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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 © 2011 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., 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-contour-inline.h"
+#include "cairo-contour-private.h"
+#include "cairo-error-private.h"
+#include "cairo-path-fixed-private.h"
+#include "cairo-slope-private.h"
+
+#define DEBUG 0
+
+struct stroker {
+ cairo_stroke_style_t style;
+
+#if DEBUG
+ cairo_contour_t path;
+#endif
+
+ struct stroke_contour {
+ /* Note that these are not strictly contours as they may intersect */
+ cairo_contour_t contour;
+ } cw, ccw;
+ cairo_uint64_t contour_tolerance;
+ cairo_polygon_t *polygon;
+
+ const cairo_matrix_t *ctm;
+ const cairo_matrix_t *ctm_inverse;
+ double tolerance;
+ double spline_cusp_tolerance;
+ double half_line_width;
+ cairo_bool_t ctm_det_positive;
+
+ 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_bool_t has_bounds;
+ cairo_box_t bounds;
+};
+
+static inline double
+normalize_slope (double *dx, double *dy);
+
+static void
+compute_face (const cairo_point_t *point,
+ const cairo_slope_t *dev_slope,
+ struct stroker *stroker,
+ cairo_stroke_face_t *face);
+
+static cairo_uint64_t
+point_distance_sq (const cairo_point_t *p1,
+ const cairo_point_t *p2)
+{
+ int32_t dx = p1->x - p2->x;
+ int32_t dy = p1->y - p2->y;
+ return _cairo_int32x32_64_mul (dx, dx) + _cairo_int32x32_64_mul (dy, dy);
+}
+
+static cairo_bool_t
+within_tolerance (const cairo_point_t *p1,
+ const cairo_point_t *p2,
+ cairo_uint64_t tolerance)
+{
+ return FALSE;
+ return _cairo_int64_lt (point_distance_sq (p1, p2), tolerance);
+}
+
+static void
+contour_add_point (struct stroker *stroker,
+ struct stroke_contour *c,
+ const cairo_point_t *point)
+{
+ if (! within_tolerance (point, _cairo_contour_last_point (&c->contour),
+ stroker->contour_tolerance))
+ _cairo_contour_add_point (&c->contour, point);
+ //*_cairo_contour_last_point (&c->contour) = *point;
+}
+
+static void
+translate_point (cairo_point_t *point, const cairo_point_t *offset)
+{
+ point->x += offset->x;
+ point->y += offset->y;
+}
+
+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 void
+add_fan (struct stroker *stroker,
+ const cairo_slope_t *in_vector,
+ const cairo_slope_t *out_vector,
+ const cairo_point_t *midpt,
+ cairo_bool_t clockwise,
+ struct stroke_contour *c)
+{
+ cairo_pen_t *pen = &stroker->pen;
+ int start, stop;
+
+ if (stroker->has_bounds &&
+ ! _cairo_box_contains_point (&stroker->bounds, midpt))
+ return;
+
+ assert (stroker->pen.num_vertices);
+
+ if (clockwise) {
+ _cairo_pen_find_active_cw_vertices (pen,
+ in_vector, out_vector,
+ &start, &stop);
+ while (start != stop) {
+ cairo_point_t p = *midpt;
+ translate_point (&p, &pen->vertices[start].point);
+ contour_add_point (stroker, c, &p);
+
+ if (++start == pen->num_vertices)
+ start = 0;
+ }
+ } else {
+ _cairo_pen_find_active_ccw_vertices (pen,
+ in_vector, out_vector,
+ &start, &stop);
+ while (start != stop) {
+ cairo_point_t p = *midpt;
+ translate_point (&p, &pen->vertices[start].point);
+ contour_add_point (stroker, c, &p);
+
+ if (start-- == 0)
+ start += pen->num_vertices;
+ }
+ }
+}
+
+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 void
+inner_join (struct stroker *stroker,
+ const cairo_stroke_face_t *in,
+ const cairo_stroke_face_t *out,
+ int clockwise)
+{
+#if 0
+ cairo_point_t last;
+ const cairo_point_t *p, *outpt;
+ struct stroke_contour *inner;
+ cairo_int64_t d_p, d_last;
+ cairo_int64_t half_line_width;
+ cairo_bool_t negate;
+
+ /* XXX line segments shorter than line-width */
+
+ if (clockwise) {
+ inner = &stroker->ccw;
+ outpt = &out->ccw;
+ negate = 1;
+ } else {
+ inner = &stroker->cw;
+ outpt = &out->cw;
+ negate = 0;
+ }
+
+ half_line_width = CAIRO_FIXED_ONE*CAIRO_FIXED_ONE/2 * stroker->style.line_width * out->length + .5;
+
+ /* On the inside, the previous end-point is always
+ * closer to the new face by definition.
+ */
+ last = *_cairo_contour_last_point (&inner->contour);
+ d_last = distance_from_face (out, &last, negate);
+ _cairo_contour_remove_last_point (&inner->contour);
+
+prev:
+ if (inner->contour.chain.num_points == 0) {
+ contour_add_point (stroker, inner, outpt);
+ return;
+ }
+ p = _cairo_contour_last_point (&inner->contour);
+ d_p = distance_from_face (out, p, negate);
+ if (_cairo_int64_lt (d_p, half_line_width) &&
+ !_cairo_int64_negative (distance_along_face (out, p)))
+ {
+ last = *p;
+ d_last = d_p;
+ _cairo_contour_remove_last_point (&inner->contour);
+ goto prev;
+ }
+
+ compute_inner_joint (&last, d_last, p, d_p, half_line_width);
+ contour_add_point (stroker, inner, &last);
+#else
+ const cairo_point_t *outpt;
+ struct stroke_contour *inner;
+
+ if (clockwise) {
+ inner = &stroker->ccw;
+ outpt = &out->ccw;
+ } else {
+ inner = &stroker->cw;
+ outpt = &out->cw;
+ }
+ contour_add_point (stroker, inner, &in->point);
+ contour_add_point (stroker, inner, outpt);
+#endif
+}
+
+static void
+inner_close (struct stroker *stroker,
+ const cairo_stroke_face_t *in,
+ cairo_stroke_face_t *out)
+{
+#if 0
+ cairo_point_t last;
+ const cairo_point_t *p, *outpt, *inpt;
+ struct stroke_contour *inner;
+ struct _cairo_contour_chain *chain;
+
+ /* XXX line segments shorter than line-width */
+
+ if (join_is_clockwise (in, out)) {
+ inner = &stroker->ccw;
+ outpt = &in->ccw;
+ inpt = &out->ccw;
+ } else {
+ inner = &stroker->cw;
+ outpt = &in->cw;
+ inpt = &out->cw;
+ }
+
+ if (inner->contour.chain.num_points == 0) {
+ contour_add_point (stroker, inner, &in->point);
+ contour_add_point (stroker, inner, inpt);
+ *_cairo_contour_first_point (&inner->contour) =
+ *_cairo_contour_last_point (&inner->contour);
+ return;
+ }
+
+ line_width = stroker->style.line_width/2;
+ line_width *= CAIRO_FIXED_ONE;
+
+ d_last = sign * distance_from_face (out, outpt);
+ last = *outpt;
+
+ for (chain = &inner->contour.chain; chain; chain = chain->next) {
+ for (i = 0; i < chain->num_points; i++) {
+ p = &chain->points[i];
+ if ((d_p = sign * distance_from_face (in, p)) >= line_width &&
+ distance_from_edge (stroker, inpt, &last, p) < line_width)
+ {
+ goto out;
+ }
+
+ if (p->x != last.x || p->y != last.y) {
+ last = *p;
+ d_last = d_p;
+ }
+ }
+ }
+out:
+
+ if (d_p != d_last) {
+ double dot = (line_width - d_last) / (d_p - d_last);
+ last.x += dot * (p->x - last.x);
+ last.y += dot * (p->y - last.y);
+ }
+ *_cairo_contour_last_point (&inner->contour) = last;
+
+ for (chain = &inner->contour.chain; chain; chain = chain->next) {
+ for (i = 0; i < chain->num_points; i++) {
+ cairo_point_t *pp = &chain->points[i];
+ if (pp == p)
+ return;
+ *pp = last;
+ }
+ }
+#else
+ const cairo_point_t *inpt;
+ struct stroke_contour *inner;
+
+ if (join_is_clockwise (in, out)) {
+ inner = &stroker->ccw;
+ inpt = &out->ccw;
+ } else {
+ inner = &stroker->cw;
+ inpt = &out->cw;
+ }
+
+ contour_add_point (stroker, inner, &in->point);
+ contour_add_point (stroker, inner, inpt);
+ *_cairo_contour_first_point (&inner->contour) =
+ *_cairo_contour_last_point (&inner->contour);
+#endif
+}
+
+static void
+outer_close (struct stroker *stroker,
+ const cairo_stroke_face_t *in,
+ const cairo_stroke_face_t *out)
+{
+ const cairo_point_t *inpt, *outpt;
+ struct stroke_contour *outer;
+ int clockwise;
+
+ 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;
+ }
+
+ clockwise = join_is_clockwise (in, out);
+ if (clockwise) {
+ inpt = &in->cw;
+ outpt = &out->cw;
+ outer = &stroker->cw;
+ } else {
+ inpt = &in->ccw;
+ outpt = &out->ccw;
+ outer = &stroker->ccw;
+ }
+
+ if (within_tolerance (inpt, outpt, stroker->contour_tolerance)) {
+ *_cairo_contour_first_point (&outer->contour) =
+ *_cairo_contour_last_point (&outer->contour);
+ return;
+ }
+
+ switch (stroker->style.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)
+ {
+ add_fan (stroker,
+ &in->dev_vector, &out->dev_vector, &in->point,
+ clockwise, outer);
+ break;
+ }
+
+ case CAIRO_LINE_JOIN_MITER:
+ default: {
+ /* dot product of incoming slope vector with outgoing slope vector */
+ double in_dot_out = in->dev_slope.x * out->dev_slope.x +
+ in->dev_slope.y * out->dev_slope.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->dev_slope.x;
+ dy1 = in->dev_slope.y;
+
+ /* outer point of outgoing line face */
+ x2 = _cairo_fixed_to_double (outpt->x);
+ y2 = _cairo_fixed_to_double (outpt->y);
+ dx2 = out->dev_slope.x;
+ dy2 = out->dev_slope.y;
+
+ /*
+ * 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))
+ {
+ cairo_point_t p;
+
+ p.x = _cairo_fixed_from_double (mx);
+ p.y = _cairo_fixed_from_double (my);
+
+ *_cairo_contour_last_point (&outer->contour) = p;
+ *_cairo_contour_first_point (&outer->contour) = p;
+ return;
+ }
+ }
+ break;
+ }
+
+ case CAIRO_LINE_JOIN_BEVEL:
+ break;
+ }
+ contour_add_point (stroker, outer, outpt);
+}
+
+static void
+outer_join (struct stroker *stroker,
+ const cairo_stroke_face_t *in,
+ const cairo_stroke_face_t *out,
+ int clockwise)
+{
+ const cairo_point_t *inpt, *outpt;
+ struct stroke_contour *outer;
+
+ 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->cw;
+ outpt = &out->cw;
+ outer = &stroker->cw;
+ } else {
+ inpt = &in->ccw;
+ outpt = &out->ccw;
+ outer = &stroker->ccw;
+ }
+
+ switch (stroker->style.line_join) {
+ case CAIRO_LINE_JOIN_ROUND:
+ /* construct a fan around the common midpoint */
+ add_fan (stroker,
+ &in->dev_vector, &out->dev_vector, &in->point,
+ clockwise, outer);
+ break;
+
+ case CAIRO_LINE_JOIN_MITER:
+ default: {
+ /* dot product of incoming slope vector with outgoing slope vector */
+ double in_dot_out = in->dev_slope.x * out->dev_slope.x +
+ in->dev_slope.y * out->dev_slope.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->dev_slope.x;
+ dy1 = in->dev_slope.y;
+
+ /* outer point of outgoing line face */
+ x2 = _cairo_fixed_to_double (outpt->x);
+ y2 = _cairo_fixed_to_double (outpt->y);
+ dx2 = out->dev_slope.x;
+ dy2 = out->dev_slope.y;
+
+ /*
+ * 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))
+ {
+ cairo_point_t p;
+
+ p.x = _cairo_fixed_from_double (mx);
+ p.y = _cairo_fixed_from_double (my);
+
+ *_cairo_contour_last_point (&outer->contour) = p;
+ return;
+ }
+ }
+ break;
+ }
+
+ case CAIRO_LINE_JOIN_BEVEL:
+ break;
+ }
+ contour_add_point (stroker,outer, outpt);
+}
+
+static void
+add_cap (struct stroker *stroker,
+ const cairo_stroke_face_t *f,
+ struct stroke_contour *c)
+{
+ 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;
+
+ add_fan (stroker, &f->dev_vector, &slope, &f->point, FALSE, c);
+ break;
+ }
+
+ case CAIRO_LINE_CAP_SQUARE: {
+ cairo_slope_t fvector;
+ cairo_point_t p;
+ double dx, dy;
+
+ 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);
+
+ p.x = f->ccw.x + fvector.dx;
+ p.y = f->ccw.y + fvector.dy;
+ contour_add_point (stroker, c, &p);
+
+ p.x = f->cw.x + fvector.dx;
+ p.y = f->cw.y + fvector.dy;
+ contour_add_point (stroker, c, &p);
+ }
+
+ case CAIRO_LINE_CAP_BUTT:
+ default:
+ break;
+ }
+ contour_add_point (stroker, c, &f->cw);
+}
+
+static void
+add_leading_cap (struct stroker *stroker,
+ const cairo_stroke_face_t *face,
+ struct stroke_contour *c)
+{
+ 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, c);
+}
+
+static void
+add_trailing_cap (struct stroker *stroker,
+ const cairo_stroke_face_t *face,
+ struct stroke_contour *c)
+{
+ add_cap (stroker, face, c);
+}
+
+static inline double
+normalize_slope (double *dx, double *dy)
+{
+ double dx0 = *dx, dy0 = *dy;
+ double mag;
+
+ assert (dx0 != 0.0 || dy0 != 0.0);
+
+ 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;
+ }
+
+ 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 (! _cairo_matrix_is_identity (stroker->ctm_inverse)) {
+ /* Normalize the matrix! */
+ 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 */
+ compute_face (&stroker->first_point, &slope, stroker, &face);
+
+ add_leading_cap (stroker, &face, &stroker->ccw);
+ add_trailing_cap (stroker, &face, &stroker->ccw);
+
+ /* ensure the circle is complete */
+ _cairo_contour_add_point (&stroker->ccw.contour,
+ _cairo_contour_first_point (&stroker->ccw.contour));
+
+ _cairo_polygon_add_contour (stroker->polygon, &stroker->ccw.contour);
+ _cairo_contour_reset (&stroker->ccw.contour);
+ } else {
+ if (stroker->has_current_face)
+ add_trailing_cap (stroker, &stroker->current_face, &stroker->ccw);
+
+#if DEBUG
+ {
+ FILE *file = fopen ("contours.txt", "a");
+ _cairo_debug_print_contour (file, &stroker->path);
+ _cairo_debug_print_contour (file, &stroker->cw.contour);
+ _cairo_debug_print_contour (file, &stroker->ccw.contour);
+ fclose (file);
+ _cairo_contour_reset (&stroker->path);
+ }
+#endif
+
+ _cairo_polygon_add_contour (stroker->polygon, &stroker->ccw.contour);
+ _cairo_contour_reset (&stroker->ccw.contour);
+
+ if (stroker->has_first_face) {
+ _cairo_contour_add_point (&stroker->ccw.contour,
+ &stroker->first_face.cw);
+ add_leading_cap (stroker, &stroker->first_face, &stroker->ccw);
+#if DEBUG
+ {
+ FILE *file = fopen ("contours.txt", "a");
+ _cairo_debug_print_contour (file, &stroker->ccw.contour);
+ fclose (file);
+ }
+#endif
+
+ _cairo_polygon_add_contour (stroker->polygon,
+ &stroker->ccw.contour);
+ _cairo_contour_reset (&stroker->ccw.contour);
+ }
+
+ _cairo_polygon_add_contour (stroker->polygon, &stroker->cw.contour);
+ _cairo_contour_reset (&stroker->cw.contour);
+ }
+}
+
+static cairo_status_t
+close_path (void *closure);
+
+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->has_first_face = FALSE;
+ stroker->has_current_face = FALSE;
+ stroker->has_initial_sub_path = FALSE;
+
+ stroker->first_point = *point;
+
+#if DEBUG
+ _cairo_contour_add_point (&stroker->path, point);
+#endif
+
+ stroker->current_face.point = *point;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+line_to (void *closure,
+ const cairo_point_t *point)
+{
+ struct stroker *stroker = closure;
+ cairo_stroke_face_t start;
+ cairo_point_t *p1 = &stroker->current_face.point;
+ cairo_slope_t dev_slope;
+
+ stroker->has_initial_sub_path = TRUE;
+
+ if (p1->x == point->x && p1->y == point->y)
+ return CAIRO_STATUS_SUCCESS;
+
+#if DEBUG
+ _cairo_contour_add_point (&stroker->path, point);
+#endif
+
+ _cairo_slope_init (&dev_slope, p1, point);
+ compute_face (p1, &dev_slope, stroker, &start);
+
+ if (stroker->has_current_face) {
+ int clockwise = _cairo_slope_compare (&stroker->current_face.dev_vector,
+ &start.dev_vector);
+ if (clockwise) {
+ clockwise = clockwise < 0;
+ /* Join with final face from previous segment */
+ if (! within_tolerance (&stroker->current_face.ccw, &start.ccw,
+ stroker->contour_tolerance) ||
+ ! within_tolerance (&stroker->current_face.cw, &start.cw,
+ stroker->contour_tolerance))
+ {
+ outer_join (stroker, &stroker->current_face, &start, clockwise);
+ inner_join (stroker, &stroker->current_face, &start, clockwise);
+ }
+ }
+ } 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->has_current_face = TRUE;
+
+ contour_add_point (stroker, &stroker->cw, &start.cw);
+ contour_add_point (stroker, &stroker->ccw, &start.ccw);
+ }
+
+ stroker->current_face = start;
+ stroker->current_face.point = *point;
+ stroker->current_face.ccw.x += dev_slope.dx;
+ stroker->current_face.ccw.y += dev_slope.dy;
+ stroker->current_face.cw.x += dev_slope.dx;
+ stroker->current_face.cw.y += dev_slope.dy;
+
+ contour_add_point (stroker, &stroker->cw, &stroker->current_face.cw);
+ contour_add_point (stroker, &stroker->ccw, &stroker->current_face.ccw);
+
+ 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 DEBUG
+ _cairo_contour_add_point (&stroker->path, point);
+#endif
+ if ((tangent->dx | tangent->dy) == 0) {
+ struct stroke_contour *outer;
+ cairo_point_t t;
+ int clockwise;
+
+ face = stroker->current_face;
+
+ face.usr_vector.x = -face.usr_vector.x;
+ face.usr_vector.y = -face.usr_vector.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;
+
+ clockwise = join_is_clockwise (&stroker->current_face, &face);
+ if (clockwise) {
+ outer = &stroker->cw;
+ } else {
+ outer = &stroker->ccw;
+ }
+
+ add_fan (stroker,
+ &stroker->current_face.dev_vector,
+ &face.dev_vector,
+ &stroker->current_face.point,
+ clockwise, outer);
+ } else {
+ compute_face (point, tangent, stroker, &face);
+
+ if ((face.dev_slope.x * stroker->current_face.dev_slope.x +
+ face.dev_slope.y * stroker->current_face.dev_slope.y) < stroker->spline_cusp_tolerance)
+ {
+ struct stroke_contour *outer;
+ int clockwise = join_is_clockwise (&stroker->current_face, &face);
+
+ stroker->current_face.cw.x += face.point.x - stroker->current_face.point.x;
+ stroker->current_face.cw.y += face.point.y - stroker->current_face.point.y;
+ contour_add_point (stroker, &stroker->cw, &stroker->current_face.cw);
+
+ stroker->current_face.ccw.x += face.point.x - stroker->current_face.point.x;
+ stroker->current_face.ccw.y += face.point.y - stroker->current_face.point.y;
+ contour_add_point (stroker, &stroker->ccw, &stroker->current_face.ccw);
+
+ if (clockwise) {
+ outer = &stroker->cw;
+ } else {
+ outer = &stroker->ccw;
+ }
+ add_fan (stroker,
+ &stroker->current_face.dev_vector,
+ &face.dev_vector,
+ &stroker->current_face.point,
+ clockwise, outer);
+ }
+
+ contour_add_point (stroker, &stroker->cw, &face.cw);
+ contour_add_point (stroker, &stroker->ccw, &face.ccw);
+ }
+
+ 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_spline_t spline;
+ cairo_stroke_face_t face;
+
+ if (stroker->has_bounds &&
+ ! _cairo_spline_intersects (&stroker->current_face.point, b, c, d,
+ &stroker->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) {
+ int clockwise = join_is_clockwise (&stroker->current_face, &face);
+ /* Join with final face from previous segment */
+ outer_join (stroker, &stroker->current_face, &face, clockwise);
+ inner_join (stroker, &stroker->current_face, &face, clockwise);
+ } 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;
+
+ contour_add_point (stroker, &stroker->cw, &face.cw);
+ contour_add_point (stroker, &stroker->ccw, &face.ccw);
+ }
+ stroker->current_face = face;
+
+ return _cairo_spline_decompose (&spline, stroker->tolerance);
+}
+
+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;
+
+ if (stroker->has_first_face && stroker->has_current_face) {
+ /* Join first and final faces of sub path */
+ outer_close (stroker, &stroker->current_face, &stroker->first_face);
+ inner_close (stroker, &stroker->current_face, &stroker->first_face);
+#if 0
+ *_cairo_contour_first_point (&stroker->ccw.contour) =
+ *_cairo_contour_last_point (&stroker->ccw.contour);
+
+ *_cairo_contour_first_point (&stroker->cw.contour) =
+ *_cairo_contour_last_point (&stroker->cw.contour);
+#endif
+
+ _cairo_polygon_add_contour (stroker->polygon, &stroker->cw.contour);
+ _cairo_polygon_add_contour (stroker->polygon, &stroker->ccw.contour);
+
+#if DEBUG
+ {
+ FILE *file = fopen ("contours.txt", "a");
+ _cairo_debug_print_contour (file, &stroker->path);
+ _cairo_debug_print_contour (file, &stroker->cw.contour);
+ _cairo_debug_print_contour (file, &stroker->ccw.contour);
+ fclose (file);
+
+ _cairo_contour_reset (&stroker->path);
+ }
+#endif
+ _cairo_contour_reset (&stroker->cw.contour);
+ _cairo_contour_reset (&stroker->ccw.contour);
+ } 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;
+}
+
+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)
+{
+ struct stroker stroker;
+ cairo_status_t status;
+
+ if (style->num_dashes) {
+ return _cairo_path_fixed_stroke_dashed_to_polygon (path,
+ style,
+ ctm,
+ ctm_inverse,
+ tolerance,
+ polygon);
+ }
+
+ stroker.has_bounds = polygon->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;
+ int i;
+
+ stroker.bounds = polygon->limits[0];
+ for (i = 1; i < polygon->num_limits; i++)
+ _cairo_box_add_box (&stroker.bounds, &polygon->limits[i]);
+
+ _cairo_stroke_style_max_distance_from_path (style, path, 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;
+ }
+
+ stroker.style = *style;
+ stroker.ctm = ctm;
+ stroker.ctm_inverse = ctm_inverse;
+ stroker.tolerance = tolerance;
+ stroker.half_line_width = style->line_width / 2.;
+ /* 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_det_positive =
+ _cairo_matrix_compute_determinant (ctm) >= 0.0;
+
+ stroker.pen.num_vertices = 0;
+ if (path->has_curve_to ||
+ style->line_join == CAIRO_LINE_JOIN_ROUND ||
+ style->line_cap == CAIRO_LINE_CAP_ROUND) {
+ status = _cairo_pen_init (&stroker.pen,
+ stroker.half_line_width,
+ 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.has_current_face = FALSE;
+ stroker.has_first_face = FALSE;
+ stroker.has_initial_sub_path = FALSE;
+
+#if DEBUG
+ remove ("contours.txt");
+ remove ("polygons.txt");
+ _cairo_contour_init (&stroker.path, 0);
+#endif
+ _cairo_contour_init (&stroker.cw.contour, 1);
+ _cairo_contour_init (&stroker.ccw.contour, -1);
+ tolerance *= CAIRO_FIXED_ONE;
+ tolerance *= tolerance;
+ stroker.contour_tolerance = tolerance;
+ stroker.polygon = polygon;
+
+ 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))
+ add_caps (&stroker);
+
+ _cairo_contour_fini (&stroker.cw.contour);
+ _cairo_contour_fini (&stroker.ccw.contour);
+ if (stroker.pen.num_vertices)
+ _cairo_pen_fini (&stroker.pen);
+
+#if DEBUG
+ {
+ FILE *file = fopen ("polygons.txt", "a");
+ _cairo_debug_print_polygon (file, polygon);
+ fclose (file);
+ }
+#endif
+
+ return status;
+}