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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

 *

 * 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 

 *	Chris Wilson 

 */

#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);