range[1] = t0;
    if (tdx < 0)
        range[0] += tdx;
    else
        range[1] += tdx;

    if (tdy < 0)
        range[0] += tdy;
    else
        range[1] += tdy;
}

static cairo_bool_t
_extend_range (double range[2], double value, cairo_bool_t valid)
{
    if (!valid)
        range[0] = range[1] = value;
    else if (value < range[0])
        range[0] = value;
    else if (value > range[1])
        range[1] = value;

    return TRUE;
}

/*
 * _cairo_radial_pattern_focus_is_inside:
 *
 * Returns %TRUE if and only if the focus point exists and is
 * contained in one of the two extreme circles. This condition is
 * equivalent to one of the two extreme circles being completely
 * contained in the other one.
 *
 * Note: if the focus is on the border of one of the two circles (in
 * which case the circles are tangent in the focus point), it is not
 * considered as contained in the circle, hence this function returns
 * %FALSE.
 *
 */
cairo_bool_t
_cairo_radial_pattern_focus_is_inside (const cairo_radial_pattern_t *radial)
{
    double cx, cy, cr, dx, dy, dr;

    cx = radial->cd1.center.x;
    cy = radial->cd1.center.y;
    cr = radial->cd1.radius;
    dx = radial->cd2.center.x - cx;
    dy = radial->cd2.center.y - cy;
    dr = radial->cd2.radius   - cr;

    return dx*dx + dy*dy < dr*dr;
}

static void
_cairo_radial_pattern_box_to_parameter (const cairo_radial_pattern_t *radial,
                                        double x0, double y0,
                                        double x1, double y1,
                                        double tolerance,
                                        double range[2])
{
    double cx, cy, cr, dx, dy, dr;
    double a, x_focus, y_focus;
    double mindr, minx, miny, maxx, maxy;
    cairo_bool_t valid;

    assert (! _radial_pattern_is_degenerate (radial));
    assert (x0 < x1);
    assert (y0 < y1);

    tolerance = MAX (tolerance, DBL_EPSILON);

    range[0] = range[1] = 0;
    valid = FALSE;

    x_focus = y_focus = 0; /* silence gcc */

    cx = radial->cd1.center.x;
    cy = radial->cd1.center.y;
    cr = radial->cd1.radius;
    dx = radial->cd2.center.x - cx;
    dy = radial->cd2.center.y - cy;
    dr = radial->cd2.radius   - cr;

    /* translate by -(cx, cy) to simplify computations */
    x0 -= cx;
    y0 -= cy;
    x1 -= cx;
    y1 -= cy;

    /* enlarge boundaries slightly to avoid rounding problems in the
     * parameter range computation */
    x0 -= DBL_EPSILON;
    y0 -= DBL_EPSILON;
    x1 += DBL_EPSILON;
    y1 += DBL_EPSILON;

    /* enlarge boundaries even more to avoid rounding problems when
     * testing if a point belongs to the box */
    minx = x0 - DBL_EPSILON;
    miny = y0 - DBL_EPSILON;
    maxx = x1 + DBL_EPSILON;
    maxy = y1 + DBL_EPSILON;

    /* we dont' allow negative radiuses, so we will be checking that
     * t*dr >= mindr to consider t valid */
    mindr = -(cr + DBL_EPSILON);

    /*
     * After the previous transformations, the start circle is
     * centered in the origin and has radius cr. A 1-unit change in
     * the t parameter corresponds to dx,dy,dr changes in the x,y,r of
     * the circle (center coordinates, radius).
     *
     * To compute the minimum range needed to correctly draw the
     * pattern, we start with an empty range and extend it to include
     * the circles touching the bounding box or within it.
     */

    /*
     * Focus, the point where the circle has radius == 0.
     *
     * r = cr + t * dr = 0
     * t = -cr / dr
     *
     * If the radius is constant (dr == 0) there is no focus (the
     * gradient represents a cylinder instead of a cone).
     */
    if (fabs (dr) >= DBL_EPSILON) {
        double t_focus;

        t_focus = -cr / dr;
        x_focus = t_focus * dx;
        y_focus = t_focus * dy;
        if (minx <= x_focus && x_focus <= maxx &&
            miny <= y_focus && y_focus <= maxy)
        {
            valid = _extend_range (range, t_focus, valid);
        }
    }

    /*
     * Circles externally tangent to box edges.
     *
     * All circles have center in (dx, dy) * t
     *
     * If the circle is tangent to the line defined by the edge of the
     * box, then at least one of the following holds true:
     *
     *   (dx*t) + (cr + dr*t) == x0 (left   edge)
     *   (dx*t) - (cr + dr*t) == x1 (right  edge)
     *   (dy*t) + (cr + dr*t) == y0 (top    edge)
     *   (dy*t) - (cr + dr*t) == y1 (bottom edge)
     *
     * The solution is only valid if the tangent point is actually on
     * the edge, i.e. if its y coordinate is in [y0,y1] for left/right
     * edges and if its x coordinate is in [x0,x1] for top/bottom
     * edges.
     *
     * For the first equation:
     *
     *   (dx + dr) * t = x0 - cr
     *   t = (x0 - cr) / (dx + dr)
     *   y = dy * t
     *
     * in the code this becomes:
     *
     *   t_edge = (num) / (den)
     *   v = (delta) * t_edge
     *
     * If the denominator in t is 0, the pattern is tangent to a line
     * parallel to the edge under examination. The corner-case where
     * the boundary line is the same as the edge is handled by the
     * focus point case and/or by the a==0 case.
     */
#define T_EDGE(num,den,delta,lower,upper)                               \
    if (fabs (den) >= DBL_EPSILON) {                                    \
        double t_edge, v;                                               \
                                                                        \
        t_edge = (num) / (den);                                         \
        v = t_edge * (delta);                                           \
        if (t_edge * dr >= mindr && (lower) <= v && v <= (upper))       \
            valid = _extend_range (range, t_edge, valid);               \
    }

    /* circles tangent (externally) to left/right/top/bottom edge */
    T_EDGE (x0 - cr, dx + dr, dy, miny, maxy);
    T_EDGE (x1 + cr, dx - dr, dy, miny, maxy);
    T_EDGE (y0 - cr, dy + dr, dx, minx, maxx);
    T_EDGE (y1 + cr, dy - dr, dx, minx, maxx);

#undef T_EDGE

    /*
     * Circles passing through a corner.
     *
     * A circle passing through the point (x,y) satisfies:
     *
     * (x-t*dx)^2 + (y-t*dy)^2 == (cr + t*dr)^2
     *
     * If we set:
     *   a = dx^2 + dy^2 - dr^2
     *   b = x*dx + y*dy + cr*dr
     *   c = x^2 + y^2 - cr^2
     * we have:
     *   a*t^2 - 2*b*t + c == 0
     */
    a = dx * dx + dy * dy - dr * dr;
    if (fabs (a) < DBL_EPSILON * DBL_EPSILON) {
        double b, maxd2;

        /* Ensure that gradients with both a and dr small are
         * considered degenerate.
         * The floating point version of the degeneracy test implemented
         * in _radial_pattern_is_degenerate() is:
         *
         *  1) The circles are practically the same size:
         *     |dr| < DBL_EPSILON
         *  AND
         *  2a) The circles are both very small:
         *      min (r0, r1) < DBL_EPSILON
         *   OR
         *  2b) The circles are very close to each other:
         *      max (|dx|, |dy|) < 2 * DBL_EPSILON
         *
         * Assuming that the gradient is not degenerate, we want to
         * show that |a| < DBL_EPSILON^2 implies |dr| >= DBL_EPSILON.
         *
         * If the gradient is not degenerate yet it has |dr| <
         * DBL_EPSILON, (2b) is false, thus:
         *
         *   max (|dx|, |dy|) >= 2*DBL_EPSILON
         * which implies:
         *   4*DBL_EPSILON^2 <= max (|dx|, |dy|)^2 <= dx^2 + dy^2
         *
         * From the definition of a, we get:
         *   a = dx^2 + dy^2 - dr^2 < DBL_EPSILON^2
         *   dx^2 + dy^2 - DBL_EPSILON^2 < dr^2
         *   3*DBL_EPSILON^2 < dr^2
         *
         * which is inconsistent with the hypotheses, thus |dr| <
         * DBL_EPSILON is false or the gradient is degenerate.
         */
        assert (fabs (dr) >= DBL_EPSILON);

        /*
         * If a == 0, all the circles are tangent to a line in the
         * focus point. If this line is within the box extents, we
         * should add the circle with infinite radius, but this would
         * make the range unbounded, so we add the smallest circle whose
         * distance to the desired (degenerate) circle within the
         * bounding box does not exceed tolerance.
         *
         * The equation of the line is b==0, i.e.:
         *   x*dx + y*dy + cr*dr == 0
         *
         * We compute the intersection of the line with the box and
         * keep the intersection with maximum square distance (maxd2)
         * from the focus point.
         *
         * In the code the intersection is represented in another
         * coordinate system, whose origin is the focus point and
         * which has a u,v axes, which are respectively orthogonal and
         * parallel to the edge being intersected.
         *
         * The intersection is valid only if it belongs to the box,
         * otherwise it is ignored.
         *
         * For example:
         *
         *   y = y0
         *   x*dx + y0*dy + cr*dr == 0
         *   x = -(y0*dy + cr*dr) / dx
         *
         * which in (u,v) is:
         *   u = y0 - y_focus
         *   v = -(y0*dy + cr*dr) / dx - x_focus
         *
         * In the code:
         *   u = (edge) - (u_origin)
         *   v = -((edge) * (delta) + cr*dr) / (den) - v_focus
         */
#define T_EDGE(edge,delta,den,lower,upper,u_origin,v_origin)    \
        if (fabs (den) >= DBL_EPSILON) {                        \
            double v;                                           \
                                                                \
            v = -((edge) * (delta) + cr * dr) / (den);          \
            if ((lower) <= v && v <= (upper)) {                 \
                double u, d2;                                   \
                                                                \
                u = (edge) - (u_origin);                        \
                v -= (v_origin);                                \
                d2 = u*u + v*v;                                 \
                if (maxd2 < d2)                                 \
                    maxd2 = d2;                                 \
            }                                                   \
        }

        maxd2 = 0;

        /* degenerate circles (lines) passing through each edge */
        T_EDGE (y0, dy, dx, minx, maxx, y_focus, x_focus);
        T_EDGE (y1, dy, dx, minx, maxx, y_focus, x_focus);
        T_EDGE (x0, dx, dy, miny, maxy, x_focus, y_focus);
        T_EDGE (x1, dx, dy, miny, maxy, x_focus, y_focus);

#undef T_EDGE

        /*
         * The limit circle can be transformed rigidly to the y=0 line
         * and the circles tangent to it in (0,0) are:
         *
         *   x^2 + (y-r)^2 = r^2  <=>  x^2 + y^2 - 2*y*r = 0
         *
         * y is the distance from the line, in our case tolerance;
         * x is the distance along the line, i.e. sqrt(maxd2),
         * so:
         *
         *   r = cr + dr * t = (maxd2 + tolerance^2) / (2*tolerance)
         *   t = (r - cr) / dr =
         *       (maxd2 + tolerance^2 - 2*tolerance*cr) / (2*tolerance*dr)
         */
        if (maxd2 > 0) {
            double t_limit = maxd2 + tolerance*tolerance - 2*tolerance*cr;
            t_limit /= 2 * tolerance * dr;
            valid = _extend_range (range, t_limit, valid);
        }

        /*
         * Nondegenerate, nonlimit circles passing through the corners.
         *
         * a == 0 && a*t^2 - 2*b*t + c == 0
         *
         * t = c / (2*b)
         *
         * The b == 0 case has just been handled, so we only have to
         * compute this if b != 0.
         */
#define T_CORNER(x,y)                                                   \
        b = (x) * dx + (y) * dy + cr * dr;                              \
        if (fabs (b) >= DBL_EPSILON) {                                  \
            double t_corner;                                            \
            double x2 = (x) * (x);                                      \
            double y2 = (y) * (y);                                      \
            double cr2 = (cr) * (cr);                                   \
            double c = x2 + y2 - cr2;                                   \
                                                                        \
            t_corner = 0.5 * c / b;                                     \
            if (t_corner * dr >= mindr)                                 \
                valid = _extend_range (range, t_corner, valid);         \
        }

        /* circles touching each corner */
        T_CORNER (x0, y0);
        T_CORNER (x0, y1);
        T_CORNER (x1, y0);
        T_CORNER (x1, y1);

#undef T_CORNER
    } else {
        double inva, b, c, d;

        inva = 1 / a;

        /*
         * Nondegenerate, nonlimit circles passing through the corners.
         *
         * a != 0 && a*t^2 - 2*b*t + c == 0
         *
         * t = (b +- sqrt (b*b - a*c)) / a
         *
         * If the argument of sqrt() is negative, then no circle
         * passes through the corner.
         */
#define T_CORNER(x,y)                                                   \
        b = (x) * dx + (y) * dy + cr * dr;                              \
        c = (x) * (x) + (y) * (y) - cr * cr;                            \
        d = b * b - a * c;                                              \
        if (d >= 0) {                                                   \
            double t_corner;                                            \
                                                                        \
            d = sqrt (d);                                               \
            t_corner = (b + d) * inva;                                  \
            if (t_corner * dr >= mindr)                                 \
                valid = _extend_range (range, t_corner, valid);         \
            t_corner = (b - d) * inva;                                  \
            if (t_corner * dr >= mindr)                                 \
                valid = _extend_range (range, t_corner, valid);         \
        }

        /* circles touching each corner */
        T_CORNER (x0, y0);
        T_CORNER (x0, y1);
        T_CORNER (x1, y0);
        T_CORNER (x1, y1);

#undef T_CORNER
    }
}

/**
 * _cairo_gradient_pattern_box_to_parameter:
 *
 * Compute a interpolation range sufficient to draw (within the given
 * tolerance) the gradient in the given box getting the same result as
 * using the (-inf, +inf) range.
 *
 * Assumes that the pattern is not degenerate. This can be guaranteed
 * by simplifying it to a solid clear if _cairo_pattern_is_clear or to
 * a solid color if _cairo_gradient_pattern_is_solid.
 *
 * The range isn't guaranteed to be minimal, but it tries to.
 **/
void
_cairo_gradient_pattern_box_to_parameter (const cairo_gradient_pattern_t *gradient,
                                          double x0, double y0,
                                          double x1, double y1,
                                          double tolerance,
                                          double out_range[2])
{
    assert (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR ||
            gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL);

    if (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR) {
        _cairo_linear_pattern_box_to_parameter ((cairo_linear_pattern_t *) gradient,
                                                x0, y0, x1, y1, out_range);
    } else {
        _cairo_radial_pattern_box_to_parameter ((cairo_radial_pattern_t *) gradient,
                                                x0, y0, x1, y1, tolerance, out_range);
    }
}

/**
 * _cairo_gradient_pattern_interpolate:
 *
 * Interpolate between the start and end objects of linear or radial
 * gradients.  The interpolated object is stored in out_circle, with
 * the radius being zero in the linear gradient case.
 **/
void
_cairo_gradient_pattern_interpolate (const cairo_gradient_pattern_t *gradient,
                                     double                          t,
                                     cairo_circle_double_t          *out_circle)
{
    assert (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR ||
            gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL);

#define lerp(a,b) (a)*(1-t) + (b)*t

    if (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR) {
        cairo_linear_pattern_t *linear = (cairo_linear_pattern_t *) gradient;
        out_circle->center.x = lerp (linear->pd1.x, linear->pd2.x);
        out_circle->center.y = lerp (linear->pd1.y, linear->pd2.y);
        out_circle->radius = 0;
    } else {
        cairo_radial_pattern_t *radial = (cairo_radial_pattern_t *) gradient;
        out_circle->center.x = lerp (radial->cd1.center.x, radial->cd2.center.x);
        out_circle->center.y = lerp (radial->cd1.center.y, radial->cd2.center.y);
        out_circle->radius   = lerp (radial->cd1.radius  , radial->cd2.radius);
    }

#undef lerp
}


/**
 * _cairo_gradient_pattern_fit_to_range:
 *
 * Scale the extremes of a gradient to guarantee that the coordinates
 * and their deltas are within the range (-max_value, max_value). The
 * new extremes are stored in out_circle.
 *
 * The pattern matrix is scaled to guarantee that the aspect of the
 * gradient is the same and the result is stored in out_matrix.
 *
 **/
void
_cairo_gradient_pattern_fit_to_range (const cairo_gradient_pattern_t *gradient,
                                      double                          max_value,
                                      cairo_matrix_t                 *out_matrix,
                                      cairo_circle_double_t           out_circle[2])
{
    double dim;

    assert (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR ||
            gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL);

    if (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR) {
        cairo_linear_pattern_t *linear = (cairo_linear_pattern_t *) gradient;

        out_circle[0].center = linear->pd1;
        out_circle[0].radius = 0;
        out_circle[1].center = linear->pd2;
        out_circle[1].radius = 0;

        dim = fabs (linear->pd1.x);
        dim = MAX (dim, fabs (linear->pd1.y));
        dim = MAX (dim, fabs (linear->pd2.x));
        dim = MAX (dim, fabs (linear->pd2.y));
        dim = MAX (dim, fabs (linear->pd1.x - linear->pd2.x));
        dim = MAX (dim, fabs (linear->pd1.y - linear->pd2.y));
    } else {
        cairo_radial_pattern_t *radial = (cairo_radial_pattern_t *) gradient;

        out_circle[0] = radial->cd1;
        out_circle[1] = radial->cd2;

        dim = fabs (radial->cd1.center.x);
        dim = MAX (dim, fabs (radial->cd1.center.y));
        dim = MAX (dim, fabs (radial->cd1.radius));
        dim = MAX (dim, fabs (radial->cd2.center.x));
        dim = MAX (dim, fabs (radial->cd2.center.y));
        dim = MAX (dim, fabs (radial->cd2.radius));
        dim = MAX (dim, fabs (radial->cd1.center.x - radial->cd2.center.x));
        dim = MAX (dim, fabs (radial->cd1.center.y - radial->cd2.center.y));
        dim = MAX (dim, fabs (radial->cd1.radius   - radial->cd2.radius));
    }

    if (unlikely (dim > max_value)) {
        cairo_matrix_t scale;

        dim = max_value / dim;

        out_circle[0].center.x *= dim;
        out_circle[0].center.y *= dim;
        out_circle[0].radius   *= dim;
        out_circle[1].center.x *= dim;
        out_circle[1].center.y *= dim;
        out_circle[1].radius   *= dim;

        cairo_matrix_init_scale (&scale, dim, dim);
        cairo_matrix_multiply (out_matrix, &gradient->base.matrix, &scale);
    } else {
        *out_matrix = gradient->base.matrix;
    }
}

static cairo_bool_t
_gradient_is_clear (const cairo_gradient_pattern_t *gradient,
                    const cairo_rectangle_int_t *extents)
{
    unsigned int i;

    assert (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR ||
            gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL);

    if (gradient->n_stops == 0 ||
        (gradient->base.extend == CAIRO_EXTEND_NONE &&
         gradient->stops[0].offset == gradient->stops[gradient->n_stops - 1].offset))
        return TRUE;

    if (gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL) {
        /* degenerate radial gradients are clear */
        if (_radial_pattern_is_degenerate ((cairo_radial_pattern_t *) gradient))
            return TRUE;
    } else if (gradient->base.extend == CAIRO_EXTEND_NONE) {
        /* EXTEND_NONE degenerate linear gradients are clear */
        if (_linear_pattern_is_degenerate ((cairo_linear_pattern_t *) gradient))
            return TRUE;
    }

    /* Check if the extents intersect the drawn part of the pattern. */
    if (extents != NULL &&
        (gradient->base.extend == CAIRO_EXTEND_NONE ||
         gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL))
    {
        double t[2];

        _cairo_gradient_pattern_box_to_parameter (gradient,
                                                  extents->x,
                                                  extents->y,
                                                  extents->x + extents->width,
                                                  extents->y + extents->height,
                                                  DBL_EPSILON,
                                                  t);

        if (gradient->base.extend == CAIRO_EXTEND_NONE &&
            (t[0] >= gradient->stops[gradient->n_stops - 1].offset ||
             t[1] <= gradient->stops[0].offset))
        {
                return TRUE;
        }

        if (t[0] == t[1])
            return TRUE;
    }

    for (i = 0; i < gradient->n_stops; i++)
        if (! CAIRO_COLOR_IS_CLEAR (&gradient->stops[i].color))
            return FALSE;

    return TRUE;
}

static void
_gradient_color_average (const cairo_gradient_pattern_t *gradient,
                         cairo_color_t *color)
{
    double delta0, delta1;
    double r, g, b, a;
    unsigned int i, start = 1, end;

    assert (gradient->n_stops > 0);
    assert (gradient->base.extend != CAIRO_EXTEND_NONE);

    if (gradient->n_stops == 1) {
        _cairo_color_init_rgba (color,
                                gradient->stops[0].color.red,
                                gradient->stops[0].color.green,
                                gradient->stops[0].color.blue,
                                gradient->stops[0].color.alpha);
        return;
    }

    end = gradient->n_stops - 1;

    switch (gradient->base.extend) {
    case CAIRO_EXTEND_REPEAT:
      /*
       * Sa, Sb and Sy, Sz are the first two and last two stops respectively.
       * The weight of the first and last stop can be computed as the area of
       * the following triangles (taken with height 1, since the whole [0-1]
       * will have total weight 1 this way): b*h/2
       *
       *              +                   +
       *            / |\                / | \
       *          /   | \             /   |   \
       *        /     |  \          /     |     \
       * ~~~~~+---+---+---+~~~~~~~+-------+---+---+~~~~~
       *   -1+Sz  0  Sa   Sb      Sy     Sz   1  1+Sa
       *
       * For the first stop: (Sb-(-1+Sz)/2 = (1+Sb-Sz)/2
       * For the last stop: ((1+Sa)-Sy)/2 = (1+Sa-Sy)/2
       * Halving the result is done after summing up all the areas.
       */
        delta0 = 1.0 + gradient->stops[1].offset - gradient->stops[end].offset;
        delta1 = 1.0 + gradient->stops[0].offset - gradient->stops[end-1].offset;
        break;

    case CAIRO_EXTEND_REFLECT:
      /*
       * Sa, Sb and Sy, Sz are the first two and last two stops respectively.
       * The weight of the first and last stop can be computed as the area of
       * the following trapezoids (taken with height 1, since the whole [0-1]
       * will have total weight 1 this way): (b+B)*h/2
       *
       * +-------+                   +---+
       * |       |\                / |   |
       * |       | \             /   |   |
       * |       |  \          /     |   |
       * +-------+---+~~~~~~~+-------+---+
       * 0      Sa   Sb      Sy     Sz   1
       *
       * For the first stop: (Sa+Sb)/2
       * For the last stop: ((1-Sz) + (1-Sy))/2 = (2-Sy-Sz)/2
       * Halving the result is done after summing up all the areas.
       */
        delta0 = gradient->stops[0].offset + gradient->stops[1].offset;
        delta1 = 2.0 - gradient->stops[end-1].offset - gradient->stops[end].offset;
        break;

    case CAIRO_EXTEND_PAD:
      /* PAD is computed as the average of the first and last stop:
       *  - take both of them with weight 1 (they will be halved
       *    after the whole sum has been computed).
       *  - avoid summing any of the inner stops.
       */
        delta0 = delta1 = 1.0;
        start = end;
        break;

    case CAIRO_EXTEND_NONE:
    default:
        ASSERT_NOT_REACHED;
        _cairo_color_init_rgba (color, 0, 0, 0, 0);
        return;
    }

    r = delta0 * gradient->stops[0].color.red;
    g = delta0 * gradient->stops[0].color.green;
    b = delta0 * gradient->stops[0].color.blue;
    a = delta0 * gradient->stops[0].color.alpha;

    for (i = start; i < end; ++i) {
      /* Inner stops weight is the same as the area of the triangle they influence
       * (which goes from the stop before to the stop after), again with height 1
       * since the whole must sum up to 1: b*h/2
       * Halving is done after the whole sum has been computed.
       */
        double delta = gradient->stops[i+1].offset - gradient->stops[i-1].offset;
        r += delta * gradient->stops[i].color.red;
        g += delta * gradient->stops[i].color.green;
        b += delta * gradient->stops[i].color.blue;
        a += delta * gradient->stops[i].color.alpha;
    }

    r += delta1 * gradient->stops[end].color.red;
    g += delta1 * gradient->stops[end].color.green;
    b += delta1 * gradient->stops[end].color.blue;
    a += delta1 * gradient->stops[end].color.alpha;

    _cairo_color_init_rgba (color, r * .5, g * .5, b * .5, a * .5);
}

/**
 * _cairo_pattern_alpha_range:
 *
 * Convenience function to determine the minimum and maximum alpha in
 * the drawn part of a pattern (i.e. ignoring clear parts caused by
 * extend modes and/or pattern shape).
 *
 * If not NULL, out_min and out_max will be set respectively to the
 * minimum and maximum alpha value of the pattern.
 **/
void
_cairo_pattern_alpha_range (const cairo_pattern_t *pattern,
                            double                *out_min,
                            double                *out_max)
{
    double alpha_min, alpha_max;

    switch (pattern->type) {
    case CAIRO_PATTERN_TYPE_SOLID: {
        const cairo_solid_pattern_t *solid = (cairo_solid_pattern_t *) pattern;
        alpha_min = alpha_max = solid->color.alpha;
        break;
    }

    case CAIRO_PATTERN_TYPE_LINEAR:
    case CAIRO_PATTERN_TYPE_RADIAL: {
        const cairo_gradient_pattern_t *gradient = (cairo_gradient_pattern_t *) pattern;
        unsigned int i;

        assert (gradient->n_stops >= 1);

        alpha_min = alpha_max = gradient->stops[0].color.alpha;
        for (i = 1; i < gradient->n_stops; i++) {
            if (alpha_min > gradient->stops[i].color.alpha)
                alpha_min = gradient->stops[i].color.alpha;
            else if (alpha_max < gradient->stops[i].color.alpha)
                alpha_max = gradient->stops[i].color.alpha;
        }

        break;
    }

    case CAIRO_PATTERN_TYPE_MESH: {
        const cairo_mesh_pattern_t *mesh = (const cairo_mesh_pattern_t *) pattern;
        const cairo_mesh_patch_t *patch = _cairo_array_index_const (&mesh->patches, 0);
        unsigned int i, j, n = _cairo_array_num_elements (&mesh->patches);

        assert (n >= 1);

        alpha_min = alpha_max = patch[0].colors[0].alpha;
        for (i = 0; i < n; i++) {
            for (j = 0; j < 4; j++) {
                if (patch[i].colors[j].alpha < alpha_min)
                    alpha_min = patch[i].colors[j].alpha;
                else if (patch[i].colors[j].alpha > alpha_max)
                    alpha_max = patch[i].colors[j].alpha;
            }
        }

        break;
    }

    default:
        ASSERT_NOT_REACHED;
        /* fall through */

    case CAIRO_PATTERN_TYPE_SURFACE:
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        alpha_min = 0;
        alpha_max = 1;
        break;
    }

    if (out_min)
        *out_min = alpha_min;
    if (out_max)
        *out_max = alpha_max;
}

/**
 * _cairo_mesh_pattern_coord_box:
 *
 * Convenience function to determine the range of the coordinates of
 * the points used to define the patches of the mesh.
 *
 * This is guaranteed to contain the pattern extents, but might not be
 * tight, just like a Bezier curve is always inside the convex hull of
 * the control points.
 *
 * This function cannot be used while the mesh is being constructed.
 *
 * The function returns TRUE and sets the output parametes to define
 * the coodrinate range if the mesh pattern contains at least one
 * patch, otherwise it returns FALSE.
 **/
cairo_bool_t
_cairo_mesh_pattern_coord_box (const cairo_mesh_pattern_t *mesh,
                               double                     *out_xmin,
                               double                     *out_ymin,
                               double                     *out_xmax,
                               double                     *out_ymax)
{
    const cairo_mesh_patch_t *patch;
    unsigned int num_patches, i, j, k;
    double x0, y0, x1, y1;

    assert (mesh->current_patch == NULL);

    num_patches = _cairo_array_num_elements (&mesh->patches);

    if (num_patches == 0)
        return FALSE;

    patch = _cairo_array_index_const (&mesh->patches, 0);
    x0 = x1 = patch->points[0][0].x;
    y0 = y1 = patch->points[0][0].y;

    for (i = 0; i < num_patches; i++) {
        for (j = 0; j < 4; j++) {
            for (k = 0; k < 4; k++) {
                x0 = MIN (x0, patch[i].points[j][k].x);
                y0 = MIN (y0, patch[i].points[j][k].y);
                x1 = MAX (x1, patch[i].points[j][k].x);
                y1 = MAX (y1, patch[i].points[j][k].y);
            }
        }
    }

    *out_xmin = x0;
    *out_ymin = y0;
    *out_xmax = x1;
    *out_ymax = y1;

    return TRUE;
}

/**
 * _cairo_gradient_pattern_is_solid:
 *
 * Convenience function to determine whether a gradient pattern is
 * a solid color within the given extents. In this case the color
 * argument is initialized to the color the pattern represents.
 * This functions doesn't handle completely transparent gradients,
 * thus it should be called only after _cairo_pattern_is_clear has
 * returned FALSE.
 *
 * Return value: %TRUE if the pattern is a solid color.
 **/
cairo_bool_t
_cairo_gradient_pattern_is_solid (const cairo_gradient_pattern_t *gradient,
                                  const cairo_rectangle_int_t *extents,
                                  cairo_color_t *color)
{
    unsigned int i;

    assert (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR ||
            gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL);

    /* TODO: radial */
    if (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR) {
        cairo_linear_pattern_t *linear = (cairo_linear_pattern_t *) gradient;
        if (_linear_pattern_is_degenerate (linear)) {
            _gradient_color_average (gradient, color);
            return TRUE;
        }

        if (gradient->base.extend == CAIRO_EXTEND_NONE) {
            double t[2];

            /* We already know that the pattern is not clear, thus if some
             * part of it is clear, the whole is not solid.
             */

            if (extents == NULL)
                return FALSE;

            _cairo_linear_pattern_box_to_parameter (linear,
                                                    extents->x,
                                                    extents->y,
                                                    extents->x + extents->width,
                                                    extents->y + extents->height,
                                                    t);

            if (t[0] < 0.0 || t[1] > 1.0)
                return FALSE;
        }
    } else
        return FALSE;

    for (i = 1; i < gradient->n_stops; i++)
        if (! _cairo_color_stop_equal (&gradient->stops[0].color,
                                       &gradient->stops[i].color))
            return FALSE;

    _cairo_color_init_rgba (color,
                            gradient->stops[0].color.red,
                            gradient->stops[0].color.green,
                            gradient->stops[0].color.blue,
                            gradient->stops[0].color.alpha);

    return TRUE;
}

static cairo_bool_t
_mesh_is_clear (const cairo_mesh_pattern_t *mesh)
{
    double x1, y1, x2, y2;
    cairo_bool_t is_valid;

    is_valid = _cairo_mesh_pattern_coord_box (mesh, &x1, &y1, &x2, &y2);
    if (!is_valid)
        return TRUE;

    if (x2 - x1 < DBL_EPSILON || y2 - y1 < DBL_EPSILON)
        return TRUE;

    return FALSE;
}

/**
 * _cairo_pattern_is_opaque_solid:
 *
 * Convenience function to determine whether a pattern is an opaque
 * (alpha==1.0) solid color pattern. This is done by testing whether
 * the pattern's alpha value when converted to a byte is 255, so if a
 * backend actually supported deep alpha channels this function might
 * not do the right thing.
 *
 * Return value: %TRUE if the pattern is an opaque, solid color.
 **/
cairo_bool_t
_cairo_pattern_is_opaque_solid (const cairo_pattern_t *pattern)
{
    cairo_solid_pattern_t *solid;

    if (pattern->type != CAIRO_PATTERN_TYPE_SOLID)
        return FALSE;

    solid = (cairo_solid_pattern_t *) pattern;

    return CAIRO_COLOR_IS_OPAQUE (&solid->color);
}

static cairo_bool_t
_surface_is_opaque (const cairo_surface_pattern_t *pattern,
                    const cairo_rectangle_int_t *sample)
{
    cairo_rectangle_int_t extents;

    if (pattern->surface->content & CAIRO_CONTENT_ALPHA)
        return FALSE;

    if (pattern->base.extend != CAIRO_EXTEND_NONE)
        return TRUE;

    if (! _cairo_surface_get_extents (pattern->surface, &extents))
        return TRUE;

    if (sample == NULL)
        return FALSE;

    return _cairo_rectangle_contains_rectangle (&extents, sample);
}

static cairo_bool_t
_raster_source_is_opaque (const cairo_raster_source_pattern_t *pattern,
                          const cairo_rectangle_int_t *sample)
{
    if (pattern->content & CAIRO_CONTENT_ALPHA)
        return FALSE;

    if (pattern->base.extend != CAIRO_EXTEND_NONE)
        return TRUE;

    if (sample == NULL)
        return FALSE;

    return _cairo_rectangle_contains_rectangle (&pattern->extents, sample);
}

static cairo_bool_t
_surface_is_clear (const cairo_surface_pattern_t *pattern)
{
    cairo_rectangle_int_t extents;

    if (_cairo_surface_get_extents (pattern->surface, &extents) &&
        (extents.width == 0 || extents.height == 0))
        return TRUE;

    return pattern->surface->is_clear &&
        pattern->surface->content & CAIRO_CONTENT_ALPHA;
}

static cairo_bool_t
_raster_source_is_clear (const cairo_raster_source_pattern_t *pattern)
{
    return pattern->extents.width == 0 || pattern->extents.height == 0;
}

static cairo_bool_t
_gradient_is_opaque (const cairo_gradient_pattern_t *gradient,
                     const cairo_rectangle_int_t *sample)
{
    unsigned int i;

    assert (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR ||
            gradient->base.type == CAIRO_PATTERN_TYPE_RADIAL);

    if (gradient->n_stops == 0 ||
        (gradient->base.extend == CAIRO_EXTEND_NONE &&
         gradient->stops[0].offset == gradient->stops[gradient->n_stops - 1].offset))
        return FALSE;

    if (gradient->base.type == CAIRO_PATTERN_TYPE_LINEAR) {
        if (gradient->base.extend == CAIRO_EXTEND_NONE) {
            double t[2];
            cairo_linear_pattern_t *linear = (cairo_linear_pattern_t *) gradient;

            /* EXTEND_NONE degenerate radial gradients are clear */
            if (_linear_pattern_is_degenerate (linear))
                return FALSE;

            if (sample == NULL)
                return FALSE;

            _cairo_linear_pattern_box_to_parameter (linear,
                                                    sample->x,
                                                    sample->y,
                                                    sample->x + sample->width,
                                                    sample->y + sample->height,
                                                    t);

            if (t[0] < 0.0 || t[1] > 1.0)
                return FALSE;
        }
    } else
        return FALSE; /* TODO: check actual intersection */

    for (i = 0; i < gradient->n_stops; i++)
        if (! CAIRO_COLOR_IS_OPAQUE (&gradient->stops[i].color))
            return FALSE;

    return TRUE;
}

/**
 * _cairo_pattern_is_opaque:
 *
 * Convenience function to determine whether a pattern is an opaque
 * pattern (of any type). The same caveats that apply to
 * _cairo_pattern_is_opaque_solid apply here as well.
 *
 * Return value: %TRUE if the pattern is a opaque.
 **/
cairo_bool_t
_cairo_pattern_is_opaque (const cairo_pattern_t *abstract_pattern,
                          const cairo_rectangle_int_t *sample)
{
    const cairo_pattern_union_t *pattern;

    if (abstract_pattern->has_component_alpha)
        return FALSE;

    pattern = (cairo_pattern_union_t *) abstract_pattern;
    switch (pattern->base.type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        return _cairo_pattern_is_opaque_solid (abstract_pattern);
    case CAIRO_PATTERN_TYPE_SURFACE:
        return _surface_is_opaque (&pattern->surface, sample);
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        return _raster_source_is_opaque (&pattern->raster_source, sample);
    case CAIRO_PATTERN_TYPE_LINEAR:
    case CAIRO_PATTERN_TYPE_RADIAL:
        return _gradient_is_opaque (&pattern->gradient.base, sample);
    case CAIRO_PATTERN_TYPE_MESH:
        return FALSE;
    }

    ASSERT_NOT_REACHED;
    return FALSE;
}

cairo_bool_t
_cairo_pattern_is_clear (const cairo_pattern_t *abstract_pattern)
{
    const cairo_pattern_union_t *pattern;

    if (abstract_pattern->has_component_alpha)
        return FALSE;

    pattern = (cairo_pattern_union_t *) abstract_pattern;
    switch (abstract_pattern->type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        return CAIRO_COLOR_IS_CLEAR (&pattern->solid.color);
    case CAIRO_PATTERN_TYPE_SURFACE:
        return _surface_is_clear (&pattern->surface);
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        return _raster_source_is_clear (&pattern->raster_source);
    case CAIRO_PATTERN_TYPE_LINEAR:
    case CAIRO_PATTERN_TYPE_RADIAL:
        return _gradient_is_clear (&pattern->gradient.base, NULL);
    case CAIRO_PATTERN_TYPE_MESH:
        return _mesh_is_clear (&pattern->mesh);
    }

    ASSERT_NOT_REACHED;
    return FALSE;
}

/*
 * Will given row of back-translation matrix work with bilinear scale?
 * This is true for scales larger than 1. Also it was judged acceptable
 * for scales larger than .75. And if there is integer translation
 * then a scale of exactly .5 works.
 */
static int
use_bilinear(double x, double y, double t)
{
    /* This is the inverse matrix! */
    double h = x*x + y*y;
    if (h < 1.0 / (0.75 * 0.75))
        return TRUE; /* scale > .75 */
    if ((h > 3.99 && h < 4.01) /* scale is 1/2 */
        && !_cairo_fixed_from_double(x*y) /* parallel to an axis */
        && _cairo_fixed_is_integer (_cairo_fixed_from_double (t)))
        return TRUE;
    return FALSE;
}

/**
 * _cairo_pattern_analyze_filter:
 * @pattern: surface pattern
 * Returns: the optimized #cairo_filter_t to use with @pattern.
 *
 * Possibly optimize the filter to a simpler value depending on transformation
 **/
cairo_filter_t
_cairo_pattern_analyze_filter (const cairo_pattern_t *pattern)
{
    switch (pattern->filter) {
    case CAIRO_FILTER_GOOD:
    case CAIRO_FILTER_BEST:
    case CAIRO_FILTER_BILINEAR:
    case CAIRO_FILTER_FAST:
        /* If source pixels map 1:1 onto destination pixels, we do
         * not need to filter (and do not want to filter, since it
         * will cause blurriness)
         */
        if (_cairo_matrix_is_pixel_exact (&pattern->matrix)) {
            return CAIRO_FILTER_NEAREST;
        } else {
            /* Use BILINEAR for any scale greater than .75 instead
             * of GOOD. For scales of 1 and larger this is identical,
             * for the smaller sizes it was judged that the artifacts
             * were not worse than the artifacts from a box filer.
             * BILINEAR can also be used if the scale is exactly .5
             * and the translation in that direction is an integer.
             */
            if (pattern->filter == CAIRO_FILTER_GOOD &&
                use_bilinear (pattern->matrix.xx, pattern->matrix.xy,
                              pattern->matrix.x0) &&
                use_bilinear (pattern->matrix.yx, pattern->matrix.yy,
                              pattern->matrix.y0))
                return CAIRO_FILTER_BILINEAR;
        }
        break;

    case CAIRO_FILTER_NEAREST:
    case CAIRO_FILTER_GAUSSIAN:
    default:
        break;
    }

    return pattern->filter;
}

/**
 * _cairo_hypot:
 * Returns: value similar to hypot(@x,@y)
 *
 * May want to replace this with Manhattan distance (abs(x)+abs(y)) if
 * hypot is too slow, as there is no need for accuracy here.
 **/
static inline double
_cairo_hypot(double x, double y)
{
    return hypot(x, y);
}

/**
 * _cairo_pattern_sampled_area:
 *
 * Return region of @pattern that will be sampled to fill @extents,
 * based on the transformation and filter.
 *
 * This does not include pixels that are mulitiplied by values very
 * close to zero by the ends of filters. This is so that transforms
 * that should be the identity or 90 degree rotations do not expand
 * the source unexpectedly.
 *
 * XXX: We don't actually have any way of querying the backend for
 *      the filter radius, so we just guess base on what we know that
 *      backends do currently (see bug #10508)
 **/
void
_cairo_pattern_sampled_area (const cairo_pattern_t *pattern,
                             const cairo_rectangle_int_t *extents,
                             cairo_rectangle_int_t *sample)
{
    double x1, x2, y1, y2;
    double padx, pady;

    /* Assume filters are interpolating, which means identity
       cannot change the image */
    if (_cairo_matrix_is_identity (&pattern->matrix)) {
        *sample = *extents;
        return;
    }

    /* Transform the centers of the corner pixels */
    x1 = extents->x + 0.5;
    y1 = extents->y + 0.5;
    x2 = x1 + (extents->width - 1);
    y2 = y1 + (extents->height - 1);
    _cairo_matrix_transform_bounding_box (&pattern->matrix,
                                          &x1, &y1, &x2, &y2,
                                          NULL);

    /* How far away from center will it actually sample?
     * This is the distance from a transformed pixel center to the
     * furthest sample of reasonable size.
     */
    switch (pattern->filter) {
    case CAIRO_FILTER_NEAREST:
    case CAIRO_FILTER_FAST:
        /* Correct value is zero, but when the sample is on an integer
         * it is unknown if the backend will sample the pixel to the
         * left or right. This value makes it include both possible pixels.
         */
        padx = pady = 0.004;
        break;
    case CAIRO_FILTER_BILINEAR:
    case CAIRO_FILTER_GAUSSIAN:
    default:
        /* Correct value is .5 */
        padx = pady = 0.495;
        break;
    case CAIRO_FILTER_GOOD:
        /* Correct value is max(width,1)*.5 */
        padx = _cairo_hypot (pattern->matrix.xx, pattern->matrix.xy);
        if (padx <= 1.0) padx = 0.495;
        else if (padx >= 16.0) padx = 7.92;
        else padx *= 0.495;
        pady = _cairo_hypot (pattern->matrix.yx, pattern->matrix.yy);
        if (pady <= 1.0) pady = 0.495;
        else if (pady >= 16.0) pady = 7.92;
        else pady *= 0.495;
        break;
    case CAIRO_FILTER_BEST:
        /* Correct value is width*2 */
        padx = _cairo_hypot (pattern->matrix.xx, pattern->matrix.xy) * 1.98;
        if (padx > 7.92) padx = 7.92;
        pady = _cairo_hypot (pattern->matrix.yx, pattern->matrix.yy) * 1.98;
        if (pady > 7.92) pady = 7.92;
        break;
    }

    /* round furthest samples to edge of pixels */
    x1 = floor (x1 - padx);
    if (x1 < CAIRO_RECT_INT_MIN) x1 = CAIRO_RECT_INT_MIN;
    sample->x = x1;

    y1 = floor (y1 - pady);
    if (y1 < CAIRO_RECT_INT_MIN) y1 = CAIRO_RECT_INT_MIN;
    sample->y = y1;

    x2 = floor (x2 + padx) + 1.0;
    if (x2 > CAIRO_RECT_INT_MAX) x2 = CAIRO_RECT_INT_MAX;
    sample->width = x2 - x1;

    y2 = floor (y2 + pady) + 1.0;
    if (y2 > CAIRO_RECT_INT_MAX) y2 = CAIRO_RECT_INT_MAX;
    sample->height = y2 - y1;
}

/**
 * _cairo_pattern_get_extents:
 *
 * Return the "target-space" extents of @pattern in @extents.
 *
 * For unbounded patterns, the @extents will be initialized with
 * "infinite" extents, (minimum and maximum fixed-point values).
 *
 * XXX: Currently, bounded gradient patterns will also return
 * "infinite" extents, though it would be possible to optimize these
 * with a little more work.
 **/
void
_cairo_pattern_get_extents (const cairo_pattern_t         *pattern,
                            cairo_rectangle_int_t         *extents)
{
    double x1, y1, x2, y2;
    int ix1, ix2, iy1, iy2;
    cairo_bool_t round_x = FALSE;
    cairo_bool_t round_y = FALSE;

    switch (pattern->type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        goto UNBOUNDED;

    case CAIRO_PATTERN_TYPE_SURFACE:
        {
            cairo_rectangle_int_t surface_extents;
            const cairo_surface_pattern_t *surface_pattern =
                (const cairo_surface_pattern_t *) pattern;
            cairo_surface_t *surface = surface_pattern->surface;

            if (! _cairo_surface_get_extents (surface, &surface_extents))
                goto UNBOUNDED;

            if (surface_extents.width == 0 || surface_extents.height == 0)
                goto EMPTY;

            if (pattern->extend != CAIRO_EXTEND_NONE)
                goto UNBOUNDED;

            x1 = surface_extents.x;
            y1 = surface_extents.y;
            x2 = surface_extents.x + (int) surface_extents.width;
            y2 = surface_extents.y + (int) surface_extents.height;

            goto HANDLE_FILTER;
        }
        break;

    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        {
            const cairo_raster_source_pattern_t *raster =
                (const cairo_raster_source_pattern_t *) pattern;

            if (raster->extents.width == 0 || raster->extents.height == 0)
                goto EMPTY;

            if (pattern->extend != CAIRO_EXTEND_NONE)
                goto UNBOUNDED;

            x1 = raster->extents.x;
            y1 = raster->extents.y;
            x2 = raster->extents.x + (int) raster->extents.width;
            y2 = raster->extents.y + (int) raster->extents.height;
        }
    HANDLE_FILTER:
        switch (pattern->filter) {
        case CAIRO_FILTER_NEAREST:
        case CAIRO_FILTER_FAST:
            round_x = round_y = TRUE;
            /* We don't know which way .5 will go, so fudge it slightly. */
            x1 -= 0.004;
            y1 -= 0.004;
            x2 += 0.004;
            y2 += 0.004;
            break;
        case CAIRO_FILTER_BEST:
            /* Assume best filter will produce nice antialiased edges */
            break;
        case CAIRO_FILTER_BILINEAR:
        case CAIRO_FILTER_GAUSSIAN:
        case CAIRO_FILTER_GOOD:
        default:
            /* These filters can blur the edge out 1/2 pixel when scaling up */
            if (_cairo_hypot (pattern->matrix.xx, pattern->matrix.yx) < 1.0) {
                x1 -= 0.5;
                x2 += 0.5;
                round_x = TRUE;
            }
            if (_cairo_hypot (pattern->matrix.xy, pattern->matrix.yy) < 1.0) {
                y1 -= 0.5;
                y2 += 0.5;
                round_y = TRUE;
            }
            break;
        }
        break;

    case CAIRO_PATTERN_TYPE_RADIAL:
        {
            const cairo_radial_pattern_t *radial =
                (const cairo_radial_pattern_t *) pattern;
            double cx1, cy1;
            double cx2, cy2;
            double r1, r2;

            if (_radial_pattern_is_degenerate (radial)) {
                /* cairo-gstate should have optimised degenerate
                 * patterns to solid clear patterns, so we can ignore
                 * them here. */
                goto EMPTY;
            }

            /* TODO: in some cases (focus outside/on the circle) it is
             * half-bounded. */
            if (pattern->extend != CAIRO_EXTEND_NONE)
                goto UNBOUNDED;

            cx1 = radial->cd1.center.x;
            cy1 = radial->cd1.center.y;
            r1  = radial->cd1.radius;

            cx2 = radial->cd2.center.x;
            cy2 = radial->cd2.center.y;
            r2  = radial->cd2.radius;

            x1 = MIN (cx1 - r1, cx2 - r2);
            y1 = MIN (cy1 - r1, cy2 - r2);
            x2 = MAX (cx1 + r1, cx2 + r2);
            y2 = MAX (cy1 + r1, cy2 + r2);
        }
        break;

    case CAIRO_PATTERN_TYPE_LINEAR:
        {
            const cairo_linear_pattern_t *linear =
                (const cairo_linear_pattern_t *) pattern;

            if (pattern->extend != CAIRO_EXTEND_NONE)
                goto UNBOUNDED;

            if (_linear_pattern_is_degenerate (linear)) {
                /* cairo-gstate should have optimised degenerate
                 * patterns to solid ones, so we can again ignore
                 * them here. */
                goto EMPTY;
            }

            /* TODO: to get tight extents, use the matrix to transform
             * the pattern instead of transforming the extents later. */
            if (pattern->matrix.xy != 0. || pattern->matrix.yx != 0.)
                goto UNBOUNDED;

            if (linear->pd1.x == linear->pd2.x) {
                x1 = -HUGE_VAL;
                x2 = HUGE_VAL;
                y1 = MIN (linear->pd1.y, linear->pd2.y);
                y2 = MAX (linear->pd1.y, linear->pd2.y);
            } else if (linear->pd1.y == linear->pd2.y) {
                x1 = MIN (linear->pd1.x, linear->pd2.x);
                x2 = MAX (linear->pd1.x, linear->pd2.x);
                y1 = -HUGE_VAL;
                y2 = HUGE_VAL;
            } else {
                goto  UNBOUNDED;
            }

            /* The current linear renderer just point-samples in the middle
               of the pixels, similar to the NEAREST filter: */
            round_x = round_y = TRUE;
        }
        break;

    case CAIRO_PATTERN_TYPE_MESH:
        {
            const cairo_mesh_pattern_t *mesh =
                (const cairo_mesh_pattern_t *) pattern;
            if (! _cairo_mesh_pattern_coord_box (mesh, &x1, &y1, &x2, &y2))
                goto EMPTY;
        }
        break;

    default:
        ASSERT_NOT_REACHED;
    }

    if (_cairo_matrix_is_translation (&pattern->matrix)) {
        x1 -= pattern->matrix.x0; x2 -= pattern->matrix.x0;
        y1 -= pattern->matrix.y0; y2 -= pattern->matrix.y0;
    } else {
        cairo_matrix_t imatrix;
        cairo_status_t status;

        imatrix = pattern->matrix;
        status = cairo_matrix_invert (&imatrix);
        /* cairo_pattern_set_matrix ensures the matrix is invertible */
        assert (status == CAIRO_STATUS_SUCCESS);

        _cairo_matrix_transform_bounding_box (&imatrix,
                                              &x1, &y1, &x2, &y2,
                                              NULL);
    }

    if (!round_x) {
        x1 -= 0.5;
        x2 += 0.5;
    }
    if (x1 < CAIRO_RECT_INT_MIN)
        ix1 = CAIRO_RECT_INT_MIN;
    else 
        ix1 = _cairo_lround (x1);
    if (x2 > CAIRO_RECT_INT_MAX)
        ix2 = CAIRO_RECT_INT_MAX;
    else
        ix2 = _cairo_lround (x2);
    extents->x = ix1; extents->width  = ix2 - ix1;

    if (!round_y) {
        y1 -= 0.5;
        y2 += 0.5;
    }
    if (y1 < CAIRO_RECT_INT_MIN)
        iy1 = CAIRO_RECT_INT_MIN;
    else
        iy1 = _cairo_lround (y1);
    if (y2 > CAIRO_RECT_INT_MAX)
        iy2 = CAIRO_RECT_INT_MAX;
    else
        iy2 = _cairo_lround (y2);
    extents->y = iy1; extents->height = iy2 - iy1;

    return;

  UNBOUNDED:
    /* unbounded patterns -> 'infinite' extents */
    _cairo_unbounded_rectangle_init (extents);
    return;

  EMPTY:
    extents->x = extents->y = 0;
    extents->width = extents->height = 0;
    return;
}

/**
 * _cairo_pattern_get_ink_extents:
 *
 * Return the "target-space" inked extents of @pattern in @extents.
 **/
cairo_int_status_t
_cairo_pattern_get_ink_extents (const cairo_pattern_t         *pattern,
                                cairo_rectangle_int_t         *extents)
{
    if (pattern->type == CAIRO_PATTERN_TYPE_SURFACE &&
        pattern->extend == CAIRO_EXTEND_NONE)
    {
        const cairo_surface_pattern_t *surface_pattern =
            (const cairo_surface_pattern_t *) pattern;
        cairo_surface_t *surface = surface_pattern->surface;

        surface = _cairo_surface_get_source (surface, NULL);
        if (_cairo_surface_is_recording (surface)) {
            cairo_matrix_t imatrix;
            cairo_box_t box;
            cairo_status_t status;

            imatrix = pattern->matrix;
            status = cairo_matrix_invert (&imatrix);
            /* cairo_pattern_set_matrix ensures the matrix is invertible */
            assert (status == CAIRO_STATUS_SUCCESS);

            status = _cairo_recording_surface_get_ink_bbox ((cairo_recording_surface_t *)surface,
                                                   &box, &imatrix);
            if (unlikely (status))
                return status;

            _cairo_box_round_to_rectangle (&box, extents);
            return CAIRO_STATUS_SUCCESS;
        }
    }

    _cairo_pattern_get_extents (pattern, extents);
    return CAIRO_STATUS_SUCCESS;
}

static unsigned long
_cairo_solid_pattern_hash (unsigned long hash,
                           const cairo_solid_pattern_t *solid)
{
    hash = _cairo_hash_bytes (hash, &solid->color, sizeof (solid->color));

    return hash;
}

static unsigned long
_cairo_gradient_color_stops_hash (unsigned long hash,
                                  const cairo_gradient_pattern_t *gradient)
{
    unsigned int n;

    hash = _cairo_hash_bytes (hash,
                              &gradient->n_stops,
                              sizeof (gradient->n_stops));

    for (n = 0; n < gradient->n_stops; n++) {
        hash = _cairo_hash_bytes (hash,
                                  &gradient->stops[n].offset,
                                  sizeof (double));
        hash = _cairo_hash_bytes (hash,
                                  &gradient->stops[n].color,
                                  sizeof (cairo_color_stop_t));
    }

    return hash;
}

unsigned long
_cairo_linear_pattern_hash (unsigned long hash,
                            const cairo_linear_pattern_t *linear)
{
    hash = _cairo_hash_bytes (hash, &linear->pd1, sizeof (linear->pd1));
    hash = _cairo_hash_bytes (hash, &linear->pd2, sizeof (linear->pd2));

    return _cairo_gradient_color_stops_hash (hash, &linear->base);
}

unsigned long
_cairo_radial_pattern_hash (unsigned long hash,
                            const cairo_radial_pattern_t *radial)
{
    hash = _cairo_hash_bytes (hash, &radial->cd1.center, sizeof (radial->cd1.center));
    hash = _cairo_hash_bytes (hash, &radial->cd1.radius, sizeof (radial->cd1.radius));
    hash = _cairo_hash_bytes (hash, &radial->cd2.center, sizeof (radial->cd2.center));
    hash = _cairo_hash_bytes (hash, &radial->cd2.radius, sizeof (radial->cd2.radius));

    return _cairo_gradient_color_stops_hash (hash, &radial->base);
}

static unsigned long
_cairo_mesh_pattern_hash (unsigned long hash, const cairo_mesh_pattern_t *mesh)
{
    const cairo_mesh_patch_t *patch = _cairo_array_index_const (&mesh->patches, 0);
    unsigned int i, n = _cairo_array_num_elements (&mesh->patches);

    for (i = 0; i < n; i++)
       hash = _cairo_hash_bytes (hash, patch + i, sizeof (cairo_mesh_patch_t));

    return hash;
}

static unsigned long
_cairo_surface_pattern_hash (unsigned long hash,
                             const cairo_surface_pattern_t *surface)
{
    hash ^= surface->surface->unique_id;

    return hash;
}

static unsigned long
_cairo_raster_source_pattern_hash (unsigned long hash,
                                   const cairo_raster_source_pattern_t *raster)
{
    hash ^= (uintptr_t)raster->user_data;

    return hash;
}

unsigned long
_cairo_pattern_hash (const cairo_pattern_t *pattern)
{
    unsigned long hash = _CAIRO_HASH_INIT_VALUE;

    if (pattern->status)
        return 0;

    hash = _cairo_hash_bytes (hash, &pattern->type, sizeof (pattern->type));
    if (pattern->type != CAIRO_PATTERN_TYPE_SOLID) {
        hash = _cairo_hash_bytes (hash,
                                  &pattern->matrix, sizeof (pattern->matrix));
        hash = _cairo_hash_bytes (hash,
                                  &pattern->filter, sizeof (pattern->filter));
        hash = _cairo_hash_bytes (hash,
                                  &pattern->extend, sizeof (pattern->extend));
        hash = _cairo_hash_bytes (hash,
                                  &pattern->has_component_alpha,
                                  sizeof (pattern->has_component_alpha));
    }

    switch (pattern->type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        return _cairo_solid_pattern_hash (hash, (cairo_solid_pattern_t *) pattern);
    case CAIRO_PATTERN_TYPE_LINEAR:
        return _cairo_linear_pattern_hash (hash, (cairo_linear_pattern_t *) pattern);
    case CAIRO_PATTERN_TYPE_RADIAL:
        return _cairo_radial_pattern_hash (hash, (cairo_radial_pattern_t *) pattern);
    case CAIRO_PATTERN_TYPE_MESH:
        return _cairo_mesh_pattern_hash (hash, (cairo_mesh_pattern_t *) pattern);
    case CAIRO_PATTERN_TYPE_SURFACE:
        return _cairo_surface_pattern_hash (hash, (cairo_surface_pattern_t *) pattern);
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        return _cairo_raster_source_pattern_hash (hash, (cairo_raster_source_pattern_t *) pattern);
    default:
        ASSERT_NOT_REACHED;
        return FALSE;
    }
}

static cairo_bool_t
_cairo_solid_pattern_equal (const cairo_solid_pattern_t *a,
                            const cairo_solid_pattern_t *b)
{
    return _cairo_color_equal (&a->color, &b->color);
}

static cairo_bool_t
_cairo_gradient_color_stops_equal (const cairo_gradient_pattern_t *a,
                                   const cairo_gradient_pattern_t *b)
{
    unsigned int n;

    if (a->n_stops != b->n_stops)
        return FALSE;

    for (n = 0; n < a->n_stops; n++) {
        if (a->stops[n].offset != b->stops[n].offset)
            return FALSE;
        if (! _cairo_color_stop_equal (&a->stops[n].color, &b->stops[n].color))
            return FALSE;
    }

    return TRUE;
}

cairo_bool_t
_cairo_linear_pattern_equal (const cairo_linear_pattern_t *a,
                             const cairo_linear_pattern_t *b)
{
    if (a->pd1.x != b->pd1.x)
        return FALSE;

    if (a->pd1.y != b->pd1.y)
        return FALSE;

    if (a->pd2.x != b->pd2.x)
        return FALSE;

    if (a->pd2.y != b->pd2.y)
        return FALSE;

    return _cairo_gradient_color_stops_equal (&a->base, &b->base);
}

cairo_bool_t
_cairo_radial_pattern_equal (const cairo_radial_pattern_t *a,
                             const cairo_radial_pattern_t *b)
{
    if (a->cd1.center.x != b->cd1.center.x)
        return FALSE;

    if (a->cd1.center.y != b->cd1.center.y)
        return FALSE;

    if (a->cd1.radius != b->cd1.radius)
        return FALSE;

    if (a->cd2.center.x != b->cd2.center.x)
        return FALSE;

    if (a->cd2.center.y != b->cd2.center.y)
        return FALSE;

    if (a->cd2.radius != b->cd2.radius)
        return FALSE;

    return _cairo_gradient_color_stops_equal (&a->base, &b->base);
}

static cairo_bool_t
_cairo_mesh_pattern_equal (const cairo_mesh_pattern_t *a,
                           const cairo_mesh_pattern_t *b)
{
    const cairo_mesh_patch_t *patch_a, *patch_b;
    unsigned int i, num_patches_a, num_patches_b;

    num_patches_a = _cairo_array_num_elements (&a->patches);
    num_patches_b = _cairo_array_num_elements (&b->patches);

    if (num_patches_a != num_patches_b)
        return FALSE;

    for (i = 0; i < num_patches_a; i++) {
        patch_a = _cairo_array_index_const (&a->patches, i);
        patch_b = _cairo_array_index_const (&b->patches, i);
        if (memcmp (patch_a, patch_b, sizeof(cairo_mesh_patch_t)) != 0)
            return FALSE;
    }

    return TRUE;
}

static cairo_bool_t
_cairo_surface_pattern_equal (const cairo_surface_pattern_t *a,
                              const cairo_surface_pattern_t *b)
{
    return a->surface->unique_id == b->surface->unique_id;
}

static cairo_bool_t
_cairo_raster_source_pattern_equal (const cairo_raster_source_pattern_t *a,
                                    const cairo_raster_source_pattern_t *b)
{
    return a->user_data == b->user_data;
}

cairo_bool_t
_cairo_pattern_equal (const cairo_pattern_t *a, const cairo_pattern_t *b)
{
    if (a->status || b->status)
        return FALSE;

    if (a == b)
        return TRUE;

    if (a->type != b->type)
        return FALSE;

    if (a->has_component_alpha != b->has_component_alpha)
        return FALSE;

    if (a->type != CAIRO_PATTERN_TYPE_SOLID) {
        if (memcmp (&a->matrix, &b->matrix, sizeof (cairo_matrix_t)))
            return FALSE;

        if (a->filter != b->filter)
            return FALSE;

        if (a->extend != b->extend)
            return FALSE;
    }

    switch (a->type) {
    case CAIRO_PATTERN_TYPE_SOLID:
        return _cairo_solid_pattern_equal ((cairo_solid_pattern_t *) a,
                                           (cairo_solid_pattern_t *) b);
    case CAIRO_PATTERN_TYPE_LINEAR:
        return _cairo_linear_pattern_equal ((cairo_linear_pattern_t *) a,
                                            (cairo_linear_pattern_t *) b);
    case CAIRO_PATTERN_TYPE_RADIAL:
        return _cairo_radial_pattern_equal ((cairo_radial_pattern_t *) a,
                                            (cairo_radial_pattern_t *) b);
    case CAIRO_PATTERN_TYPE_MESH:
        return _cairo_mesh_pattern_equal ((cairo_mesh_pattern_t *) a,
                                          (cairo_mesh_pattern_t *) b);
    case CAIRO_PATTERN_TYPE_SURFACE:
        return _cairo_surface_pattern_equal ((cairo_surface_pattern_t *) a,
                                             (cairo_surface_pattern_t *) b);
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        return _cairo_raster_source_pattern_equal ((cairo_raster_source_pattern_t *) a,
                                                   (cairo_raster_source_pattern_t *) b);
    default:
        ASSERT_NOT_REACHED;
        return FALSE;
    }
}

/**
 * cairo_pattern_get_rgba:
 * @pattern: a #cairo_pattern_t
 * @red: return value for red component of color, or %NULL
 * @green: return value for green component of color, or %NULL
 * @blue: return value for blue component of color, or %NULL
 * @alpha: return value for alpha component of color, or %NULL
 *
 * Gets the solid color for a solid color pattern.
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH if the pattern is not a solid
 * color pattern.
 *
 * Since: 1.4
 **/
cairo_status_t
cairo_pattern_get_rgba (cairo_pattern_t *pattern,
                        double *red, double *green,
                        double *blue, double *alpha)
{
    cairo_solid_pattern_t *solid = (cairo_solid_pattern_t*) pattern;
    double r0, g0, b0, a0;

    if (pattern->status)
        return pattern->status;

    if (pattern->type != CAIRO_PATTERN_TYPE_SOLID)
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    _cairo_color_get_rgba (&solid->color, &r0, &g0, &b0, &a0);

    if (red)
        *red = r0;
    if (green)
        *green = g0;
    if (blue)
        *blue = b0;
    if (alpha)
        *alpha = a0;

    return CAIRO_STATUS_SUCCESS;
}

/**
 * cairo_pattern_get_surface:
 * @pattern: a #cairo_pattern_t
 * @surface: return value for surface of pattern, or %NULL
 *
 * Gets the surface of a surface pattern.  The reference returned in
 * @surface is owned by the pattern; the caller should call
 * cairo_surface_reference() if the surface is to be retained.
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH if the pattern is not a surface
 * pattern.
 *
 * Since: 1.4
 **/
cairo_status_t
cairo_pattern_get_surface (cairo_pattern_t *pattern,
                           cairo_surface_t **surface)
{
    cairo_surface_pattern_t *spat = (cairo_surface_pattern_t*) pattern;

    if (pattern->status)
        return pattern->status;

    if (pattern->type != CAIRO_PATTERN_TYPE_SURFACE)
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (surface)
        *surface = spat->surface;

    return CAIRO_STATUS_SUCCESS;
}

/**
 * cairo_pattern_get_color_stop_rgba:
 * @pattern: a #cairo_pattern_t
 * @index: index of the stop to return data for
 * @offset: return value for the offset of the stop, or %NULL
 * @red: return value for red component of color, or %NULL
 * @green: return value for green component of color, or %NULL
 * @blue: return value for blue component of color, or %NULL
 * @alpha: return value for alpha component of color, or %NULL
 *
 * Gets the color and offset information at the given @index for a
 * gradient pattern.  Values of @index range from 0 to n-1
 * where n is the number returned
 * by cairo_pattern_get_color_stop_count().
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or %CAIRO_STATUS_INVALID_INDEX
 * if @index is not valid for the given pattern.  If the pattern is
 * not a gradient pattern, %CAIRO_STATUS_PATTERN_TYPE_MISMATCH is
 * returned.
 *
 * Since: 1.4
 **/
cairo_status_t
cairo_pattern_get_color_stop_rgba (cairo_pattern_t *pattern,
                                   int index, double *offset,
                                   double *red, double *green,
                                   double *blue, double *alpha)
{
    cairo_gradient_pattern_t *gradient = (cairo_gradient_pattern_t*) pattern;

    if (pattern->status)
        return pattern->status;

    if (pattern->type != CAIRO_PATTERN_TYPE_LINEAR &&
        pattern->type != CAIRO_PATTERN_TYPE_RADIAL)
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (index < 0 || (unsigned int) index >= gradient->n_stops)
        return _cairo_error (CAIRO_STATUS_INVALID_INDEX);

    if (offset)
        *offset = gradient->stops[index].offset;
    if (red)
        *red = gradient->stops[index].color.red;
    if (green)
        *green = gradient->stops[index].color.green;
    if (blue)
        *blue = gradient->stops[index].color.blue;
    if (alpha)
        *alpha = gradient->stops[index].color.alpha;

    return CAIRO_STATUS_SUCCESS;
}

/**
 * cairo_pattern_get_color_stop_count:
 * @pattern: a #cairo_pattern_t
 * @count: return value for the number of color stops, or %NULL
 *
 * Gets the number of color stops specified in the given gradient
 * pattern.
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH if @pattern is not a gradient
 * pattern.
 *
 * Since: 1.4
 **/
cairo_status_t
cairo_pattern_get_color_stop_count (cairo_pattern_t *pattern,
                                    int *count)
{
    cairo_gradient_pattern_t *gradient = (cairo_gradient_pattern_t*) pattern;

    if (pattern->status)
        return pattern->status;

    if (pattern->type != CAIRO_PATTERN_TYPE_LINEAR &&
        pattern->type != CAIRO_PATTERN_TYPE_RADIAL)
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (count)
        *count = gradient->n_stops;

    return CAIRO_STATUS_SUCCESS;
}

/**
 * cairo_pattern_get_linear_points:
 * @pattern: a #cairo_pattern_t
 * @x0: return value for the x coordinate of the first point, or %NULL
 * @y0: return value for the y coordinate of the first point, or %NULL
 * @x1: return value for the x coordinate of the second point, or %NULL
 * @y1: return value for the y coordinate of the second point, or %NULL
 *
 * Gets the gradient endpoints for a linear gradient.
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH if @pattern is not a linear
 * gradient pattern.
 *
 * Since: 1.4
 **/
cairo_status_t
cairo_pattern_get_linear_points (cairo_pattern_t *pattern,
                                 double *x0, double *y0,
                                 double *x1, double *y1)
{
    cairo_linear_pattern_t *linear = (cairo_linear_pattern_t*) pattern;

    if (pattern->status)
        return pattern->status;

    if (pattern->type != CAIRO_PATTERN_TYPE_LINEAR)
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (x0)
        *x0 = linear->pd1.x;
    if (y0)
        *y0 = linear->pd1.y;
    if (x1)
        *x1 = linear->pd2.x;
    if (y1)
        *y1 = linear->pd2.y;

    return CAIRO_STATUS_SUCCESS;
}

/**
 * cairo_pattern_get_radial_circles:
 * @pattern: a #cairo_pattern_t
 * @x0: return value for the x coordinate of the center of the first circle, or %NULL
 * @y0: return value for the y coordinate of the center of the first circle, or %NULL
 * @r0: return value for the radius of the first circle, or %NULL
 * @x1: return value for the x coordinate of the center of the second circle, or %NULL
 * @y1: return value for the y coordinate of the center of the second circle, or %NULL
 * @r1: return value for the radius of the second circle, or %NULL
 *
 * Gets the gradient endpoint circles for a radial gradient, each
 * specified as a center coordinate and a radius.
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH if @pattern is not a radial
 * gradient pattern.
 *
 * Since: 1.4
 **/
cairo_status_t
cairo_pattern_get_radial_circles (cairo_pattern_t *pattern,
                                  double *x0, double *y0, double *r0,
                                  double *x1, double *y1, double *r1)
{
    cairo_radial_pattern_t *radial = (cairo_radial_pattern_t*) pattern;

    if (pattern->status)
        return pattern->status;

    if (pattern->type != CAIRO_PATTERN_TYPE_RADIAL)
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (x0)
        *x0 = radial->cd1.center.x;
    if (y0)
        *y0 = radial->cd1.center.y;
    if (r0)
        *r0 = radial->cd1.radius;
    if (x1)
        *x1 = radial->cd2.center.x;
    if (y1)
        *y1 = radial->cd2.center.y;
    if (r1)
        *r1 = radial->cd2.radius;

    return CAIRO_STATUS_SUCCESS;
}

/**
 * cairo_mesh_pattern_get_patch_count:
 * @pattern: a #cairo_pattern_t
 * @count: return value for the number patches, or %NULL
 *
 * Gets the number of patches specified in the given mesh pattern.
 *
 * The number only includes patches which have been finished by
 * calling cairo_mesh_pattern_end_patch(). For example it will be 0
 * during the definition of the first patch.
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or
 * %CAIRO_STATUS_PATTERN_TYPE_MISMATCH if @pattern is not a mesh
 * pattern.
 *
 * Since: 1.12
 **/
cairo_status_t
cairo_mesh_pattern_get_patch_count (cairo_pattern_t *pattern,
                                    unsigned int *count)
{
    cairo_mesh_pattern_t *mesh = (cairo_mesh_pattern_t *) pattern;

    if (unlikely (pattern->status))
        return pattern->status;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH))
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (count) {
        *count = _cairo_array_num_elements (&mesh->patches);
        if (mesh->current_patch)
            *count -= 1;
    }

    return CAIRO_STATUS_SUCCESS;
}
slim_hidden_def (cairo_mesh_pattern_get_patch_count);

/**
 * cairo_mesh_pattern_get_path:
 * @pattern: a #cairo_pattern_t
 * @patch_num: the patch number to return data for
 *
 * Gets path defining the patch @patch_num for a mesh
 * pattern.
 *
 * @patch_num can range from 0 to n-1 where n is the number returned by
 * cairo_mesh_pattern_get_patch_count().
 *
 * Return value: the path defining the patch, or a path with status
 * %CAIRO_STATUS_INVALID_INDEX if @patch_num or @point_num is not
 * valid for @pattern. If @pattern is not a mesh pattern, a path with
 * status %CAIRO_STATUS_PATTERN_TYPE_MISMATCH is returned.
 *
 * Since: 1.12
 **/
cairo_path_t *
cairo_mesh_pattern_get_path (cairo_pattern_t *pattern,
                             unsigned int patch_num)
{
    cairo_mesh_pattern_t *mesh = (cairo_mesh_pattern_t *) pattern;
    const cairo_mesh_patch_t *patch;
    cairo_path_t *path;
    cairo_path_data_t *data;
    unsigned int patch_count;
    int l, current_point;

    if (unlikely (pattern->status))
        return _cairo_path_create_in_error (pattern->status);

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH))
        return _cairo_path_create_in_error (_cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH));

    patch_count = _cairo_array_num_elements (&mesh->patches);
    if (mesh->current_patch)
        patch_count--;

    if (unlikely (patch_num >= patch_count))
        return _cairo_path_create_in_error (_cairo_error (CAIRO_STATUS_INVALID_INDEX));

    patch = _cairo_array_index_const (&mesh->patches, patch_num);

    path = malloc (sizeof (cairo_path_t));
    if (path == NULL)
        return _cairo_path_create_in_error (_cairo_error (CAIRO_STATUS_NO_MEMORY));

    path->num_data = 18;
    path->data = _cairo_malloc_ab (path->num_data,
                                   sizeof (cairo_path_data_t));
    if (path->data == NULL) {
        free (path);
        return _cairo_path_create_in_error (_cairo_error (CAIRO_STATUS_NO_MEMORY));
    }

    data = path->data;
    data[0].header.type = CAIRO_PATH_MOVE_TO;
    data[0].header.length = 2;
    data[1].point.x = patch->points[0][0].x;
    data[1].point.y = patch->points[0][0].y;
    data += data[0].header.length;

    current_point = 0;

    for (l = 0; l < 4; l++) {
        int i, j, k;

        data[0].header.type = CAIRO_PATH_CURVE_TO;
        data[0].header.length = 4;

        for (k = 1; k < 4; k++) {
            current_point = (current_point + 1) % 12;
            i = mesh_path_point_i[current_point];
            j = mesh_path_point_j[current_point];
            data[k].point.x = patch->points[i][j].x;
            data[k].point.y = patch->points[i][j].y;
        }

        data += data[0].header.length;
    }

    path->status = CAIRO_STATUS_SUCCESS;

    return path;
}
slim_hidden_def (cairo_mesh_pattern_get_path);

/**
 * cairo_mesh_pattern_get_corner_color_rgba:
 * @pattern: a #cairo_pattern_t
 * @patch_num: the patch number to return data for
 * @corner_num: the corner number to return data for
 * @red: return value for red component of color, or %NULL
 * @green: return value for green component of color, or %NULL
 * @blue: return value for blue component of color, or %NULL
 * @alpha: return value for alpha component of color, or %NULL
 *
 * Gets the color information in corner @corner_num of patch
 * @patch_num for a mesh pattern.
 *
 * @patch_num can range from 0 to n-1 where n is the number returned by
 * cairo_mesh_pattern_get_patch_count().
 *
 * Valid values for @corner_num are from 0 to 3 and identify the
 * corners as explained in cairo_pattern_create_mesh().
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or %CAIRO_STATUS_INVALID_INDEX
 * if @patch_num or @corner_num is not valid for @pattern. If
 * @pattern is not a mesh pattern, %CAIRO_STATUS_PATTERN_TYPE_MISMATCH
 * is returned.
 *
 * Since: 1.12
 **/
cairo_status_t
cairo_mesh_pattern_get_corner_color_rgba (cairo_pattern_t *pattern,
                                          unsigned int patch_num,
                                          unsigned int corner_num,
                                          double *red, double *green,
                                          double *blue, double *alpha)
{
    cairo_mesh_pattern_t *mesh = (cairo_mesh_pattern_t *) pattern;
    unsigned int patch_count;
    const cairo_mesh_patch_t *patch;

    if (unlikely (pattern->status))
        return pattern->status;

    if (unlikely (pattern->type != CAIRO_PATTERN_TYPE_MESH))
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (unlikely (corner_num > 3))
        return _cairo_error (CAIRO_STATUS_INVALID_INDEX);

    patch_count = _cairo_array_num_elements (&mesh->patches);
    if (mesh->current_patch)
        patch_count--;

    if (unlikely (patch_num >= patch_count))
        return _cairo_error (CAIRO_STATUS_INVALID_INDEX);

    patch = _cairo_array_index_const (&mesh->patches, patch_num);

    if (red)
        *red = patch->colors[corner_num].red;
    if (green)
        *green = patch->colors[corner_num].green;
    if (blue)
        *blue = patch->colors[corner_num].blue;
    if (alpha)
        *alpha = patch->colors[corner_num].alpha;

    return CAIRO_STATUS_SUCCESS;
}
slim_hidden_def (cairo_mesh_pattern_get_corner_color_rgba);

/**
 * cairo_mesh_pattern_get_control_point:
 * @pattern: a #cairo_pattern_t
 * @patch_num: the patch number to return data for
 * @point_num: the control point number to return data for
 * @x: return value for the x coordinate of the control point, or %NULL
 * @y: return value for the y coordinate of the control point, or %NULL
 *
 * Gets the control point @point_num of patch @patch_num for a mesh
 * pattern.
 *
 * @patch_num can range from 0 to n-1 where n is the number returned by
 * cairo_mesh_pattern_get_patch_count().
 *
 * Valid values for @point_num are from 0 to 3 and identify the
 * control points as explained in cairo_pattern_create_mesh().
 *
 * Return value: %CAIRO_STATUS_SUCCESS, or %CAIRO_STATUS_INVALID_INDEX
 * if @patch_num or @point_num is not valid for @pattern. If @pattern
 * is not a mesh pattern, %CAIRO_STATUS_PATTERN_TYPE_MISMATCH is
 * returned.
 *
 * Since: 1.12
 **/
cairo_status_t
cairo_mesh_pattern_get_control_point (cairo_pattern_t *pattern,
                                      unsigned int patch_num,
                                      unsigned int point_num,
                                      double *x, double *y)
{
    cairo_mesh_pattern_t *mesh = (cairo_mesh_pattern_t *) pattern;
    const cairo_mesh_patch_t *patch;
    unsigned int patch_count;
    int i, j;

    if (pattern->status)
        return pattern->status;

    if (pattern->type != CAIRO_PATTERN_TYPE_MESH)
        return _cairo_error (CAIRO_STATUS_PATTERN_TYPE_MISMATCH);

    if (point_num > 3)
        return _cairo_error (CAIRO_STATUS_INVALID_INDEX);

    patch_count = _cairo_array_num_elements (&mesh->patches);
    if (mesh->current_patch)
        patch_count--;

    if (unlikely (patch_num >= patch_count))
        return _cairo_error (CAIRO_STATUS_INVALID_INDEX);

    patch = _cairo_array_index_const (&mesh->patches, patch_num);

    i = mesh_control_point_i[point_num];
    j = mesh_control_point_j[point_num];

    if (x)
        *x = patch->points[i][j].x;
    if (y)
        *y = patch->points[i][j].y;

    return CAIRO_STATUS_SUCCESS;
}
slim_hidden_def (cairo_mesh_pattern_get_control_point);

void
_cairo_pattern_reset_static_data (void)
{
    int i;

    for (i = 0; i < ARRAY_LENGTH (freed_pattern_pool); i++)
        _freed_pool_reset (&freed_pattern_pool[i]);
}

static void
_cairo_debug_print_surface_pattern (FILE *file,
                                    const cairo_surface_pattern_t *pattern)
{
    printf ("  surface type: %d\n", pattern->surface->type);
}

static void
_cairo_debug_print_raster_source_pattern (FILE *file,
                                          const cairo_raster_source_pattern_t *raster)
{
    printf ("  content: %x, size %dx%d\n", raster->content, raster->extents.width, raster->extents.height);
}

static void
_cairo_debug_print_linear_pattern (FILE *file,
                                    const cairo_linear_pattern_t *pattern)
{
}

static void
_cairo_debug_print_radial_pattern (FILE *file,
                                   const cairo_radial_pattern_t *pattern)
{
}

static void
_cairo_debug_print_mesh_pattern (FILE *file,
                                 const cairo_mesh_pattern_t *pattern)
{
}

void
_cairo_debug_print_pattern (FILE *file, const cairo_pattern_t *pattern)
{
    const char *s;
    switch (pattern->type) {
    case CAIRO_PATTERN_TYPE_SOLID: s = "solid"; break;
    case CAIRO_PATTERN_TYPE_SURFACE: s = "surface"; break;
    case CAIRO_PATTERN_TYPE_LINEAR: s = "linear"; break;
    case CAIRO_PATTERN_TYPE_RADIAL: s = "radial"; break;
    case CAIRO_PATTERN_TYPE_MESH: s = "mesh"; break;
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE: s = "raster"; break;
    default: s = "invalid"; ASSERT_NOT_REACHED; break;
    }

    fprintf (file, "pattern: %s\n", s);
    if (pattern->type == CAIRO_PATTERN_TYPE_SOLID)
        return;

    switch (pattern->extend) {
    case CAIRO_EXTEND_NONE: s = "none"; break;
    case CAIRO_EXTEND_REPEAT: s = "repeat"; break;
    case CAIRO_EXTEND_REFLECT: s = "reflect"; break;
    case CAIRO_EXTEND_PAD: s = "pad"; break;
    default: s = "invalid"; ASSERT_NOT_REACHED; break;
    }
    fprintf (file, "  extend: %s\n", s);

    switch (pattern->filter) {
    case CAIRO_FILTER_FAST: s = "fast"; break;
    case CAIRO_FILTER_GOOD: s = "good"; break;
    case CAIRO_FILTER_BEST: s = "best"; break;
    case CAIRO_FILTER_NEAREST: s = "nearest"; break;
    case CAIRO_FILTER_BILINEAR: s = "bilinear"; break;
    case CAIRO_FILTER_GAUSSIAN: s = "guassian"; break;
    default: s = "invalid"; ASSERT_NOT_REACHED; break;
    }
    fprintf (file, "  filter: %s\n", s);
    fprintf (file, "  matrix: [%g %g %g %g %g %g]\n",
             pattern->matrix.xx, pattern->matrix.yx,
             pattern->matrix.xy, pattern->matrix.yy,
             pattern->matrix.x0, pattern->matrix.y0);
    switch (pattern->type) {
    default:
    case CAIRO_PATTERN_TYPE_SOLID:
        break;
    case CAIRO_PATTERN_TYPE_RASTER_SOURCE:
        _cairo_debug_print_raster_source_pattern (file, (cairo_raster_source_pattern_t *)pattern);
        break;
    case CAIRO_PATTERN_TYPE_SURFACE:
        _cairo_debug_print_surface_pattern (file, (cairo_surface_pattern_t *)pattern);
        break;
    case CAIRO_PATTERN_TYPE_LINEAR:
        _cairo_debug_print_linear_pattern (file, (cairo_linear_pattern_t *)pattern);
        break;
    case CAIRO_PATTERN_TYPE_RADIAL:
        _cairo_debug_print_radial_pattern (file, (cairo_radial_pattern_t *)pattern);
        break;
    case CAIRO_PATTERN_TYPE_MESH:
        _cairo_debug_print_mesh_pattern (file, (cairo_mesh_pattern_t *)pattern);
        break;
    }
}