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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 <cworth@cworth.org>
+ * Chris Wilson <chris@chris-wilson.co.uk>
+ */
+
+#define _BSD_SOURCE /* for hypot() */
+#include "cairoint.h"
+
+#include "cairo-box-inline.h"
+#include "cairo-boxes-private.h"
+#include "cairo-error-private.h"
+#include "cairo-path-fixed-private.h"
+#include "cairo-slope-private.h"
+#include "cairo-stroke-dash-private.h"
+#include "cairo-traps-private.h"
+
+typedef struct cairo_stroker {
+ cairo_stroke_style_t style;
+
+ const cairo_matrix_t *ctm;
+ const cairo_matrix_t *ctm_inverse;
+ double half_line_width;
+ double tolerance;
+ double spline_cusp_tolerance;
+ double ctm_determinant;
+ cairo_bool_t ctm_det_positive;
+
+ void *closure;
+ cairo_status_t (*add_external_edge) (void *closure,
+ const cairo_point_t *p1,
+ const cairo_point_t *p2);
+ cairo_status_t (*add_triangle) (void *closure,
+ const cairo_point_t triangle[3]);
+ cairo_status_t (*add_triangle_fan) (void *closure,
+ const cairo_point_t *midpt,
+ const cairo_point_t *points,
+ int npoints);
+ cairo_status_t (*add_convex_quad) (void *closure,
+ const cairo_point_t quad[4]);
+
+ cairo_pen_t pen;
+
+ cairo_point_t current_point;
+ cairo_point_t first_point;
+
+ cairo_bool_t has_initial_sub_path;
+
+ cairo_bool_t has_current_face;
+ cairo_stroke_face_t current_face;
+
+ cairo_bool_t has_first_face;
+ cairo_stroke_face_t first_face;
+
+ cairo_stroker_dash_t dash;
+
+ cairo_bool_t has_bounds;
+ cairo_box_t bounds;
+} cairo_stroker_t;
+
+static void
+_cairo_stroker_limit (cairo_stroker_t *stroker,
+ const cairo_path_fixed_t *path,
+ const cairo_box_t *boxes,
+ int num_boxes)
+{
+ double dx, dy;
+ cairo_fixed_t fdx, fdy;
+
+ stroker->has_bounds = TRUE;
+ _cairo_boxes_get_extents (boxes, num_boxes, &stroker->bounds);
+
+ /* Extend the bounds in each direction to account for the maximum area
+ * we might generate trapezoids, to capture line segments that are outside
+ * of the bounds but which might generate rendering that's within bounds.
+ */
+
+ _cairo_stroke_style_max_distance_from_path (&stroker->style, path,
+ stroker->ctm, &dx, &dy);
+
+ fdx = _cairo_fixed_from_double (dx);
+ fdy = _cairo_fixed_from_double (dy);
+
+ stroker->bounds.p1.x -= fdx;
+ stroker->bounds.p2.x += fdx;
+
+ stroker->bounds.p1.y -= fdy;
+ stroker->bounds.p2.y += fdy;
+}
+
+static cairo_status_t
+_cairo_stroker_init (cairo_stroker_t *stroker,
+ const cairo_path_fixed_t *path,
+ const cairo_stroke_style_t *stroke_style,
+ const cairo_matrix_t *ctm,
+ const cairo_matrix_t *ctm_inverse,
+ double tolerance,
+ const cairo_box_t *limits,
+ int num_limits)
+{
+ cairo_status_t status;
+
+ stroker->style = *stroke_style;
+ stroker->ctm = ctm;
+ stroker->ctm_inverse = ctm_inverse;
+ stroker->tolerance = tolerance;
+ stroker->half_line_width = stroke_style->line_width / 2.0;
+
+ /* To test whether we need to join two segments of a spline using
+ * a round-join or a bevel-join, we can inspect the angle between the
+ * two segments. If the difference between the chord distance
+ * (half-line-width times the cosine of the bisection angle) and the
+ * half-line-width itself is greater than tolerance then we need to
+ * inject a point.
+ */
+ stroker->spline_cusp_tolerance = 1 - tolerance / stroker->half_line_width;
+ stroker->spline_cusp_tolerance *= stroker->spline_cusp_tolerance;
+ stroker->spline_cusp_tolerance *= 2;
+ stroker->spline_cusp_tolerance -= 1;
+
+ stroker->ctm_determinant = _cairo_matrix_compute_determinant (stroker->ctm);
+ stroker->ctm_det_positive = stroker->ctm_determinant >= 0.0;
+
+ status = _cairo_pen_init (&stroker->pen,
+ stroker->half_line_width, tolerance, ctm);
+ if (unlikely (status))
+ return status;
+
+ stroker->has_current_face = FALSE;
+ stroker->has_first_face = FALSE;
+ stroker->has_initial_sub_path = FALSE;
+
+ _cairo_stroker_dash_init (&stroker->dash, stroke_style);
+
+ stroker->add_external_edge = NULL;
+
+ stroker->has_bounds = FALSE;
+ if (num_limits)
+ _cairo_stroker_limit (stroker, path, limits, num_limits);
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+static void
+_cairo_stroker_fini (cairo_stroker_t *stroker)
+{
+ _cairo_pen_fini (&stroker->pen);
+}
+
+static void
+_translate_point (cairo_point_t *point, const cairo_point_t *offset)
+{
+ point->x += offset->x;
+ point->y += offset->y;
+}
+
+static int
+_cairo_stroker_join_is_clockwise (const cairo_stroke_face_t *in,
+ const cairo_stroke_face_t *out)
+{
+ cairo_slope_t in_slope, out_slope;
+
+ _cairo_slope_init (&in_slope, &in->point, &in->cw);
+ _cairo_slope_init (&out_slope, &out->point, &out->cw);
+
+ return _cairo_slope_compare (&in_slope, &out_slope) < 0;
+}
+
+/**
+ * _cairo_slope_compare_sgn:
+ *
+ * Return -1, 0 or 1 depending on the relative slopes of
+ * two lines.
+ **/
+static int
+_cairo_slope_compare_sgn (double dx1, double dy1, double dx2, double dy2)
+{
+ double c = (dx1 * dy2 - dx2 * dy1);
+
+ if (c > 0) return 1;
+ if (c < 0) return -1;
+ return 0;
+}
+
+static inline int
+_range_step (int i, int step, int max)
+{
+ i += step;
+ if (i < 0)
+ i = max - 1;
+ if (i >= max)
+ i = 0;
+ return i;
+}
+
+/*
+ * Construct a fan around the midpoint using the vertices from pen between
+ * inpt and outpt.
+ */
+static cairo_status_t
+_tessellate_fan (cairo_stroker_t *stroker,
+ const cairo_slope_t *in_vector,
+ const cairo_slope_t *out_vector,
+ const cairo_point_t *midpt,
+ const cairo_point_t *inpt,
+ const cairo_point_t *outpt,
+ cairo_bool_t clockwise)
+{
+ cairo_point_t stack_points[64], *points = stack_points;
+ cairo_pen_t *pen = &stroker->pen;
+ int start, stop, num_points = 0;
+ cairo_status_t status;
+
+ if (stroker->has_bounds &&
+ ! _cairo_box_contains_point (&stroker->bounds, midpt))
+ goto BEVEL;
+
+ assert (stroker->pen.num_vertices);
+
+ if (clockwise) {
+ _cairo_pen_find_active_ccw_vertices (pen,
+ in_vector, out_vector,
+ &start, &stop);
+ if (stroker->add_external_edge) {
+ cairo_point_t last;
+ last = *inpt;
+ while (start != stop) {
+ cairo_point_t p = *midpt;
+ _translate_point (&p, &pen->vertices[start].point);
+
+ status = stroker->add_external_edge (stroker->closure,
+ &last, &p);
+ if (unlikely (status))
+ return status;
+ last = p;
+
+ if (start-- == 0)
+ start += pen->num_vertices;
+ }
+ status = stroker->add_external_edge (stroker->closure,
+ &last, outpt);
+ } else {
+ if (start == stop)
+ goto BEVEL;
+
+ num_points = stop - start;
+ if (num_points < 0)
+ num_points += pen->num_vertices;
+ num_points += 2;
+ if (num_points > ARRAY_LENGTH(stack_points)) {
+ points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
+ if (unlikely (points == NULL))
+ return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+ }
+
+ points[0] = *inpt;
+ num_points = 1;
+ while (start != stop) {
+ points[num_points] = *midpt;
+ _translate_point (&points[num_points], &pen->vertices[start].point);
+ num_points++;
+
+ if (start-- == 0)
+ start += pen->num_vertices;
+ }
+ points[num_points++] = *outpt;
+ }
+ } else {
+ _cairo_pen_find_active_cw_vertices (pen,
+ in_vector, out_vector,
+ &start, &stop);
+ if (stroker->add_external_edge) {
+ cairo_point_t last;
+ last = *inpt;
+ while (start != stop) {
+ cairo_point_t p = *midpt;
+ _translate_point (&p, &pen->vertices[start].point);
+
+ status = stroker->add_external_edge (stroker->closure,
+ &p, &last);
+ if (unlikely (status))
+ return status;
+ last = p;
+
+ if (++start == pen->num_vertices)
+ start = 0;
+ }
+ status = stroker->add_external_edge (stroker->closure,
+ outpt, &last);
+ } else {
+ if (start == stop)
+ goto BEVEL;
+
+ num_points = stop - start;
+ if (num_points < 0)
+ num_points += pen->num_vertices;
+ num_points += 2;
+ if (num_points > ARRAY_LENGTH(stack_points)) {
+ points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
+ if (unlikely (points == NULL))
+ return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+ }
+
+ points[0] = *inpt;
+ num_points = 1;
+ while (start != stop) {
+ points[num_points] = *midpt;
+ _translate_point (&points[num_points], &pen->vertices[start].point);
+ num_points++;
+
+ if (++start == pen->num_vertices)
+ start = 0;
+ }
+ points[num_points++] = *outpt;
+ }
+ }
+
+ if (num_points) {
+ status = stroker->add_triangle_fan (stroker->closure,
+ midpt, points, num_points);
+ }
+
+ if (points != stack_points)
+ free (points);
+
+ return status;
+
+BEVEL:
+ /* Ensure a leak free connection... */
+ if (stroker->add_external_edge != NULL) {
+ if (clockwise)
+ return stroker->add_external_edge (stroker->closure, inpt, outpt);
+ else
+ return stroker->add_external_edge (stroker->closure, outpt, inpt);
+ } else {
+ stack_points[0] = *midpt;
+ stack_points[1] = *inpt;
+ stack_points[2] = *outpt;
+ return stroker->add_triangle (stroker->closure, stack_points);
+ }
+}
+
+static cairo_status_t
+_cairo_stroker_join (cairo_stroker_t *stroker,
+ const cairo_stroke_face_t *in,
+ const cairo_stroke_face_t *out)
+{
+ int clockwise = _cairo_stroker_join_is_clockwise (out, in);
+ const cairo_point_t *inpt, *outpt;
+ cairo_point_t points[4];
+ cairo_status_t status;
+
+ if (in->cw.x == out->cw.x && in->cw.y == out->cw.y &&
+ in->ccw.x == out->ccw.x && in->ccw.y == out->ccw.y)
+ {
+ return CAIRO_STATUS_SUCCESS;
+ }
+
+ if (clockwise) {
+ if (stroker->add_external_edge != NULL) {
+ status = stroker->add_external_edge (stroker->closure,
+ &out->cw, &in->point);
+ if (unlikely (status))
+ return status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &in->point, &in->cw);
+ if (unlikely (status))
+ return status;
+ }
+
+ inpt = &in->ccw;
+ outpt = &out->ccw;
+ } else {
+ if (stroker->add_external_edge != NULL) {
+ status = stroker->add_external_edge (stroker->closure,
+ &in->ccw, &in->point);
+ if (unlikely (status))
+ return status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &in->point, &out->ccw);
+ if (unlikely (status))
+ return status;
+ }
+
+ inpt = &in->cw;
+ outpt = &out->cw;
+ }
+
+ switch (stroker->style.line_join) {
+ case CAIRO_LINE_JOIN_ROUND:
+ /* construct a fan around the common midpoint */
+ return _tessellate_fan (stroker,
+ &in->dev_vector,
+ &out->dev_vector,
+ &in->point, inpt, outpt,
+ clockwise);
+
+ case CAIRO_LINE_JOIN_MITER:
+ default: {
+ /* dot product of incoming slope vector with outgoing slope vector */
+ double in_dot_out = -in->usr_vector.x * out->usr_vector.x +
+ -in->usr_vector.y * out->usr_vector.y;
+ double ml = stroker->style.miter_limit;
+
+ /* Check the miter limit -- lines meeting at an acute angle
+ * can generate long miters, the limit converts them to bevel
+ *
+ * Consider the miter join formed when two line segments
+ * meet at an angle psi:
+ *
+ * /.\
+ * /. .\
+ * /./ \.\
+ * /./psi\.\
+ *
+ * We can zoom in on the right half of that to see:
+ *
+ * |\
+ * | \ psi/2
+ * | \
+ * | \
+ * | \
+ * | \
+ * miter \
+ * length \
+ * | \
+ * | .\
+ * | . \
+ * |. line \
+ * \ width \
+ * \ \
+ *
+ *
+ * The right triangle in that figure, (the line-width side is
+ * shown faintly with three '.' characters), gives us the
+ * following expression relating miter length, angle and line
+ * width:
+ *
+ * 1 /sin (psi/2) = miter_length / line_width
+ *
+ * The right-hand side of this relationship is the same ratio
+ * in which the miter limit (ml) is expressed. We want to know
+ * when the miter length is within the miter limit. That is
+ * when the following condition holds:
+ *
+ * 1/sin(psi/2) <= ml
+ * 1 <= ml sin(psi/2)
+ * 1 <= ml² sin²(psi/2)
+ * 2 <= ml² 2 sin²(psi/2)
+ * 2·sin²(psi/2) = 1-cos(psi)
+ * 2 <= ml² (1-cos(psi))
+ *
+ * in · out = |in| |out| cos (psi)
+ *
+ * in and out are both unit vectors, so:
+ *
+ * in · out = cos (psi)
+ *
+ * 2 <= ml² (1 - in · out)
+ *
+ */
+ if (2 <= ml * ml * (1 - in_dot_out)) {
+ double x1, y1, x2, y2;
+ double mx, my;
+ double dx1, dx2, dy1, dy2;
+ double ix, iy;
+ double fdx1, fdy1, fdx2, fdy2;
+ double mdx, mdy;
+
+ /*
+ * we've got the points already transformed to device
+ * space, but need to do some computation with them and
+ * also need to transform the slope from user space to
+ * device space
+ */
+ /* outer point of incoming line face */
+ x1 = _cairo_fixed_to_double (inpt->x);
+ y1 = _cairo_fixed_to_double (inpt->y);
+ dx1 = in->usr_vector.x;
+ dy1 = in->usr_vector.y;
+ cairo_matrix_transform_distance (stroker->ctm, &dx1, &dy1);
+
+ /* outer point of outgoing line face */
+ x2 = _cairo_fixed_to_double (outpt->x);
+ y2 = _cairo_fixed_to_double (outpt->y);
+ dx2 = out->usr_vector.x;
+ dy2 = out->usr_vector.y;
+ cairo_matrix_transform_distance (stroker->ctm, &dx2, &dy2);
+
+ /*
+ * Compute the location of the outer corner of the miter.
+ * That's pretty easy -- just the intersection of the two
+ * outer edges. We've got slopes and points on each
+ * of those edges. Compute my directly, then compute
+ * mx by using the edge with the larger dy; that avoids
+ * dividing by values close to zero.
+ */
+ my = (((x2 - x1) * dy1 * dy2 - y2 * dx2 * dy1 + y1 * dx1 * dy2) /
+ (dx1 * dy2 - dx2 * dy1));
+ if (fabs (dy1) >= fabs (dy2))
+ mx = (my - y1) * dx1 / dy1 + x1;
+ else
+ mx = (my - y2) * dx2 / dy2 + x2;
+
+ /*
+ * When the two outer edges are nearly parallel, slight
+ * perturbations in the position of the outer points of the lines
+ * caused by representing them in fixed point form can cause the
+ * intersection point of the miter to move a large amount. If
+ * that moves the miter intersection from between the two faces,
+ * then draw a bevel instead.
+ */
+
+ ix = _cairo_fixed_to_double (in->point.x);
+ iy = _cairo_fixed_to_double (in->point.y);
+
+ /* slope of one face */
+ fdx1 = x1 - ix; fdy1 = y1 - iy;
+
+ /* slope of the other face */
+ fdx2 = x2 - ix; fdy2 = y2 - iy;
+
+ /* slope from the intersection to the miter point */
+ mdx = mx - ix; mdy = my - iy;
+
+ /*
+ * Make sure the miter point line lies between the two
+ * faces by comparing the slopes
+ */
+ if (_cairo_slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
+ _cairo_slope_compare_sgn (fdx2, fdy2, mdx, mdy))
+ {
+ if (stroker->add_external_edge != NULL) {
+ points[0].x = _cairo_fixed_from_double (mx);
+ points[0].y = _cairo_fixed_from_double (my);
+
+ if (clockwise) {
+ status = stroker->add_external_edge (stroker->closure,
+ inpt, &points[0]);
+ if (unlikely (status))
+ return status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &points[0], outpt);
+ if (unlikely (status))
+ return status;
+ } else {
+ status = stroker->add_external_edge (stroker->closure,
+ outpt, &points[0]);
+ if (unlikely (status))
+ return status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &points[0], inpt);
+ if (unlikely (status))
+ return status;
+ }
+
+ return CAIRO_STATUS_SUCCESS;
+ } else {
+ points[0] = in->point;
+ points[1] = *inpt;
+ points[2].x = _cairo_fixed_from_double (mx);
+ points[2].y = _cairo_fixed_from_double (my);
+ points[3] = *outpt;
+
+ return stroker->add_convex_quad (stroker->closure, points);
+ }
+ }
+ }
+ }
+
+ /* fall through ... */
+
+ case CAIRO_LINE_JOIN_BEVEL:
+ if (stroker->add_external_edge != NULL) {
+ if (clockwise) {
+ return stroker->add_external_edge (stroker->closure,
+ inpt, outpt);
+ } else {
+ return stroker->add_external_edge (stroker->closure,
+ outpt, inpt);
+ }
+ } else {
+ points[0] = in->point;
+ points[1] = *inpt;
+ points[2] = *outpt;
+
+ return stroker->add_triangle (stroker->closure, points);
+ }
+ }
+}
+
+static cairo_status_t
+_cairo_stroker_add_cap (cairo_stroker_t *stroker,
+ const cairo_stroke_face_t *f)
+{
+ switch (stroker->style.line_cap) {
+ case CAIRO_LINE_CAP_ROUND: {
+ cairo_slope_t slope;
+
+ slope.dx = -f->dev_vector.dx;
+ slope.dy = -f->dev_vector.dy;
+
+ return _tessellate_fan (stroker,
+ &f->dev_vector,
+ &slope,
+ &f->point, &f->cw, &f->ccw,
+ FALSE);
+
+ }
+
+ case CAIRO_LINE_CAP_SQUARE: {
+ double dx, dy;
+ cairo_slope_t fvector;
+ cairo_point_t quad[4];
+
+ dx = f->usr_vector.x;
+ dy = f->usr_vector.y;
+ dx *= stroker->half_line_width;
+ dy *= stroker->half_line_width;
+ cairo_matrix_transform_distance (stroker->ctm, &dx, &dy);
+ fvector.dx = _cairo_fixed_from_double (dx);
+ fvector.dy = _cairo_fixed_from_double (dy);
+
+ quad[0] = f->ccw;
+ quad[1].x = f->ccw.x + fvector.dx;
+ quad[1].y = f->ccw.y + fvector.dy;
+ quad[2].x = f->cw.x + fvector.dx;
+ quad[2].y = f->cw.y + fvector.dy;
+ quad[3] = f->cw;
+
+ if (stroker->add_external_edge != NULL) {
+ cairo_status_t status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &quad[0], &quad[1]);
+ if (unlikely (status))
+ return status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &quad[1], &quad[2]);
+ if (unlikely (status))
+ return status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &quad[2], &quad[3]);
+ if (unlikely (status))
+ return status;
+
+ return CAIRO_STATUS_SUCCESS;
+ } else {
+ return stroker->add_convex_quad (stroker->closure, quad);
+ }
+ }
+
+ case CAIRO_LINE_CAP_BUTT:
+ default:
+ if (stroker->add_external_edge != NULL) {
+ return stroker->add_external_edge (stroker->closure,
+ &f->ccw, &f->cw);
+ } else {
+ return CAIRO_STATUS_SUCCESS;
+ }
+ }
+}
+
+static cairo_status_t
+_cairo_stroker_add_leading_cap (cairo_stroker_t *stroker,
+ const cairo_stroke_face_t *face)
+{
+ cairo_stroke_face_t reversed;
+ cairo_point_t t;
+
+ reversed = *face;
+
+ /* The initial cap needs an outward facing vector. Reverse everything */
+ reversed.usr_vector.x = -reversed.usr_vector.x;
+ reversed.usr_vector.y = -reversed.usr_vector.y;
+ reversed.dev_vector.dx = -reversed.dev_vector.dx;
+ reversed.dev_vector.dy = -reversed.dev_vector.dy;
+ t = reversed.cw;
+ reversed.cw = reversed.ccw;
+ reversed.ccw = t;
+
+ return _cairo_stroker_add_cap (stroker, &reversed);
+}
+
+static cairo_status_t
+_cairo_stroker_add_trailing_cap (cairo_stroker_t *stroker,
+ const cairo_stroke_face_t *face)
+{
+ return _cairo_stroker_add_cap (stroker, face);
+}
+
+static inline cairo_bool_t
+_compute_normalized_device_slope (double *dx, double *dy,
+ const cairo_matrix_t *ctm_inverse,
+ double *mag_out)
+{
+ double dx0 = *dx, dy0 = *dy;
+ double mag;
+
+ cairo_matrix_transform_distance (ctm_inverse, &dx0, &dy0);
+
+ if (dx0 == 0.0 && dy0 == 0.0) {
+ if (mag_out)
+ *mag_out = 0.0;
+ return FALSE;
+ }
+
+ if (dx0 == 0.0) {
+ *dx = 0.0;
+ if (dy0 > 0.0) {
+ mag = dy0;
+ *dy = 1.0;
+ } else {
+ mag = -dy0;
+ *dy = -1.0;
+ }
+ } else if (dy0 == 0.0) {
+ *dy = 0.0;
+ if (dx0 > 0.0) {
+ mag = dx0;
+ *dx = 1.0;
+ } else {
+ mag = -dx0;
+ *dx = -1.0;
+ }
+ } else {
+ mag = hypot (dx0, dy0);
+ *dx = dx0 / mag;
+ *dy = dy0 / mag;
+ }
+
+ if (mag_out)
+ *mag_out = mag;
+
+ return TRUE;
+}
+
+static void
+_compute_face (const cairo_point_t *point,
+ const cairo_slope_t *dev_slope,
+ double slope_dx,
+ double slope_dy,
+ cairo_stroker_t *stroker,
+ cairo_stroke_face_t *face)
+{
+ double face_dx, face_dy;
+ cairo_point_t offset_ccw, offset_cw;
+
+ /*
+ * rotate to get a line_width/2 vector along the face, note that
+ * the vector must be rotated the right direction in device space,
+ * but by 90° in user space. So, the rotation depends on
+ * whether the ctm reflects or not, and that can be determined
+ * by looking at the determinant of the matrix.
+ */
+ if (stroker->ctm_det_positive)
+ {
+ face_dx = - slope_dy * stroker->half_line_width;
+ face_dy = slope_dx * stroker->half_line_width;
+ }
+ else
+ {
+ face_dx = slope_dy * stroker->half_line_width;
+ face_dy = - slope_dx * stroker->half_line_width;
+ }
+
+ /* back to device space */
+ cairo_matrix_transform_distance (stroker->ctm, &face_dx, &face_dy);
+
+ offset_ccw.x = _cairo_fixed_from_double (face_dx);
+ offset_ccw.y = _cairo_fixed_from_double (face_dy);
+ offset_cw.x = -offset_ccw.x;
+ offset_cw.y = -offset_ccw.y;
+
+ face->ccw = *point;
+ _translate_point (&face->ccw, &offset_ccw);
+
+ face->point = *point;
+
+ face->cw = *point;
+ _translate_point (&face->cw, &offset_cw);
+
+ face->usr_vector.x = slope_dx;
+ face->usr_vector.y = slope_dy;
+
+ face->dev_vector = *dev_slope;
+}
+
+static cairo_status_t
+_cairo_stroker_add_caps (cairo_stroker_t *stroker)
+{
+ cairo_status_t status;
+
+ /* check for a degenerative sub_path */
+ if (stroker->has_initial_sub_path
+ && ! stroker->has_first_face
+ && ! stroker->has_current_face
+ && stroker->style.line_cap == CAIRO_LINE_CAP_ROUND)
+ {
+ /* pick an arbitrary slope to use */
+ double dx = 1.0, dy = 0.0;
+ cairo_slope_t slope = { CAIRO_FIXED_ONE, 0 };
+ cairo_stroke_face_t face;
+
+ _compute_normalized_device_slope (&dx, &dy,
+ stroker->ctm_inverse, NULL);
+
+ /* arbitrarily choose first_point
+ * first_point and current_point should be the same */
+ _compute_face (&stroker->first_point, &slope, dx, dy, stroker, &face);
+
+ status = _cairo_stroker_add_leading_cap (stroker, &face);
+ if (unlikely (status))
+ return status;
+
+ status = _cairo_stroker_add_trailing_cap (stroker, &face);
+ if (unlikely (status))
+ return status;
+ }
+
+ if (stroker->has_first_face) {
+ status = _cairo_stroker_add_leading_cap (stroker,
+ &stroker->first_face);
+ if (unlikely (status))
+ return status;
+ }
+
+ if (stroker->has_current_face) {
+ status = _cairo_stroker_add_trailing_cap (stroker,
+ &stroker->current_face);
+ if (unlikely (status))
+ return status;
+ }
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+_cairo_stroker_add_sub_edge (cairo_stroker_t *stroker,
+ const cairo_point_t *p1,
+ const cairo_point_t *p2,
+ cairo_slope_t *dev_slope,
+ double slope_dx, double slope_dy,
+ cairo_stroke_face_t *start,
+ cairo_stroke_face_t *end)
+{
+ _compute_face (p1, dev_slope, slope_dx, slope_dy, stroker, start);
+ *end = *start;
+
+ if (p1->x == p2->x && p1->y == p2->y)
+ return CAIRO_STATUS_SUCCESS;
+
+ end->point = *p2;
+ end->ccw.x += p2->x - p1->x;
+ end->ccw.y += p2->y - p1->y;
+ end->cw.x += p2->x - p1->x;
+ end->cw.y += p2->y - p1->y;
+
+ if (stroker->add_external_edge != NULL) {
+ cairo_status_t status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &end->cw, &start->cw);
+ if (unlikely (status))
+ return status;
+
+ status = stroker->add_external_edge (stroker->closure,
+ &start->ccw, &end->ccw);
+ if (unlikely (status))
+ return status;
+
+ return CAIRO_STATUS_SUCCESS;
+ } else {
+ cairo_point_t quad[4];
+
+ quad[0] = start->cw;
+ quad[1] = end->cw;
+ quad[2] = end->ccw;
+ quad[3] = start->ccw;
+
+ return stroker->add_convex_quad (stroker->closure, quad);
+ }
+}
+
+static cairo_status_t
+_cairo_stroker_move_to (void *closure,
+ const cairo_point_t *point)
+{
+ cairo_stroker_t *stroker = closure;
+ cairo_status_t status;
+
+ /* reset the dash pattern for new sub paths */
+ _cairo_stroker_dash_start (&stroker->dash);
+
+ /* Cap the start and end of the previous sub path as needed */
+ status = _cairo_stroker_add_caps (stroker);
+ if (unlikely (status))
+ return status;
+
+ stroker->first_point = *point;
+ stroker->current_point = *point;
+
+ stroker->has_first_face = FALSE;
+ stroker->has_current_face = FALSE;
+ stroker->has_initial_sub_path = FALSE;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+_cairo_stroker_line_to (void *closure,
+ const cairo_point_t *point)
+{
+ cairo_stroker_t *stroker = closure;
+ cairo_stroke_face_t start, end;
+ cairo_point_t *p1 = &stroker->current_point;
+ cairo_slope_t dev_slope;
+ double slope_dx, slope_dy;
+ cairo_status_t status;
+
+ stroker->has_initial_sub_path = TRUE;
+
+ if (p1->x == point->x && p1->y == point->y)
+ return CAIRO_STATUS_SUCCESS;
+
+ _cairo_slope_init (&dev_slope, p1, point);
+ slope_dx = _cairo_fixed_to_double (point->x - p1->x);
+ slope_dy = _cairo_fixed_to_double (point->y - p1->y);
+ _compute_normalized_device_slope (&slope_dx, &slope_dy,
+ stroker->ctm_inverse, NULL);
+
+ status = _cairo_stroker_add_sub_edge (stroker,
+ p1, point,
+ &dev_slope,
+ slope_dx, slope_dy,
+ &start, &end);
+ if (unlikely (status))
+ return status;
+
+ if (stroker->has_current_face) {
+ /* Join with final face from previous segment */
+ status = _cairo_stroker_join (stroker,
+ &stroker->current_face,
+ &start);
+ if (unlikely (status))
+ return status;
+ } else if (! stroker->has_first_face) {
+ /* Save sub path's first face in case needed for closing join */
+ stroker->first_face = start;
+ stroker->has_first_face = TRUE;
+ }
+ stroker->current_face = end;
+ stroker->has_current_face = TRUE;
+
+ stroker->current_point = *point;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+_cairo_stroker_spline_to (void *closure,
+ const cairo_point_t *point,
+ const cairo_slope_t *tangent)
+{
+ cairo_stroker_t *stroker = closure;
+ cairo_stroke_face_t new_face;
+ double slope_dx, slope_dy;
+ cairo_point_t points[3];
+ cairo_point_t intersect_point;
+
+ stroker->has_initial_sub_path = TRUE;
+
+ if (stroker->current_point.x == point->x &&
+ stroker->current_point.y == point->y)
+ return CAIRO_STATUS_SUCCESS;
+
+ slope_dx = _cairo_fixed_to_double (tangent->dx);
+ slope_dy = _cairo_fixed_to_double (tangent->dy);
+
+ if (! _compute_normalized_device_slope (&slope_dx, &slope_dy,
+ stroker->ctm_inverse, NULL))
+ return CAIRO_STATUS_SUCCESS;
+
+ _compute_face (point, tangent,
+ slope_dx, slope_dy,
+ stroker, &new_face);
+
+ assert (stroker->has_current_face);
+
+ if ((new_face.dev_slope.x * stroker->current_face.dev_slope.x +
+ new_face.dev_slope.y * stroker->current_face.dev_slope.y) < stroker->spline_cusp_tolerance) {
+
+ const cairo_point_t *inpt, *outpt;
+ int clockwise = _cairo_stroker_join_is_clockwise (&new_face,
+ &stroker->current_face);
+
+ if (clockwise) {
+ inpt = &stroker->current_face.cw;
+ outpt = &new_face.cw;
+ } else {
+ inpt = &stroker->current_face.ccw;
+ outpt = &new_face.ccw;
+ }
+
+ _tessellate_fan (stroker,
+ &stroker->current_face.dev_vector,
+ &new_face.dev_vector,
+ &stroker->current_face.point,
+ inpt, outpt,
+ clockwise);
+ }
+
+ if (_slow_segment_intersection (&stroker->current_face.cw,
+ &stroker->current_face.ccw,
+ &new_face.cw,
+ &new_face.ccw,
+ &intersect_point)) {
+ points[0] = stroker->current_face.ccw;
+ points[1] = new_face.ccw;
+ points[2] = intersect_point;
+ stroker->add_triangle (stroker->closure, points);
+
+ points[0] = stroker->current_face.cw;
+ points[1] = new_face.cw;
+ stroker->add_triangle (stroker->closure, points);
+ } else {
+ points[0] = stroker->current_face.ccw;
+ points[1] = stroker->current_face.cw;
+ points[2] = new_face.cw;
+ stroker->add_triangle (stroker->closure, points);
+
+ points[0] = stroker->current_face.ccw;
+ points[1] = new_face.cw;
+ points[2] = new_face.ccw;
+ stroker->add_triangle (stroker->closure, points);
+ }
+
+ stroker->current_face = new_face;
+ stroker->has_current_face = TRUE;
+ stroker->current_point = *point;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+/*
+ * Dashed lines. Cap each dash end, join around turns when on
+ */
+static cairo_status_t
+_cairo_stroker_line_to_dashed (void *closure,
+ const cairo_point_t *p2)
+{
+ cairo_stroker_t *stroker = closure;
+ double mag, remain, step_length = 0;
+ double slope_dx, slope_dy;
+ double dx2, dy2;
+ cairo_stroke_face_t sub_start, sub_end;
+ cairo_point_t *p1 = &stroker->current_point;
+ cairo_slope_t dev_slope;
+ cairo_line_t segment;
+ cairo_bool_t fully_in_bounds;
+ cairo_status_t status;
+
+ stroker->has_initial_sub_path = stroker->dash.dash_starts_on;
+
+ if (p1->x == p2->x && p1->y == p2->y)
+ return CAIRO_STATUS_SUCCESS;
+
+ fully_in_bounds = TRUE;
+ if (stroker->has_bounds &&
+ (! _cairo_box_contains_point (&stroker->bounds, p1) ||
+ ! _cairo_box_contains_point (&stroker->bounds, p2)))
+ {
+ fully_in_bounds = FALSE;
+ }
+
+ _cairo_slope_init (&dev_slope, p1, p2);
+
+ slope_dx = _cairo_fixed_to_double (p2->x - p1->x);
+ slope_dy = _cairo_fixed_to_double (p2->y - p1->y);
+
+ if (! _compute_normalized_device_slope (&slope_dx, &slope_dy,
+ stroker->ctm_inverse, &mag))
+ {
+ return CAIRO_STATUS_SUCCESS;
+ }
+
+ remain = mag;
+ segment.p1 = *p1;
+ while (remain) {
+ step_length = MIN (stroker->dash.dash_remain, remain);
+ remain -= step_length;
+ dx2 = slope_dx * (mag - remain);
+ dy2 = slope_dy * (mag - remain);
+ cairo_matrix_transform_distance (stroker->ctm, &dx2, &dy2);
+ segment.p2.x = _cairo_fixed_from_double (dx2) + p1->x;
+ segment.p2.y = _cairo_fixed_from_double (dy2) + p1->y;
+
+ if (stroker->dash.dash_on &&
+ (fully_in_bounds ||
+ (! stroker->has_first_face && stroker->dash.dash_starts_on) ||
+ _cairo_box_intersects_line_segment (&stroker->bounds, &segment)))
+ {
+ status = _cairo_stroker_add_sub_edge (stroker,
+ &segment.p1, &segment.p2,
+ &dev_slope,
+ slope_dx, slope_dy,
+ &sub_start, &sub_end);
+ if (unlikely (status))
+ return status;
+
+ if (stroker->has_current_face)
+ {
+ /* Join with final face from previous segment */
+ status = _cairo_stroker_join (stroker,
+ &stroker->current_face,
+ &sub_start);
+ if (unlikely (status))
+ return status;
+
+ stroker->has_current_face = FALSE;
+ }
+ else if (! stroker->has_first_face &&
+ stroker->dash.dash_starts_on)
+ {
+ /* Save sub path's first face in case needed for closing join */
+ stroker->first_face = sub_start;
+ stroker->has_first_face = TRUE;
+ }
+ else
+ {
+ /* Cap dash start if not connecting to a previous segment */
+ status = _cairo_stroker_add_leading_cap (stroker, &sub_start);
+ if (unlikely (status))
+ return status;
+ }
+
+ if (remain) {
+ /* Cap dash end if not at end of segment */
+ status = _cairo_stroker_add_trailing_cap (stroker, &sub_end);
+ if (unlikely (status))
+ return status;
+ } else {
+ stroker->current_face = sub_end;
+ stroker->has_current_face = TRUE;
+ }
+ } else {
+ if (stroker->has_current_face) {
+ /* Cap final face from previous segment */
+ status = _cairo_stroker_add_trailing_cap (stroker,
+ &stroker->current_face);
+ if (unlikely (status))
+ return status;
+
+ stroker->has_current_face = FALSE;
+ }
+ }
+
+ _cairo_stroker_dash_step (&stroker->dash, step_length);
+ segment.p1 = segment.p2;
+ }
+
+ if (stroker->dash.dash_on && ! stroker->has_current_face) {
+ /* This segment ends on a transition to dash_on, compute a new face
+ * and add cap for the beginning of the next dash_on step.
+ *
+ * Note: this will create a degenerate cap if this is not the last line
+ * in the path. Whether this behaviour is desirable or not is debatable.
+ * On one side these degenerate caps can not be reproduced with regular
+ * path stroking.
+ * On the other hand, Acroread 7 also produces the degenerate caps.
+ */
+ _compute_face (p2, &dev_slope,
+ slope_dx, slope_dy,
+ stroker,
+ &stroker->current_face);
+
+ status = _cairo_stroker_add_leading_cap (stroker,
+ &stroker->current_face);
+ if (unlikely (status))
+ return status;
+
+ stroker->has_current_face = TRUE;
+ }
+
+ stroker->current_point = *p2;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+_cairo_stroker_curve_to (void *closure,
+ const cairo_point_t *b,
+ const cairo_point_t *c,
+ const cairo_point_t *d)
+{
+ cairo_stroker_t *stroker = closure;
+ cairo_spline_t spline;
+ cairo_line_join_t line_join_save;
+ cairo_stroke_face_t face;
+ double slope_dx, slope_dy;
+ cairo_spline_add_point_func_t line_to;
+ cairo_spline_add_point_func_t spline_to;
+ cairo_status_t status = CAIRO_STATUS_SUCCESS;
+
+ line_to = stroker->dash.dashed ?
+ (cairo_spline_add_point_func_t) _cairo_stroker_line_to_dashed :
+ (cairo_spline_add_point_func_t) _cairo_stroker_line_to;
+
+ /* spline_to is only capable of rendering non-degenerate splines. */
+ spline_to = stroker->dash.dashed ?
+ (cairo_spline_add_point_func_t) _cairo_stroker_line_to_dashed :
+ (cairo_spline_add_point_func_t) _cairo_stroker_spline_to;
+
+ if (! _cairo_spline_init (&spline,
+ spline_to,
+ stroker,
+ &stroker->current_point, b, c, d))
+ {
+ cairo_slope_t fallback_slope;
+ _cairo_slope_init (&fallback_slope, &stroker->current_point, d);
+ return line_to (closure, d, &fallback_slope);
+ }
+
+ /* If the line width is so small that the pen is reduced to a
+ single point, then we have nothing to do. */
+ if (stroker->pen.num_vertices <= 1)
+ return CAIRO_STATUS_SUCCESS;
+
+ /* Compute the initial face */
+ if (! stroker->dash.dashed || stroker->dash.dash_on) {
+ slope_dx = _cairo_fixed_to_double (spline.initial_slope.dx);
+ slope_dy = _cairo_fixed_to_double (spline.initial_slope.dy);
+ if (_compute_normalized_device_slope (&slope_dx, &slope_dy,
+ stroker->ctm_inverse, NULL))
+ {
+ _compute_face (&stroker->current_point,
+ &spline.initial_slope,
+ slope_dx, slope_dy,
+ stroker, &face);
+ }
+ if (stroker->has_current_face) {
+ status = _cairo_stroker_join (stroker,
+ &stroker->current_face, &face);
+ if (unlikely (status))
+ return status;
+ } else if (! stroker->has_first_face) {
+ stroker->first_face = face;
+ stroker->has_first_face = TRUE;
+ }
+
+ stroker->current_face = face;
+ stroker->has_current_face = TRUE;
+ }
+
+ /* Temporarily modify the stroker to use round joins to guarantee
+ * smooth stroked curves. */
+ line_join_save = stroker->style.line_join;
+ stroker->style.line_join = CAIRO_LINE_JOIN_ROUND;
+
+ status = _cairo_spline_decompose (&spline, stroker->tolerance);
+ if (unlikely (status))
+ return status;
+
+ /* And join the final face */
+ if (! stroker->dash.dashed || stroker->dash.dash_on) {
+ slope_dx = _cairo_fixed_to_double (spline.final_slope.dx);
+ slope_dy = _cairo_fixed_to_double (spline.final_slope.dy);
+ if (_compute_normalized_device_slope (&slope_dx, &slope_dy,
+ stroker->ctm_inverse, NULL))
+ {
+ _compute_face (&stroker->current_point,
+ &spline.final_slope,
+ slope_dx, slope_dy,
+ stroker, &face);
+ }
+
+ status = _cairo_stroker_join (stroker, &stroker->current_face, &face);
+ if (unlikely (status))
+ return status;
+
+ stroker->current_face = face;
+ }
+
+ stroker->style.line_join = line_join_save;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+static cairo_status_t
+_cairo_stroker_close_path (void *closure)
+{
+ cairo_stroker_t *stroker = closure;
+ cairo_status_t status;
+
+ if (stroker->dash.dashed)
+ status = _cairo_stroker_line_to_dashed (stroker, &stroker->first_point);
+ else
+ status = _cairo_stroker_line_to (stroker, &stroker->first_point);
+ if (unlikely (status))
+ return status;
+
+ if (stroker->has_first_face && stroker->has_current_face) {
+ /* Join first and final faces of sub path */
+ status = _cairo_stroker_join (stroker,
+ &stroker->current_face,
+ &stroker->first_face);
+ if (unlikely (status))
+ return status;
+ } else {
+ /* Cap the start and end of the sub path as needed */
+ status = _cairo_stroker_add_caps (stroker);
+ if (unlikely (status))
+ return status;
+ }
+
+ stroker->has_initial_sub_path = FALSE;
+ stroker->has_first_face = FALSE;
+ stroker->has_current_face = FALSE;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+cairo_status_t
+_cairo_path_fixed_stroke_to_shaper (cairo_path_fixed_t *path,
+ const cairo_stroke_style_t *stroke_style,
+ const cairo_matrix_t *ctm,
+ const cairo_matrix_t *ctm_inverse,
+ double tolerance,
+ cairo_status_t (*add_triangle) (void *closure,
+ const cairo_point_t triangle[3]),
+ cairo_status_t (*add_triangle_fan) (void *closure,
+ const cairo_point_t *midpt,
+ const cairo_point_t *points,
+ int npoints),
+ cairo_status_t (*add_convex_quad) (void *closure,
+ const cairo_point_t quad[4]),
+ void *closure)
+{
+ cairo_stroker_t stroker;
+ cairo_status_t status;
+
+ status = _cairo_stroker_init (&stroker, path, stroke_style,
+ ctm, ctm_inverse, tolerance,
+ NULL, 0);
+ if (unlikely (status))
+ return status;
+
+ stroker.add_triangle = add_triangle;
+ stroker.add_triangle_fan = add_triangle_fan;
+ stroker.add_convex_quad = add_convex_quad;
+ stroker.closure = closure;
+
+ status = _cairo_path_fixed_interpret (path,
+ _cairo_stroker_move_to,
+ stroker.dash.dashed ?
+ _cairo_stroker_line_to_dashed :
+ _cairo_stroker_line_to,
+ _cairo_stroker_curve_to,
+ _cairo_stroker_close_path,
+ &stroker);
+
+ if (unlikely (status))
+ goto BAIL;
+
+ /* Cap the start and end of the final sub path as needed */
+ status = _cairo_stroker_add_caps (&stroker);
+
+BAIL:
+ _cairo_stroker_fini (&stroker);
+
+ return status;
+}
+
+cairo_status_t
+_cairo_path_fixed_stroke_dashed_to_polygon (const cairo_path_fixed_t *path,
+ const cairo_stroke_style_t *stroke_style,
+ const cairo_matrix_t *ctm,
+ const cairo_matrix_t *ctm_inverse,
+ double tolerance,
+ cairo_polygon_t *polygon)
+{
+ cairo_stroker_t stroker;
+ cairo_status_t status;
+
+ status = _cairo_stroker_init (&stroker, path, stroke_style,
+ ctm, ctm_inverse, tolerance,
+ polygon->limits, polygon->num_limits);
+ if (unlikely (status))
+ return status;
+
+ stroker.add_external_edge = _cairo_polygon_add_external_edge,
+ stroker.closure = polygon;
+
+ status = _cairo_path_fixed_interpret (path,
+ _cairo_stroker_move_to,
+ stroker.dash.dashed ?
+ _cairo_stroker_line_to_dashed :
+ _cairo_stroker_line_to,
+ _cairo_stroker_curve_to,
+ _cairo_stroker_close_path,
+ &stroker);
+
+ if (unlikely (status))
+ goto BAIL;
+
+ /* Cap the start and end of the final sub path as needed */
+ status = _cairo_stroker_add_caps (&stroker);
+
+BAIL:
+ _cairo_stroker_fini (&stroker);
+
+ return status;
+}
+
+cairo_int_status_t
+_cairo_path_fixed_stroke_polygon_to_traps (const cairo_path_fixed_t *path,
+ const cairo_stroke_style_t *stroke_style,
+ const cairo_matrix_t *ctm,
+ const cairo_matrix_t *ctm_inverse,
+ double tolerance,
+ cairo_traps_t *traps)
+{
+ cairo_int_status_t status;
+ cairo_polygon_t polygon;
+
+ _cairo_polygon_init (&polygon, traps->limits, traps->num_limits);
+ status = _cairo_path_fixed_stroke_to_polygon (path,
+ stroke_style,
+ ctm,
+ ctm_inverse,
+ tolerance,
+ &polygon);
+ if (unlikely (status))
+ goto BAIL;
+
+ status = _cairo_polygon_status (&polygon);
+ if (unlikely (status))
+ goto BAIL;
+
+ status = _cairo_bentley_ottmann_tessellate_polygon (traps, &polygon,
+ CAIRO_FILL_RULE_WINDING);
+
+BAIL:
+ _cairo_polygon_fini (&polygon);
+
+ return status;
+}