stroke: move normal stroker to new file

Step 1 of enhancing the speed of the stroker is to segregate from the
rest of the complex code.

Signed-off-by: Chris Wilson <chris@chris-wilson.co.uk>

1 files changed, 1002 insertions, 0 deletions

diff --git a/src/cairo-path-stroke-polygon.c b/src/cairo-path-stroke-polygon.c
new file mode 100644
index 000000000..c60c2c069
--- /dev/null
+++ b/src/cairo-path-stroke-polygon.c
@@ -0,0 +1,1002 @@
+/* -*- 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-private.h"
+#include "cairo-boxes-private.h"
+#include "cairo-error-private.h"
+#include "cairo-path-fixed-private.h"
+#include "cairo-slope-private.h"
+
+typedef struct cairo_stroker {
+    cairo_stroke_style_t style;
+
+    const cairo_matrix_t *ctm;
+    const cairo_matrix_t *ctm_inverse;
+    double tolerance;
+    double ctm_determinant;
+    cairo_bool_t ctm_det_positive;
+
+    cairo_polygon_t *polygon;
+    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_bool_t has_bounds;
+    cairo_box_t bounds;
+} cairo_stroker_t;
+
+static void
+stroker_limit (cairo_stroker_t *stroker,
+	       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, 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 void
+translate_point (cairo_point_t *point, const 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;
+}
+
+/**
+ * slope_compare_sgn
+ *
+ * Return -1, 0 or 1 depending on the relative slopes of
+ * two lines.
+ */
+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 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;
+    int start, stop, step, i, npoints;
+    cairo_status_t status;
+
+    if (clockwise) {
+	step  = -1;
+
+	start = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
+							 in_vector);
+	if (_cairo_slope_compare (&stroker->pen.vertices[start].slope_ccw,
+				  in_vector) < 0)
+	    start = range_step (start, -1, stroker->pen.num_vertices);
+
+	stop  = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
+							 out_vector);
+	if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_cw,
+				  out_vector) > 0)
+	{
+	    stop = range_step (stop, 1, stroker->pen.num_vertices);
+	    if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_ccw,
+				      in_vector) < 0)
+	    {
+		goto BEVEL;
+	    }
+	}
+
+	npoints = start - stop;
+    } else {
+	step  = 1;
+
+	start = _cairo_pen_find_active_cw_vertex_index (&stroker->pen,
+							in_vector);
+	if (_cairo_slope_compare (&stroker->pen.vertices[start].slope_cw,
+				  in_vector) < 0)
+	    start = range_step (start, 1, stroker->pen.num_vertices);
+
+	stop  = _cairo_pen_find_active_cw_vertex_index (&stroker->pen,
+							out_vector);
+	if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_ccw,
+				  out_vector) > 0)
+	{
+	    stop = range_step (stop, -1, stroker->pen.num_vertices);
+	    if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_cw,
+				      in_vector) < 0)
+	    {
+		goto BEVEL;
+	    }
+	}
+
+	npoints = stop - start;
+    }
+    stop = range_step (stop, step, stroker->pen.num_vertices);
+
+    if (npoints < 0)
+	npoints += stroker->pen.num_vertices;
+    npoints += 3;
+
+    if (npoints <= 1)
+	goto BEVEL;
+
+    if (npoints > ARRAY_LENGTH (stack_points)) {
+	points = _cairo_malloc_ab (npoints, sizeof (cairo_point_t));
+	if (unlikely (points == NULL))
+	    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+    }
+
+
+    /* Construct the fan. */
+    npoints = 0;
+    points[npoints++] = *inpt;
+    for (i = start;
+	 i != stop;
+	i = range_step (i, step, stroker->pen.num_vertices))
+    {
+	points[npoints] = *midpt;
+	translate_point (&points[npoints], &stroker->pen.vertices[i].point);
+	npoints++;
+    }
+    points[npoints++] = *outpt;
+
+    for (i = 0; i < npoints - 1; i++) {
+	if (clockwise) {
+	    status = _cairo_polygon_add_external_edge (stroker->polygon,
+						       &points[i], &points[i+1]);
+	} else {
+	    status = _cairo_polygon_add_external_edge (stroker->polygon,
+						       &points[i+1], &points[i]);
+	}
+	if (unlikely (status))
+	    break;
+    }
+
+    if (points != stack_points)
+	free (points);
+
+    return status;
+
+BEVEL:
+    /* Ensure a leak free connection... */
+    if (clockwise)
+	return _cairo_polygon_add_external_edge (stroker->polygon, inpt, outpt);
+    else
+	return _cairo_polygon_add_external_edge (stroker->polygon, outpt, inpt);
+}
+
+static cairo_status_t
+join (cairo_stroker_t *stroker,
+      const cairo_stroke_face_t *in,
+      const cairo_stroke_face_t *out)
+{
+    int	 clockwise = 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) {
+	status = _cairo_polygon_add_external_edge (stroker->polygon,
+						   &out->cw, &in->point);
+	if (unlikely (status))
+	    return status;
+
+	status = _cairo_polygon_add_external_edge (stroker->polygon,
+						   &in->point, &in->cw);
+	if (unlikely (status))
+	    return status;
+
+	inpt = &in->ccw;
+	outpt = &out->ccw;
+    } else {
+	status = _cairo_polygon_add_external_edge (stroker->polygon,
+						   &in->ccw, &in->point);
+	if (unlikely (status))
+	    return status;
+
+	status = _cairo_polygon_add_external_edge (stroker->polygon,
+						   &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 (slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
+		slope_compare_sgn (fdx2, fdy2, mdx, mdy))
+	    {
+		points[0].x = _cairo_fixed_from_double (mx);
+		points[0].y = _cairo_fixed_from_double (my);
+
+		if (clockwise) {
+		    status = _cairo_polygon_add_external_edge (stroker->polygon,
+							 inpt, &points[0]);
+		    if (unlikely (status))
+			return status;
+
+		    status = _cairo_polygon_add_external_edge (stroker->polygon,
+							 &points[0], outpt);
+		    if (unlikely (status))
+			return status;
+		} else {
+		    status = _cairo_polygon_add_external_edge (stroker->polygon,
+							 outpt, &points[0]);
+		    if (unlikely (status))
+			return status;
+
+		    status = _cairo_polygon_add_external_edge (stroker->polygon,
+							 &points[0], inpt);
+		    if (unlikely (status))
+			return status;
+		}
+
+		return CAIRO_STATUS_SUCCESS;
+	    }
+	}
+    }
+
+    /* fall through ... */
+
+    case CAIRO_LINE_JOIN_BEVEL:
+	if (clockwise) {
+	    return _cairo_polygon_add_external_edge (stroker->polygon,
+					       inpt, outpt);
+	} else {
+	    return _cairo_polygon_add_external_edge (stroker->polygon,
+					       outpt, inpt);
+	}
+    }
+}
+
+static cairo_status_t
+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];
+	cairo_status_t status;
+
+	dx = f->usr_vector.x;
+	dy = f->usr_vector.y;
+	dx *= stroker->style.line_width / 2.0;
+	dy *= stroker->style.line_width / 2.0;
+	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;
+
+	status = _cairo_polygon_add_external_edge (stroker->polygon,
+					     &quad[0], &quad[1]);
+	if (unlikely (status))
+	    return status;
+
+	status = _cairo_polygon_add_external_edge (stroker->polygon,
+					     &quad[1], &quad[2]);
+	if (unlikely (status))
+	    return status;
+
+	status = _cairo_polygon_add_external_edge (stroker->polygon,
+					     &quad[2], &quad[3]);
+	if (unlikely (status))
+	    return status;
+
+	return CAIRO_STATUS_SUCCESS;
+    }
+
+    case CAIRO_LINE_CAP_BUTT:
+    default:
+	return _cairo_polygon_add_external_edge (stroker->polygon,
+					   &f->ccw, &f->cw);
+    }
+}
+
+static cairo_status_t
+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 add_cap (stroker, &reversed);
+}
+
+static cairo_status_t
+add_trailing_cap (cairo_stroker_t     *stroker,
+		  const cairo_stroke_face_t *face)
+{
+    return 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, 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->style.line_width / 2.0);
+	face_dy = slope_dx * (stroker->style.line_width / 2.0);
+    }
+    else
+    {
+	face_dx = slope_dy * (stroker->style.line_width / 2.0);
+	face_dy = - slope_dx * (stroker->style.line_width / 2.0);
+    }
+
+    /* 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
+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 = add_leading_cap (stroker, &face);
+	if (unlikely (status))
+	    return status;
+
+	status = add_trailing_cap (stroker, &face);
+	if (unlikely (status))
+	    return status;
+    }
+
+    if (stroker->has_first_face) {
+	status = add_leading_cap (stroker, &stroker->first_face);
+	if (unlikely (status))
+	    return status;
+    }
+
+    if (stroker->has_current_face) {
+	status = add_trailing_cap (stroker, &stroker->current_face);
+	if (unlikely (status))
+	    return status;
+    }
+
+    return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+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)
+{
+    cairo_status_t status;
+
+    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;
+
+    status = _cairo_polygon_add_external_edge (stroker->polygon,
+					 &end->cw, &start->cw);
+    if (unlikely (status))
+	return status;
+
+    status = _cairo_polygon_add_external_edge (stroker->polygon,
+					 &start->ccw, &end->ccw);
+    if (unlikely (status))
+	return status;
+
+    return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+move_to (void *closure,
+	 const cairo_point_t *point)
+{
+    cairo_stroker_t *stroker = closure;
+    cairo_status_t status;
+
+    /* Cap the start and end of the previous sub path as needed */
+    status = 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
+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 = 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 = 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
+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_status_t status = CAIRO_STATUS_SUCCESS;
+
+    if (! _cairo_spline_init (&spline, line_to, stroker,
+			      &stroker->current_point, b, c, d))
+    {
+	return line_to (closure, d);
+    }
+
+    /* Compute the initial face */
+    if (1) {
+	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 = 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 (1) {
+	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 = 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
+close_path (void *closure)
+{
+    cairo_stroker_t *stroker = closure;
+    cairo_status_t status;
+
+    status = 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 = 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 = 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_polygon (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_polygon_t *polygon)
+{
+    cairo_stroker_t stroker;
+    cairo_status_t status;
+
+    if (style->dash)
+	return _cairo_path_fixed_stroke_dashed_to_polygon (path,
+							   style,
+							   ctm,
+							   ctm_inverse,
+							   tolerance,
+							   polygon);
+
+    stroker.style = *style;
+    stroker.ctm = ctm;
+    stroker.ctm_inverse = ctm_inverse;
+    stroker.tolerance = tolerance;
+
+    stroker.ctm_det_positive = _cairo_matrix_compute_determinant (ctm) >= 0.;
+
+    status = _cairo_pen_init (&stroker.pen,
+		              style->line_width / 2.0,
+			      tolerance, ctm);
+    if (unlikely (status))
+	return status;
+
+    /* 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;
+
+    stroker.polygon = polygon;
+
+    stroker.has_current_face = FALSE;
+    stroker.has_first_face = FALSE;
+    stroker.has_initial_sub_path = FALSE;
+
+    stroker.has_bounds = FALSE;
+    if (polygon->num_limits)
+	stroker_limit (&stroker, polygon->limits, polygon->num_limits);
+
+    status = _cairo_path_fixed_interpret (path,
+					  move_to,
+					  line_to,
+					  curve_to,
+					  close_path,
+					  &stroker);
+
+    /* Cap the start and end of the final sub path as needed */
+    if (likely (status == CAIRO_STATUS_SUCCESS))
+	status = add_caps (&stroker);
+
+    _cairo_pen_fini (&stroker.pen);
+
+    return status;
+}