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/* -*- Mode: c; tab-width: 8; c-basic-offset: 4; indent-tabs-mode: t; -*- */

/* cairo - a vector graphics library with display and print output

 *

 * Copyright © 2002 University of Southern California

 * Copyright © 2013 Intel Corporation

 *

 * This library is free software; you can redistribute it and/or

 * modify it either under the terms of the GNU Lesser General Public

 * License version 2.1 as published by the Free Software Foundation

 * (the "LGPL") or, at your option, under the terms of the Mozilla

 * Public License Version 1.1 (the "MPL"). If you do not alter this

 * notice, a recipient may use your version of this file under either

 * the MPL or the LGPL.

 *

 * You should have received a copy of the LGPL along with this library

 * in the file COPYING-LGPL-2.1; if not, write to the Free Software

 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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 

 *	Chris Wilson 

 */

#include "cairoint.h"

#include "cairo-box-inline.h"

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

#include "cairo-slope-private.h"

#include "cairo-stroke-dash-private.h"

#include "cairo-traps-private.h"

#include 

struct stroker {

    const cairo_stroke_style_t	*style;

    const cairo_matrix_t *ctm;

    const cairo_matrix_t *ctm_inverse;

    double spline_cusp_tolerance;

    double half_line_width;

    double tolerance;

    double ctm_determinant;

    cairo_bool_t ctm_det_positive;

    cairo_line_join_t line_join;

    cairo_traps_t *traps;

    cairo_pen_t pen;

    cairo_point_t first_point;

    cairo_bool_t has_initial_sub_path;

    cairo_bool_t has_current_face;

    cairo_stroke_face_t current_face;

    cairo_bool_t has_first_face;

    cairo_stroke_face_t first_face;

    cairo_stroker_dash_t dash;

    cairo_bool_t has_bounds;

    cairo_box_t tight_bounds;

    cairo_box_t line_bounds;

    cairo_box_t join_bounds;

};

static cairo_status_t

stroker_init (struct stroker		*stroker,

	      const cairo_path_fixed_t	*path,

	      const cairo_stroke_style_t	*style,

	      const cairo_matrix_t	*ctm,

	      const cairo_matrix_t	*ctm_inverse,

	      double			 tolerance,

	      cairo_traps_t		*traps)

{

    cairo_status_t status;

    stroker->style = style;

    stroker->ctm = ctm;

    stroker->ctm_inverse = NULL;

    if (! _cairo_matrix_is_identity (ctm_inverse))

	stroker->ctm_inverse = ctm_inverse;

    stroker->line_join = style->line_join;

    stroker->half_line_width = style->line_width / 2.0;

    stroker->tolerance = tolerance;

    stroker->traps = traps;

    /* 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, style);

    stroker->has_bounds = traps->num_limits;

    if (stroker->has_bounds) {

	/* Extend the bounds in each direction to account for the maximum area

	 * we might generate trapezoids, to capture line segments that are outside

	 * of the bounds but which might generate rendering that's within bounds.

	 */

	double dx, dy;

	cairo_fixed_t fdx, fdy;

	stroker->tight_bounds = traps->bounds;

	_cairo_stroke_style_max_distance_from_path (stroker->style, path,

						    stroker->ctm, &dx, &dy);

	_cairo_stroke_style_max_line_distance_from_path (stroker->style, path,

							 stroker->ctm, &dx, &dy);

	fdx = _cairo_fixed_from_double (dx);

	fdy = _cairo_fixed_from_double (dy);

	stroker->line_bounds = stroker->tight_bounds;

	stroker->line_bounds.p1.x -= fdx;

	stroker->line_bounds.p2.x += fdx;

	stroker->line_bounds.p1.y -= fdy;

	stroker->line_bounds.p2.y += fdy;

	_cairo_stroke_style_max_join_distance_from_path (stroker->style, path,

							 stroker->ctm, &dx, &dy);

	fdx = _cairo_fixed_from_double (dx);

	fdy = _cairo_fixed_from_double (dy);

	stroker->join_bounds = stroker->tight_bounds;

	stroker->join_bounds.p1.x -= fdx;

	stroker->join_bounds.p2.x += fdx;

	stroker->join_bounds.p1.y -= fdy;

	stroker->join_bounds.p2.y += fdy;

    }

    return CAIRO_STATUS_SUCCESS;

}

static void

stroker_fini (struct stroker *stroker)

{

    _cairo_pen_fini (&stroker->pen);

}

static void

translate_point (cairo_point_t *point, cairo_point_t *offset)

{

    point->x += offset->x;

    point->y += offset->y;

}

static int

join_is_clockwise (const cairo_stroke_face_t *in,

		   const cairo_stroke_face_t *out)

{

    return _cairo_slope_compare (&in->dev_vector, &out->dev_vector) < 0;

}

static int

slope_compare_sgn (double dx1, double dy1, double dx2, double dy2)

{

    double c = dx1 * dy2 - dx2 * dy1;

    if (c > 0) return 1;

    if (c < 0) return -1;

    return 0;

}

static cairo_bool_t

stroker_intersects_join (const struct stroker *stroker,

			 const cairo_point_t *in,

			 const cairo_point_t *out)

{

    cairo_line_t segment;

    if (! stroker->has_bounds)

	return TRUE;

    segment.p1 = *in;

    segment.p2 = *out;

    return _cairo_box_intersects_line_segment (&stroker->join_bounds, &segment);

}

static void

join (struct stroker *stroker,

      cairo_stroke_face_t *in,

      cairo_stroke_face_t *out)

{

    int clockwise = join_is_clockwise (out, in);

    cairo_point_t *inpt, *outpt;

    if (in->cw.x == out->cw.x &&

	in->cw.y == out->cw.y &&

	in->ccw.x == out->ccw.x &&

	in->ccw.y == out->ccw.y)

    {

	return;

    }

    if (clockwise) {

	inpt = &in->ccw;

	outpt = &out->ccw;

    } else {

	inpt = &in->cw;

	outpt = &out->cw;

    }

    if (! stroker_intersects_join (stroker, inpt, outpt))

	    return;

    switch (stroker->line_join) {

    case CAIRO_LINE_JOIN_ROUND:

	/* construct a fan around the common midpoint */

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

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

	{

	    int start, stop;

	    cairo_point_t tri[3];

	    cairo_pen_t *pen = &stroker->pen;

	    tri[0] = in->point;

	    tri[1] = *inpt;

	    if (clockwise) {

		_cairo_pen_find_active_ccw_vertices (pen,

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

						     &start, &stop);

		while (start != stop) {

		    tri[2] = in->point;

		    translate_point (&tri[2], &pen->vertices[start].point);

		    _cairo_traps_tessellate_triangle (stroker->traps, tri);

		    tri[1] = tri[2];

		    if (start-- == 0)

			start += pen->num_vertices;

		}

	    } else {

		_cairo_pen_find_active_cw_vertices (pen,

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

						    &start, &stop);

		while (start != stop) {

		    tri[2] = in->point;

		    translate_point (&tri[2], &pen->vertices[start].point);

		    _cairo_traps_tessellate_triangle (stroker->traps, tri);

		    tri[1] = tri[2];

		    if (++start == pen->num_vertices)

			start = 0;

		}

	    }

	    tri[2] = *outpt;

	    _cairo_traps_tessellate_triangle (stroker->traps, tri);

	    break;

	}

    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;

	    cairo_point_t	outer;

	    cairo_point_t	quad[4];

	    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 (slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=

		slope_compare_sgn (fdx2, fdy2, mdx, mdy))

	    {

		/*

		 * Draw the quadrilateral

		 */

		outer.x = _cairo_fixed_from_double (mx);

		outer.y = _cairo_fixed_from_double (my);

		quad[0] = in->point;

		quad[1] = *inpt;

		quad[2] = outer;

		quad[3] = *outpt;

		_cairo_traps_tessellate_convex_quad (stroker->traps, quad);

		break;

	    }

	}

	/* fall through ... */

    }

    case CAIRO_LINE_JOIN_BEVEL: {

	cairo_point_t tri[3];

	tri[0] = in->point;

	tri[1] = *inpt;

	tri[2] = *outpt;

	_cairo_traps_tessellate_triangle (stroker->traps, tri);

	break;

    }

    }

}

static void

add_cap (struct stroker *stroker, cairo_stroke_face_t *f)

{

    switch (stroker->style->line_cap) {

    case CAIRO_LINE_CAP_ROUND: {

	int start, stop;

	cairo_slope_t in_slope, out_slope;

	cairo_point_t tri[3];

	cairo_pen_t *pen = &stroker->pen;

	in_slope = f->dev_vector;

	out_slope.dx = -in_slope.dx;

	out_slope.dy = -in_slope.dy;

	_cairo_pen_find_active_cw_vertices (pen, &in_slope, &out_slope,

					    &start, &stop);

	tri[0] = f->point;

	tri[1] = f->cw;

	while (start != stop) {

	    tri[2] = f->point;

	    translate_point (&tri[2], &pen->vertices[start].point);

	    _cairo_traps_tessellate_triangle (stroker->traps, tri);

	    tri[1] = tri[2];

	    if (++start == pen->num_vertices)

		start = 0;

	}

	tri[2] = f->ccw;

	_cairo_traps_tessellate_triangle (stroker->traps, tri);

	break;

    }

    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->cw;

	quad[1].x = f->cw.x + fvector.dx;

	quad[1].y = f->cw.y + fvector.dy;

	quad[2].x = f->ccw.x + fvector.dx;

	quad[2].y = f->ccw.y + fvector.dy;

	quad[3] = f->ccw;

	_cairo_traps_tessellate_convex_quad (stroker->traps, quad);

	break;

    }

    case CAIRO_LINE_CAP_BUTT:

    default:

	break;

    }

}

static void

add_leading_cap (struct stroker     *stroker,

		 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;

    add_cap (stroker, &reversed);

}

static void

add_trailing_cap (struct stroker *stroker, cairo_stroke_face_t *face)

{

    add_cap (stroker, face);

}

static inline double

normalize_slope (double *dx, double *dy)

{

    double dx0 = *dx, dy0 = *dy;

    if (dx0 == 0.0 && dy0 == 0.0)

	return 0;

    if (dx0 == 0.0) {

	*dx = 0.0;

	if (dy0 > 0.0) {

	    *dy = 1.0;

	    return dy0;

	} else {

	    *dy = -1.0;

	    return -dy0;

	}

    } else if (dy0 == 0.0) {

	*dy = 0.0;

	if (dx0 > 0.0) {

	    *dx = 1.0;

	    return dx0;

	} else {

	    *dx = -1.0;

	    return -dx0;

	}

    } else {

	double mag = hypot (dx0, dy0);

	*dx = dx0 / mag;

	*dy = dy0 / mag;

	return mag;

    }

}

static void

compute_face (const cairo_point_t *point,

	      const cairo_slope_t *dev_slope,

	      struct stroker *stroker,

	      cairo_stroke_face_t *face)

{

    double face_dx, face_dy;

    cairo_point_t offset_ccw, offset_cw;

    double slope_dx, slope_dy;

    slope_dx = _cairo_fixed_to_double (dev_slope->dx);

    slope_dy = _cairo_fixed_to_double (dev_slope->dy);

    face->length = normalize_slope (&slope_dx, &slope_dy);

    face->dev_slope.x = slope_dx;

    face->dev_slope.y = slope_dy;

    /*

     * rotate to get a line_width/2 vector along the face, note that

     * the vector must be rotated the right direction in device space,

     * but by 90° in user space. So, the rotation depends on

     * whether the ctm reflects or not, and that can be determined

     * by looking at the determinant of the matrix.

     */

    if (stroker->ctm_inverse) {

	cairo_matrix_transform_distance (stroker->ctm_inverse, &slope_dx, &slope_dy);

	normalize_slope (&slope_dx, &slope_dy);

	if (stroker->ctm_det_positive) {

	    face_dx = - slope_dy * stroker->half_line_width;

	    face_dy = slope_dx * stroker->half_line_width;

	} else {

	    face_dx = slope_dy * stroker->half_line_width;

	    face_dy = - slope_dx * stroker->half_line_width;

	}

	/* back to device space */

	cairo_matrix_transform_distance (stroker->ctm, &face_dx, &face_dy);

    } else {

	face_dx = - slope_dy * stroker->half_line_width;

	face_dy = slope_dx * stroker->half_line_width;

    }

    offset_ccw.x = _cairo_fixed_from_double (face_dx);

    offset_ccw.y = _cairo_fixed_from_double (face_dy);

    offset_cw.x = -offset_ccw.x;

    offset_cw.y = -offset_ccw.y;

    face->ccw = *point;

    translate_point (&face->ccw, &offset_ccw);

    face->point = *point;

    face->cw = *point;

    translate_point (&face->cw, &offset_cw);

    face->usr_vector.x = slope_dx;

    face->usr_vector.y = slope_dy;

    face->dev_vector = *dev_slope;

}

static void

add_caps (struct stroker *stroker)

{

    /* check for a degenerative sub_path */

    if (stroker->has_initial_sub_path &&

	!stroker->has_first_face &&

	!stroker->has_current_face &&

	stroker->style->line_cap == CAIRO_LINE_CAP_ROUND)

    {

	/* pick an arbitrary slope to use */

	cairo_slope_t slope = { CAIRO_FIXED_ONE, 0 };

	cairo_stroke_face_t face;

	/* arbitrarily choose first_point

	 * first_point and current_point should be the same */

	compute_face (&stroker->first_point, &slope, stroker, &face);

	add_leading_cap (stroker, &face);

	add_trailing_cap (stroker, &face);

    }

    if (stroker->has_first_face)

	add_leading_cap (stroker, &stroker->first_face);

    if (stroker->has_current_face)

	add_trailing_cap (stroker, &stroker->current_face);

}

static cairo_bool_t

stroker_intersects_edge (const struct stroker *stroker,

			 const cairo_stroke_face_t *start,

			 const cairo_stroke_face_t *end)

{

    cairo_box_t box;

    if (! stroker->has_bounds)

	return TRUE;

    if (_cairo_box_contains_point (&stroker->tight_bounds, &start->cw))

	return TRUE;

    box.p2 = box.p1 = start->cw;

    if (_cairo_box_contains_point (&stroker->tight_bounds, &start->ccw))

	return TRUE;

    _cairo_box_add_point (&box, &start->ccw);

    if (_cairo_box_contains_point (&stroker->tight_bounds, &end->cw))

	return TRUE;

    _cairo_box_add_point (&box, &end->cw);

    if (_cairo_box_contains_point (&stroker->tight_bounds, &end->ccw))

	return TRUE;

    _cairo_box_add_point (&box, &end->ccw);

    return (box.p2.x > stroker->tight_bounds.p1.x &&

	    box.p1.x < stroker->tight_bounds.p2.x &&

	    box.p2.y > stroker->tight_bounds.p1.y &&

	    box.p1.y < stroker->tight_bounds.p2.y);

}

static void

add_sub_edge (struct stroker *stroker,

	      const cairo_point_t *p1, const cairo_point_t *p2,

	      const cairo_slope_t *dev_slope,

	      cairo_stroke_face_t *start, cairo_stroke_face_t *end)

{

    cairo_point_t rectangle[4];

    compute_face (p1, dev_slope, stroker, start);

    *end = *start;

    end->point = *p2;

    rectangle[0].x = p2->x - p1->x;

    rectangle[0].y = p2->y - p1->y;

    translate_point (&end->ccw, &rectangle[0]);

    translate_point (&end->cw, &rectangle[0]);

    if (p1->x == p2->x && p1->y == p2->y)

	return;

    if (! stroker_intersects_edge (stroker, start, end))

	return;

    rectangle[0] = start->cw;

    rectangle[1] = start->ccw;

    rectangle[2] = end->ccw;

    rectangle[3] = end->cw;

    _cairo_traps_tessellate_convex_quad (stroker->traps, rectangle);

}

static cairo_status_t

move_to (void *closure, const cairo_point_t *point)

{

    struct stroker *stroker = closure;

    /* Cap the start and end of the previous sub path as needed */

    add_caps (stroker);

    stroker->first_point = *point;

    stroker->current_face.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

move_to_dashed (void *closure, const cairo_point_t *point)

{

    /* reset the dash pattern for new sub paths */

    struct stroker *stroker = closure;

    _cairo_stroker_dash_start (&stroker->dash);

    return move_to (closure, point);

}

static cairo_status_t

line_to (void *closure, const cairo_point_t *point)

{

    struct stroker *stroker = closure;

    cairo_stroke_face_t start, end;

    const cairo_point_t *p1 = &stroker->current_face.point;

    const cairo_point_t *p2 = point;

    cairo_slope_t dev_slope;

    stroker->has_initial_sub_path = TRUE;

    if (p1->x == p2->x && p1->y == p2->y)

	return CAIRO_STATUS_SUCCESS;

    _cairo_slope_init (&dev_slope, p1, p2);

    add_sub_edge (stroker, p1, p2, &dev_slope, &start, &end);

    if (stroker->has_current_face) {

	/* Join with final face from previous segment */

	join (stroker, &stroker->current_face, &start);

    } 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;

    return CAIRO_STATUS_SUCCESS;

}

/*

 * Dashed lines.  Cap each dash end, join around turns when on

 */

static cairo_status_t

line_to_dashed (void *closure, const cairo_point_t *point)

{

    struct stroker *stroker = closure;

    double mag, remain, step_length = 0;

    double slope_dx, slope_dy;

    double dx2, dy2;

    cairo_stroke_face_t sub_start, sub_end;

    const cairo_point_t *p1 = &stroker->current_face.point;

    const cairo_point_t *p2 = point;

    cairo_slope_t dev_slope;

    cairo_line_t segment;

    cairo_bool_t fully_in_bounds;

    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->join_bounds, p1) ||

	 ! _cairo_box_contains_point (&stroker->join_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 (stroker->ctm_inverse)

	cairo_matrix_transform_distance (stroker->ctm_inverse, &slope_dx, &slope_dy);

    mag = normalize_slope (&slope_dx, &slope_dy);

    if (mag <= DBL_EPSILON)

	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->join_bounds, &segment)))

	{

	    add_sub_edge (stroker,

			  &segment.p1, &segment.p2,

			  &dev_slope,

			  &sub_start, &sub_end);

	    if (stroker->has_current_face) {

		/* Join with final face from previous segment */

		join (stroker, &stroker->current_face, &sub_start);

		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 */

		add_leading_cap (stroker, &sub_start);

	    }

	    if (remain) {

		/* Cap dash end if not at end of segment */

		add_trailing_cap (stroker, &sub_end);

	    } else {

		stroker->current_face = sub_end;

		stroker->has_current_face = TRUE;

	    }

	} else {

	    if (stroker->has_current_face) {

		/* Cap final face from previous segment */

		add_trailing_cap (stroker, &stroker->current_face);

		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 (point, &dev_slope, stroker, &stroker->current_face);

	add_leading_cap (stroker, &stroker->current_face);

	stroker->has_current_face = TRUE;

    } else

	stroker->current_face.point = *point;

    return CAIRO_STATUS_SUCCESS;

}

static cairo_status_t

spline_to (void *closure,

	   const cairo_point_t *point,

	   const cairo_slope_t *tangent)

{

    struct stroker *stroker = closure;

    cairo_stroke_face_t face;

    if ((tangent->dx | tangent->dy) == 0) {

	cairo_point_t t;

	face = stroker->current_face;

	face.usr_vector.x = -face.usr_vector.x;

	face.usr_vector.y = -face.usr_vector.y;

	face.dev_slope.x = -face.dev_slope.x;

	face.dev_slope.y = -face.dev_slope.y;

	face.dev_vector.dx = -face.dev_vector.dx;

	face.dev_vector.dy = -face.dev_vector.dy;

	t = face.cw;

	face.cw = face.ccw;

	face.ccw = t;

	join (stroker, &stroker->current_face, &face);

    } else {

	cairo_point_t rectangle[4];

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

	join (stroker, &stroker->current_face, &face);

	rectangle[0] = face.cw;

	rectangle[1] = face.ccw;

	rectangle[2].x = point->x - face.point.x;

	rectangle[2].y = point->y - face.point.y;

	face.point = *point;

	translate_point (&face.ccw, &rectangle[2]);

	translate_point (&face.cw, &rectangle[2]);

	rectangle[2] = face.ccw;

	rectangle[3] = face.cw;

	_cairo_traps_tessellate_convex_quad (stroker->traps, rectangle);

    }

    stroker->current_face = face;

    return CAIRO_STATUS_SUCCESS;

}

static cairo_status_t

curve_to (void *closure,

	  const cairo_point_t *b,

	  const cairo_point_t *c,

	  const cairo_point_t *d)

{

    struct stroker *stroker = closure;

    cairo_line_join_t line_join_save;

    cairo_spline_t spline;

    cairo_stroke_face_t face;

    cairo_status_t status;

    if (stroker->has_bounds &&

	! _cairo_spline_intersects (&stroker->current_face.point, b, c, d,

				    &stroker->line_bounds))

	return line_to (closure, d);

    if (! _cairo_spline_init (&spline, spline_to, stroker,

			      &stroker->current_face.point, b, c, d))

	return line_to (closure, d);

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

		  stroker, &face);

    if (stroker->has_current_face) {

	/* Join with final face from previous segment */

	join (stroker, &stroker->current_face, &face);

    } else {

	if (! stroker->has_first_face) {

	    /* Save sub path's first face in case needed for closing join */

	    stroker->first_face = face;

	    stroker->has_first_face = TRUE;

	}

	stroker->has_current_face = TRUE;

    }

    stroker->current_face = face;

    /* Temporarily modify the stroker to use round joins to guarantee

     * smooth stroked curves. */

    line_join_save = stroker->line_join;

    stroker->line_join = CAIRO_LINE_JOIN_ROUND;

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

    stroker->line_join = line_join_save;

    return status;

}

static cairo_status_t

curve_to_dashed (void *closure,

		 const cairo_point_t *b,

		 const cairo_point_t *c,

		 const cairo_point_t *d)

{

    struct stroker *stroker = closure;

    cairo_spline_t spline;

    cairo_line_join_t line_join_save;

    cairo_spline_add_point_func_t func;

    cairo_status_t status;

    func = (cairo_spline_add_point_func_t)line_to_dashed;

    if (stroker->has_bounds &&

	! _cairo_spline_intersects (&stroker->current_face.point, b, c, b,

				    &stroker->line_bounds))

	return func (closure, d, NULL);

    if (! _cairo_spline_init (&spline, func, stroker,

			      &stroker->current_face.point, b, c, d))

	return func (closure, d, NULL);

    /* Temporarily modify the stroker to use round joins to guarantee

     * smooth stroked curves. */

    line_join_save = stroker->line_join;

    stroker->line_join = CAIRO_LINE_JOIN_ROUND;

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

    stroker->line_join = line_join_save;

    return status;

}

static cairo_status_t

_close_path (struct stroker *stroker)

{

    if (stroker->has_first_face && stroker->has_current_face) {

	/* Join first and final faces of sub path */

	join (stroker, &stroker->current_face, &stroker->first_face);

    } else {

	/* Cap the start and end of the sub path as needed */

	add_caps (stroker);

    }

    stroker->has_initial_sub_path = FALSE;

    stroker->has_first_face = FALSE;

    stroker->has_current_face = FALSE;

    return CAIRO_STATUS_SUCCESS;

}

static cairo_status_t

close_path (void *closure)

{

    struct stroker *stroker = closure;

    cairo_status_t status;

    status = line_to (stroker, &stroker->first_point);

    if (unlikely (status))

	return status;

    return _close_path (stroker);

}

static cairo_status_t

close_path_dashed (void *closure)

{

    struct stroker *stroker = closure;

    cairo_status_t status;

    status = line_to_dashed (stroker, &stroker->first_point);

    if (unlikely (status))

	return status;

    return _close_path (stroker);

}

cairo_int_status_t

_cairo_path_fixed_stroke_to_traps (const cairo_path_fixed_t	*path,

				   const cairo_stroke_style_t	*style,

				   const cairo_matrix_t		*ctm,

				   const cairo_matrix_t		*ctm_inverse,

				   double			 tolerance,

				   cairo_traps_t		*traps)

{

    struct stroker stroker;

    cairo_status_t status;

    status = stroker_init (&stroker, path, style,

			   ctm, ctm_inverse, tolerance,

			   traps);

    if (unlikely (status))

	return status;

    if (stroker.dash.dashed)

	status = _cairo_path_fixed_interpret (path,

					      move_to_dashed,

					      line_to_dashed,

					      curve_to_dashed,

					      close_path_dashed,

					      &stroker);

    else

	status = _cairo_path_fixed_interpret (path,

					      move_to,

					      line_to,

					      curve_to,

					      close_path,

					      &stroker);

    assert(status == CAIRO_STATUS_SUCCESS);

    add_caps (&stroker);

    stroker_fini (&stroker);

    return traps->status;

}