/* cairo - a vector graphics library with display and print output
*
* Copyright © 2005 Red Hat, Inc
*
* 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 Red Hat, Inc.
*
* Contributor(s):
* Carl Worth <cworth@cworth.org>
*/
#include "cairoint.h"
#include "cairo-error-private.h"
void
_cairo_stroke_style_init (cairo_stroke_style_t *style)
{
VG (VALGRIND_MAKE_MEM_UNDEFINED (style, sizeof (cairo_stroke_style_t)));
style->line_width = CAIRO_GSTATE_LINE_WIDTH_DEFAULT;
style->line_cap = CAIRO_GSTATE_LINE_CAP_DEFAULT;
style->line_join = CAIRO_GSTATE_LINE_JOIN_DEFAULT;
style->miter_limit = CAIRO_GSTATE_MITER_LIMIT_DEFAULT;
style->dash = NULL;
style->num_dashes = 0;
style->dash_offset = 0.0;
}
cairo_status_t
_cairo_stroke_style_init_copy (cairo_stroke_style_t *style,
const cairo_stroke_style_t *other)
{
if (CAIRO_INJECT_FAULT ())
return _cairo_error (CAIRO_STATUS_NO_MEMORY);
VG (VALGRIND_MAKE_MEM_UNDEFINED (style, sizeof (cairo_stroke_style_t)));
style->line_width = other->line_width;
style->line_cap = other->line_cap;
style->line_join = other->line_join;
style->miter_limit = other->miter_limit;
style->num_dashes = other->num_dashes;
if (other->dash == NULL) {
style->dash = NULL;
} else {
style->dash = _cairo_malloc_ab (style->num_dashes, sizeof (double));
if (unlikely (style->dash == NULL))
return _cairo_error (CAIRO_STATUS_NO_MEMORY);
memcpy (style
->dash
, other
->dash
, style->num_dashes * sizeof (double));
}
style->dash_offset = other->dash_offset;
return CAIRO_STATUS_SUCCESS;
}
void
_cairo_stroke_style_fini (cairo_stroke_style_t *style)
{
if (style->dash) {
style->dash = NULL;
}
style->num_dashes = 0;
VG (VALGRIND_MAKE_MEM_NOACCESS (style, sizeof (cairo_stroke_style_t)));
}
/*
* For a stroke in the given style, compute the maximum distance
* from the path that vertices could be generated. In the case
* of rotation in the ctm, the distance will not be exact.
*/
void
_cairo_stroke_style_max_distance_from_path (const cairo_stroke_style_t *style,
const cairo_matrix_t *ctm,
double *dx, double *dy)
{
double style_expansion = 0.5;
if (style->line_cap == CAIRO_LINE_CAP_SQUARE)
style_expansion = M_SQRT1_2;
if (style->line_join == CAIRO_LINE_JOIN_MITER &&
style_expansion < M_SQRT2 * style->miter_limit)
{
style_expansion = M_SQRT2 * style->miter_limit;
}
style_expansion *= style->line_width;
*dx = style_expansion * hypot (ctm->xx, ctm->xy);
*dy = style_expansion * hypot (ctm->yy, ctm->yx);
}
/*
* Computes the period of a dashed stroke style.
* Returns 0 for non-dashed styles.
*/
double
_cairo_stroke_style_dash_period (const cairo_stroke_style_t *style)
{
double period;
unsigned int i;
period = 0.0;
for (i = 0; i < style->num_dashes; i++)
period += style->dash[i];
if (style->num_dashes & 1)
period *= 2.0;
return period;
}
/*
* Coefficient of the linear approximation (minimizing square difference)
* of the surface covered by round caps
*
* This can be computed in the following way:
* the area inside the circle with radius w/2 and the region -d/2 <= x <= d/2 is:
* f(w,d) = 2 * integrate (sqrt (w*w/4 - x*x), x, -d/2, d/2)
* The square difference to a generic linear approximation (c*d) in the range (0,w) would be:
* integrate ((f(w,d) - c*d)^2, d, 0, w)
* To minimize this difference it is sufficient to find a solution of the differential with
* respect to c:
* solve ( diff (integrate ((f(w,d) - c*d)^2, d, 0, w), c), c)
* Which leads to c = 9/32*pi*w
* Since we're not interested in the true area, but just in a coverage extimate,
* we always divide the real area by the line width (w).
* The same computation for square caps would be
* f(w,d) = 2 * integrate(w/2, x, -d/2, d/2)
* c = 1*w
* but in this case it would not be an approximation, since f is already linear in d.
*/
#define ROUND_MINSQ_APPROXIMATION (9*M_PI/32)
/*
* Computes the length of the "on" part of a dashed stroke style,
* taking into account also line caps.
* Returns 0 for non-dashed styles.
*/
double
_cairo_stroke_style_dash_stroked (const cairo_stroke_style_t *style)
{
double stroked, cap_scale;
unsigned int i;
switch (style->line_cap) {
default: ASSERT_NOT_REACHED;
case CAIRO_LINE_CAP_BUTT: cap_scale = 0.0; break;
case CAIRO_LINE_CAP_ROUND: cap_scale = ROUND_MINSQ_APPROXIMATION; break;
case CAIRO_LINE_CAP_SQUARE: cap_scale = 1.0; break;
}
stroked = 0.0;
if (style->num_dashes & 1) {
/* Each dash element is used both as on and as off. The order in which they are summed is
* irrelevant, so sum the coverage of one dash element, taken both on and off at each iteration */
for (i = 0; i < style->num_dashes; i++)
stroked += style->dash[i] + cap_scale * MIN (style->dash[i], style->line_width);
} else {
/* Even (0, 2, ...) dashes are on and simply counted for the coverage, odd dashes are off, thus
* their coverage is approximated based on the area covered by the caps of adjacent on dases. */
for (i = 0; i < style->num_dashes; i+=2)
stroked += style->dash[i] + cap_scale * MIN (style->dash[i+1], style->line_width);
}
return stroked;
}
/*
* Verifies if _cairo_stroke_style_dash_approximate should be used to generate
* an approximation of the dash pattern in the specified style, when used for
* stroking a path with the given CTM and tolerance.
* Always %FALSE for non-dashed styles.
*/
cairo_bool_t
_cairo_stroke_style_dash_can_approximate (const cairo_stroke_style_t *style,
const cairo_matrix_t *ctm,
double tolerance)
{
double period;
if (! style->num_dashes)
return FALSE;
period = _cairo_stroke_style_dash_period (style);
return _cairo_matrix_transformed_circle_major_axis (ctm, period) < tolerance;
}
/*
* Create a 2-dashes approximation of a dashed style, by making the "on" and "off"
* parts respect the original ratio.
*/
void
_cairo_stroke_style_dash_approximate (const cairo_stroke_style_t *style,
const cairo_matrix_t *ctm,
double tolerance,
double *dash_offset,
double *dashes,
unsigned int *num_dashes)
{
double coverage, scale, offset;
cairo_bool_t on = TRUE;
unsigned int i = 0;
coverage = _cairo_stroke_style_dash_stroked (style) / _cairo_stroke_style_dash_period (style);
coverage = MIN (coverage, 1.0);
scale = tolerance / _cairo_matrix_transformed_circle_major_axis (ctm, 1.0);
/* We stop searching for a starting point as soon as the
* offset reaches zero. Otherwise when an initial dash
* segment shrinks to zero it will be skipped over. */
offset = style->dash_offset;
while (offset > 0.0 && offset >= style->dash[i]) {
offset -= style->dash[i];
on = !on;
if (++i == style->num_dashes)
i = 0;
}
*num_dashes = 2;
/*
* We want to create a new dash pattern with the same relative coverage,
* but composed of just 2 elements with total length equal to scale.
* Based on the formula in _cairo_stroke_style_dash_stroked:
* scale * coverage = dashes[0] + cap_scale * MIN (dashes[1], line_width)
* = MIN (dashes[0] + cap_scale * (scale - dashes[0]),
* dashes[0] + cap_scale * line_width) =
* = MIN (dashes[0] * (1 - cap_scale) + cap_scale * scale,
* dashes[0] + cap_scale * line_width)
*
* Solving both cases we get:
* dashes[0] = scale * (coverage - cap_scale) / (1 - cap_scale)
* when scale - dashes[0] <= line_width
* dashes[0] = scale * coverage - cap_scale * line_width
* when scale - dashes[0] > line_width.
*
* Comparing the two cases we get:
* second > first
* second > scale * (coverage - cap_scale) / (1 - cap_scale)
* second - cap_scale * second - scale * coverage + scale * cap_scale > 0
* (scale * coverage - cap_scale * line_width) - cap_scale * second - scale * coverage + scale * cap_scale > 0
* - line_width - second + scale > 0
* scale - second > line_width
* which is the condition for the second solution to be the valid one.
* So when second > first, the second solution is the correct one (i.e.
* the solution is always MAX (first, second).
*/
switch (style->line_cap) {
default:
ASSERT_NOT_REACHED;
dashes[0] = 0.0;
break;
case CAIRO_LINE_CAP_BUTT:
/* Simplified formula (substituting 0 for cap_scale): */
dashes[0] = scale * coverage;
break;
case CAIRO_LINE_CAP_ROUND:
dashes[0] = MAX(scale * (coverage - ROUND_MINSQ_APPROXIMATION) / (1.0 - ROUND_MINSQ_APPROXIMATION),
scale * coverage - ROUND_MINSQ_APPROXIMATION * style->line_width);
break;
case CAIRO_LINE_CAP_SQUARE:
/*
* Special attention is needed to handle the case cap_scale == 1 (since the first solution
* is either indeterminate or -inf in this case). Since dash lengths are always >=0, using
* 0 as first solution always leads to the correct solution.
*/
dashes[0] = MAX(0.0, scale * coverage - style->line_width);
break;
}
dashes[1] = scale - dashes[0];
*dash_offset = on ? 0.0 : dashes[0];
}