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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 _DEFAULT_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-tristrip-private.h"
struct stroker {
cairo_stroke_style_t style;
cairo_tristrip_t *strip;
const cairo_matrix_t *ctm;
const cairo_matrix_t *ctm_inverse;
double tolerance;
cairo_bool_t ctm_det_positive;
cairo_pen_t pen;
cairo_bool_t has_sub_path;
cairo_point_t first_point;
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_box_t limit;
cairo_bool_t has_limits;
};
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);
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.
add_fan (struct stroker *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)
int start, stop, step, i, npoints;
if (clockwise) {
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,
return;
npoints = stop - start;
} else {
step = -1;
start = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
if (_cairo_slope_compare (&stroker->pen.vertices[start].slope_ccw,
start = range_step (start, -1, stroker->pen.num_vertices);
stop = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
stop = range_step (stop, 1, stroker->pen.num_vertices);
npoints = start - stop;
stop = range_step (stop, step, stroker->pen.num_vertices);
if (npoints < 0)
npoints += stroker->pen.num_vertices;
if (npoints <= 1)
for (i = start;
i != stop;
i = range_step (i, step, stroker->pen.num_vertices))
cairo_point_t p = *midpt;
translate_point (&p, &stroker->pen.vertices[i].point);
//contour_add_point (stroker, c, &p);
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;
inner_join (struct stroker *stroker,
const cairo_stroke_face_t *in,
const cairo_stroke_face_t *out,
int clockwise)
const cairo_point_t *outpt;
outpt = &out->ccw;
outpt = &out->cw;
//contour_add_point (stroker, inner, &in->point);
//contour_add_point (stroker, inner, outpt);
inner_close (struct stroker *stroker,
cairo_stroke_face_t *out)
const cairo_point_t *inpt;
if (join_is_clockwise (in, out)) {
inpt = &out->ccw;
inpt = &out->cw;
//contour_add_point (stroker, inner, inpt);
//*_cairo_contour_first_point (&inner->contour) =
//*_cairo_contour_last_point (&inner->contour);
outer_close (struct stroker *stroker,
const cairo_point_t *inpt, *outpt;
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)
clockwise = join_is_clockwise (in, out);
inpt = &in->cw;
inpt = &in->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, inpt, outpt,
clockwise);
break;
case CAIRO_LINE_JOIN_MITER:
default: {
/* dot product of incoming slope vector with outgoing slope vector */
double in_dot_out = -in->usr_vector.x * out->usr_vector.x +
-in->usr_vector.y * out->usr_vector.y;
double ml = stroker->style.miter_limit;
/* Check the miter limit -- lines meeting at an acute angle
* can generate long miters, the limit converts them to bevel
* Consider the miter join formed when two line segments
* meet at an angle psi:
* /.\
* /. .\
* /./ \.\
* /./psi\.\
* We can zoom in on the right half of that to see:
* |\
* | \ psi/2
* | \
* miter \
* length \
* | .\
* | . \
* |. line \
* \ width \
* \ \
* The right triangle in that figure, (the line-width side is
* shown faintly with three '.' characters), gives us the
* following expression relating miter length, angle and line
* width:
* 1 /sin (psi/2) = miter_length / line_width
* The right-hand side of this relationship is the same ratio
* in which the miter limit (ml) is expressed. We want to know
* when the miter length is within the miter limit. That is
* when the following condition holds:
* 1/sin(psi/2) <= ml
* 1 <= ml sin(psi/2)
* 1 <= ml² sin²(psi/2)
* 2 <= ml² 2 sin²(psi/2)
* 2·sin²(psi/2) = 1-cos(psi)
* 2 <= ml² (1-cos(psi))
* in · out = |in| |out| cos (psi)
* in and out are both unit vectors, so:
* in · out = cos (psi)
* 2 <= ml² (1 - in · out)
if (2 <= ml * ml * (1 - in_dot_out)) {
double x1, y1, x2, y2;
double mx, my;
double dx1, dx2, dy1, dy2;
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))
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;
case CAIRO_LINE_JOIN_BEVEL:
//contour_add_point (stroker, outer, outpt);
outer_join (struct stroker *stroker,
//contour_add_point (stroker,outer, outpt);
add_cap (struct stroker *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;
add_fan (stroker, &f->dev_vector, &slope,
&f->point, &f->ccw, &f->cw,
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->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;
//contour_add_point (stroker, c, &quad[1]);
//contour_add_point (stroker, c, &quad[2]);
case CAIRO_LINE_CAP_BUTT:
default:
//contour_add_point (stroker, c, &f->cw);
add_leading_cap (struct stroker *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;
add_cap (stroker, &reversed);
add_trailing_cap (struct stroker *stroker,
add_cap (stroker, face);
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;
mag = -dy0;
*dy = -1.0;
} else if (dy0 == 0.0) {
*dy = 0.0;
if (dx0 > 0.0) {
mag = dx0;
*dx = 1.0;
mag = -dx0;
*dx = -1.0;
mag = hypot (dx0, dy0);
*dx = dx0 / mag;
*dy = dy0 / mag;
return mag;
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->style.line_width / 2.0);
face_dy = slope_dx * (stroker->style.line_width / 2.0);
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;
add_caps (struct stroker *stroker)
/* check for a degenerative sub_path */
if (stroker->has_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);
add_trailing_cap (stroker, &face);
/* ensure the circle is complete */
//_cairo_contour_add_point (&stroker->ccw.contour,
//_cairo_contour_first_point (&stroker->ccw.contour));
if (stroker->has_current_face)
add_trailing_cap (stroker, &stroker->current_face);
//_cairo_polygon_add_contour (stroker->polygon, &stroker->ccw.contour);
//_cairo_contour_reset (&stroker->ccw.contour);
if (stroker->has_first_face) {
//&stroker->first_face.cw);
add_leading_cap (stroker, &stroker->first_face);
//_cairo_polygon_add_contour (stroker->polygon,
//&stroker->ccw.contour);
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_sub_path = FALSE;
stroker->first_point = *point;
stroker->current_face.point = *point;
return CAIRO_STATUS_SUCCESS;
line_to (void *closure,
cairo_stroke_face_t start;
cairo_point_t *p1 = &stroker->current_face.point;
cairo_slope_t dev_slope;
stroker->has_sub_path = TRUE;
if (p1->x == point->x && p1->y == point->y)
_cairo_slope_init (&dev_slope, p1, point);
compute_face (p1, &dev_slope, stroker, &start);
if (stroker->has_current_face) {
int clockwise = join_is_clockwise (&stroker->current_face, &start);
/* Join with final face from previous segment */
outer_join (stroker, &stroker->current_face, &start, clockwise);
inner_join (stroker, &stroker->current_face, &start, clockwise);
if (! stroker->has_first_face) {
/* Save sub path's first face in case needed for closing join */
stroker->first_face = start;
_cairo_tristrip_move_to (stroker->strip, &start.cw);
stroker->has_first_face = TRUE;
stroker->has_current_face = TRUE;
_cairo_tristrip_add_point (stroker->strip, &start.cw);
_cairo_tristrip_add_point (stroker->strip, &start.ccw);
stroker->current_face = start;
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;
_cairo_tristrip_add_point (stroker->strip, &stroker->current_face.cw);
_cairo_tristrip_add_point (stroker->strip, &stroker->current_face.ccw);
spline_to (void *closure,
const cairo_point_t *point,
const cairo_slope_t *tangent)
if (tangent->dx == 0 && tangent->dy == 0) {
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);
inpt = &stroker->current_face.cw;
outpt = &face.cw;
inpt = &stroker->current_face.ccw;
outpt = &face.ccw;
&stroker->current_face.dev_vector,
&face.dev_vector,
&stroker->current_face.point, inpt, outpt,
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 < 0)
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);
_cairo_tristrip_add_point (stroker->strip, &face.cw);
_cairo_tristrip_add_point (stroker->strip, &face.ccw);
stroker->current_face = face;
curve_to (void *closure,
const cairo_point_t *b,
const cairo_point_t *c,
const cairo_point_t *d)
cairo_spline_t spline;
if (stroker->has_limits) {
if (! _cairo_spline_intersects (&stroker->current_face.point, b, c, d,
&stroker->limit))
return line_to (closure, d);
if (! _cairo_spline_init (&spline, spline_to, stroker,
&stroker->current_face.point, b, c, d))
compute_face (&stroker->current_face.point, &spline.initial_slope,
stroker, &face);
outer_join (stroker, &stroker->current_face, &face, clockwise);
inner_join (stroker, &stroker->current_face, &face, clockwise);
stroker->first_face = face;
_cairo_tristrip_move_to (stroker->strip, &face.cw);
return _cairo_spline_decompose (&spline, stroker->tolerance);
close_path (void *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);
/* Cap the start and end of the sub path as needed */
cairo_int_status_t
_cairo_path_fixed_stroke_to_tristrip (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_tristrip_t *strip)
struct stroker stroker;
cairo_int_status_t status;
int i;
if (style->num_dashes)
return CAIRO_INT_STATUS_UNSUPPORTED;
stroker.style = *style;
stroker.ctm = ctm;
stroker.ctm_inverse = ctm_inverse;
stroker.tolerance = tolerance;
stroker.ctm_det_positive =
_cairo_matrix_compute_determinant (ctm) >= 0.0;
status = _cairo_pen_init (&stroker.pen,
style->line_width / 2.0,
tolerance, ctm);
if (stroker.pen.num_vertices <= 1)
return CAIRO_INT_STATUS_NOTHING_TO_DO;
stroker.has_current_face = FALSE;
stroker.has_first_face = FALSE;
stroker.has_sub_path = FALSE;
stroker.has_limits = strip->num_limits > 0;
stroker.limit = strip->limits[0];
for (i = 1; i < strip->num_limits; i++)
_cairo_box_add_box (&stroker.limit, &strip->limits[i]);
stroker.strip = strip;
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_INT_STATUS_SUCCESS))
add_caps (&stroker);
_cairo_pen_fini (&stroker.pen);