new beta-0.90.0

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

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

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

#include "cairo-box-inline.h"
#include "cairo-boxes-private.h"
#include "cairo-error-private.h"
#include "cairo-path-fixed-private.h"
#include "cairo-slope-private.h"
#include "cairo-stroke-dash-private.h"
#include "cairo-traps-private.h"

typedef struct cairo_stroker {
    cairo_stroke_style_t style;

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

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

    cairo_pen_t   pen;

    cairo_point_t current_point;
    cairo_point_t first_point;

    cairo_bool_t has_initial_sub_path;

    cairo_bool_t has_current_face;
    cairo_stroke_face_t current_face;

    cairo_bool_t has_first_face;
    cairo_stroke_face_t first_face;

    cairo_stroker_dash_t dash;

    cairo_bool_t has_bounds;
    cairo_box_t bounds;
} cairo_stroker_t;

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

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

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

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

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

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

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

static cairo_status_t
_cairo_stroker_init (cairo_stroker_t            *stroker,
                     const cairo_path_fixed_t   *path,
                     const cairo_stroke_style_t *stroke_style,
                     const cairo_matrix_t       *ctm,
                     const cairo_matrix_t       *ctm_inverse,
                     double                      tolerance,
                     const cairo_box_t          *limits,
                     int                         num_limits)
{
    cairo_status_t status;

    stroker->style = *stroke_style;
    stroker->ctm = ctm;
    stroker->ctm_inverse = ctm_inverse;
    stroker->tolerance = tolerance;
    stroker->half_line_width = stroke_style->line_width / 2.0;

    /* To test whether we need to join two segments of a spline using
     * a round-join or a bevel-join, we can inspect the angle between the
     * two segments. If the difference between the chord distance
     * (half-line-width times the cosine of the bisection angle) and the
     * half-line-width itself is greater than tolerance then we need to
     * inject a point.
     */
    stroker->spline_cusp_tolerance = 1 - tolerance / stroker->half_line_width;
    stroker->spline_cusp_tolerance *= stroker->spline_cusp_tolerance;
    stroker->spline_cusp_tolerance *= 2;
    stroker->spline_cusp_tolerance -= 1;

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

    status = _cairo_pen_init (&stroker->pen,
                              stroker->half_line_width, tolerance, ctm);
    if (unlikely (status))
        return status;

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

    _cairo_stroker_dash_init (&stroker->dash, stroke_style);

    stroker->add_external_edge = NULL;

    stroker->has_bounds = FALSE;
    if (num_limits)
        _cairo_stroker_limit (stroker, path, limits, num_limits);

    return CAIRO_STATUS_SUCCESS;
}

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

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

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

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

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

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

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

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

/*
 * Construct a fan around the midpoint using the vertices from pen between
 * inpt and outpt.
 */
static cairo_status_t
_tessellate_fan (cairo_stroker_t *stroker,
                 const cairo_slope_t *in_vector,
                 const cairo_slope_t *out_vector,
                 const cairo_point_t *midpt,
                 const cairo_point_t *inpt,
                 const cairo_point_t *outpt,
                 cairo_bool_t clockwise)
{
    cairo_point_t stack_points[64], *points = stack_points;
    cairo_pen_t *pen = &stroker->pen;
    int start, stop, num_points = 0;
    cairo_status_t status;

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

    assert (stroker->pen.num_vertices);

    if (clockwise) {
        _cairo_pen_find_active_ccw_vertices (pen,
                                             in_vector, out_vector,
                                             &start, &stop);
        if (stroker->add_external_edge) {
            cairo_point_t last;
            last = *inpt;
            while (start != stop) {
                cairo_point_t p = *midpt;
                _translate_point (&p, &pen->vertices[start].point);

                status = stroker->add_external_edge (stroker->closure,
                                                     &last, &p);
                if (unlikely (status))
                    return status;
                last = p;

                if (start-- == 0)
                    start += pen->num_vertices;
            }
            status = stroker->add_external_edge (stroker->closure,
                                                 &last, outpt);
        } else {
            if (start == stop)
                goto BEVEL;

            num_points = stop - start;
            if (num_points < 0)
                num_points += pen->num_vertices;
            num_points += 2;
            if (num_points > ARRAY_LENGTH(stack_points)) {
                points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
                if (unlikely (points == NULL))
                    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
            }

            points[0] = *inpt;
            num_points = 1;
            while (start != stop) {
                points[num_points] = *midpt;
                _translate_point (&points[num_points], &pen->vertices[start].point);
                num_points++;

                if (start-- == 0)
                    start += pen->num_vertices;
            }
            points[num_points++] = *outpt;
        }
    } else {
        _cairo_pen_find_active_cw_vertices (pen,
                                            in_vector, out_vector,
                                            &start, &stop);
        if (stroker->add_external_edge) {
            cairo_point_t last;
            last = *inpt;
            while (start != stop) {
                cairo_point_t p = *midpt;
                _translate_point (&p, &pen->vertices[start].point);

                status = stroker->add_external_edge (stroker->closure,
                                                     &p, &last);
                if (unlikely (status))
                    return status;
                last = p;

                if (++start == pen->num_vertices)
                    start = 0;
            }
            status = stroker->add_external_edge (stroker->closure,
                                                 outpt, &last);
        } else {
            if (start == stop)
                goto BEVEL;

            num_points = stop - start;
            if (num_points < 0)
                num_points += pen->num_vertices;
            num_points += 2;
            if (num_points > ARRAY_LENGTH(stack_points)) {
                points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
                if (unlikely (points == NULL))
                    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
            }

            points[0] = *inpt;
            num_points = 1;
            while (start != stop) {
                points[num_points] = *midpt;
                _translate_point (&points[num_points], &pen->vertices[start].point);
                num_points++;

                if (++start == pen->num_vertices)
                    start = 0;
            }
            points[num_points++] = *outpt;
        }
    }

    if (num_points) {
        status = stroker->add_triangle_fan (stroker->closure,
                                            midpt, points, num_points);
    }

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

    return status;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    /* fall through ... */

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

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

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

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

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

    }

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

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

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

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

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

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

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

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

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

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

    reversed = *face;

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

    return _cairo_stroker_add_cap (stroker, &reversed);
}

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

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

    cairo_matrix_transform_distance (ctm_inverse, &dx0, &dy0);

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

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

    if (mag_out)
        *mag_out = mag;

    return TRUE;
}

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

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

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

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

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

    face->point = *point;

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

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

    face->dev_vector = *dev_slope;
}

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

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

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

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

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

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

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

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

    return CAIRO_STATUS_SUCCESS;
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    return CAIRO_STATUS_SUCCESS;
}

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

    stroker->has_initial_sub_path = TRUE;

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

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

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

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

    stroker->current_point = *point;

    return CAIRO_STATUS_SUCCESS;
}

static cairo_status_t
_cairo_stroker_spline_to (void *closure,
                          const cairo_point_t *point,
                          const cairo_slope_t *tangent)
{
    cairo_stroker_t *stroker = closure;
    cairo_stroke_face_t new_face;
    double slope_dx, slope_dy;
    cairo_point_t points[3];
    cairo_point_t intersect_point;

    stroker->has_initial_sub_path = TRUE;

    if (stroker->current_point.x == point->x &&
        stroker->current_point.y == point->y)
        return CAIRO_STATUS_SUCCESS;

    slope_dx = _cairo_fixed_to_double (tangent->dx);
    slope_dy = _cairo_fixed_to_double (tangent->dy);

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

    _compute_face (point, tangent,
                   slope_dx, slope_dy,
                   stroker, &new_face);

    assert (stroker->has_current_face);

    if ((new_face.dev_slope.x * stroker->current_face.dev_slope.x +
         new_face.dev_slope.y * stroker->current_face.dev_slope.y) < stroker->spline_cusp_tolerance) {

        const cairo_point_t *inpt, *outpt;
        int clockwise = _cairo_stroker_join_is_clockwise (&new_face,
                                                          &stroker->current_face);

        if (clockwise) {
            inpt = &stroker->current_face.cw;
            outpt = &new_face.cw;
        } else {
            inpt = &stroker->current_face.ccw;
            outpt = &new_face.ccw;
        }

        _tessellate_fan (stroker,
                         &stroker->current_face.dev_vector,
                         &new_face.dev_vector,
                         &stroker->current_face.point,
                         inpt, outpt,
                         clockwise);
    }

    if (_slow_segment_intersection (&stroker->current_face.cw,
                                    &stroker->current_face.ccw,
                                    &new_face.cw,
                                    &new_face.ccw,
                                    &intersect_point)) {
        points[0] = stroker->current_face.ccw;
        points[1] = new_face.ccw;
        points[2] = intersect_point;
        stroker->add_triangle (stroker->closure, points);

        points[0] = stroker->current_face.cw;
        points[1] = new_face.cw;
        stroker->add_triangle (stroker->closure, points);
    } else {
        points[0] = stroker->current_face.ccw;
        points[1] = stroker->current_face.cw;
        points[2] = new_face.cw;
        stroker->add_triangle (stroker->closure, points);

        points[0] = stroker->current_face.ccw;
        points[1] = new_face.cw;
        points[2] = new_face.ccw;
        stroker->add_triangle (stroker->closure, points);
    }

    stroker->current_face = new_face;
    stroker->has_current_face = TRUE;
    stroker->current_point = *point;

    return CAIRO_STATUS_SUCCESS;
}

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

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

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

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

    _cairo_slope_init (&dev_slope, p1, p2);

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

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

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

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

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

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

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

                stroker->has_current_face = FALSE;
            }
        }

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

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

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

        stroker->has_current_face = TRUE;
    }

    stroker->current_point = *p2;

    return CAIRO_STATUS_SUCCESS;
}

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

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

    /* spline_to is only capable of rendering non-degenerate splines. */
    spline_to = stroker->dash.dashed ?
        (cairo_spline_add_point_func_t) _cairo_stroker_line_to_dashed :
        (cairo_spline_add_point_func_t) _cairo_stroker_spline_to;

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

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

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

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

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

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

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

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

        stroker->current_face = face;
    }

    stroker->style.line_join = line_join_save;

    return CAIRO_STATUS_SUCCESS;
}

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

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

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

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

    return CAIRO_STATUS_SUCCESS;
}

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

    status = _cairo_stroker_init (&stroker, path, stroke_style,
                                  ctm, ctm_inverse, tolerance,
                                  NULL, 0);
    if (unlikely (status))
        return status;

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

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

    if (unlikely (status))
        goto BAIL;

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

BAIL:
    _cairo_stroker_fini (&stroker);

    return status;
}

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

    status = _cairo_stroker_init (&stroker, path, stroke_style,
                                  ctm, ctm_inverse, tolerance,
                                  polygon->limits, polygon->num_limits);
    if (unlikely (status))
        return status;

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

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

    if (unlikely (status))
        goto BAIL;

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

BAIL:
    _cairo_stroker_fini (&stroker);

    return status;
}

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

    _cairo_polygon_init (&polygon, traps->limits, traps->num_limits);
    status = _cairo_path_fixed_stroke_to_polygon (path,
                                                  stroke_style,
                                                  ctm,
                                                  ctm_inverse,
                                                  tolerance,
                                                  &polygon);
    if (unlikely (status))
        goto BAIL;

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

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

BAIL:
    _cairo_polygon_fini (&polygon);

    return status;
}