311 lines
10 KiB
C
311 lines
10 KiB
C
/* cairo - a vector graphics library with display and print output
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*
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* Copyright © 2005 Red Hat, Inc
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*
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* This library is free software; you can redistribute it and/or
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* modify it either under the terms of the GNU Lesser General Public
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* License version 2.1 as published by the Free Software Foundation
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* (the "LGPL") or, at your option, under the terms of the Mozilla
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* Public License Version 1.1 (the "MPL"). If you do not alter this
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* notice, a recipient may use your version of this file under either
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* the MPL or the LGPL.
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*
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* You should have received a copy of the LGPL along with this library
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* in the file COPYING-LGPL-2.1; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
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* You should have received a copy of the MPL along with this library
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* in the file COPYING-MPL-1.1
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*
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* The contents of this file are subject to the Mozilla Public License
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* Version 1.1 (the "License"); you may not use this file except in
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* compliance with the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
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* OF ANY KIND, either express or implied. See the LGPL or the MPL for
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* the specific language governing rights and limitations.
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*
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* The Original Code is the cairo graphics library.
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*
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* The Initial Developer of the Original Code is Red Hat, Inc.
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*
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* Contributor(s):
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* Carl Worth <cworth@cworth.org>
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*/
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#include "cairoint.h"
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#include "cairo-error-private.h"
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void
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_cairo_stroke_style_init (cairo_stroke_style_t *style)
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{
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VG (VALGRIND_MAKE_MEM_UNDEFINED (style, sizeof (cairo_stroke_style_t)));
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style->line_width = CAIRO_GSTATE_LINE_WIDTH_DEFAULT;
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style->line_cap = CAIRO_GSTATE_LINE_CAP_DEFAULT;
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style->line_join = CAIRO_GSTATE_LINE_JOIN_DEFAULT;
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style->miter_limit = CAIRO_GSTATE_MITER_LIMIT_DEFAULT;
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style->dash = NULL;
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style->num_dashes = 0;
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style->dash_offset = 0.0;
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}
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cairo_status_t
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_cairo_stroke_style_init_copy (cairo_stroke_style_t *style,
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const cairo_stroke_style_t *other)
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{
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if (CAIRO_INJECT_FAULT ())
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return _cairo_error (CAIRO_STATUS_NO_MEMORY);
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VG (VALGRIND_MAKE_MEM_UNDEFINED (style, sizeof (cairo_stroke_style_t)));
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style->line_width = other->line_width;
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style->line_cap = other->line_cap;
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style->line_join = other->line_join;
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style->miter_limit = other->miter_limit;
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style->num_dashes = other->num_dashes;
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if (other->dash == NULL) {
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style->dash = NULL;
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} else {
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style->dash = _cairo_malloc_ab (style->num_dashes, sizeof (double));
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if (unlikely (style->dash == NULL))
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return _cairo_error (CAIRO_STATUS_NO_MEMORY);
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memcpy (style->dash, other->dash,
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style->num_dashes * sizeof (double));
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}
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style->dash_offset = other->dash_offset;
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return CAIRO_STATUS_SUCCESS;
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}
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void
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_cairo_stroke_style_fini (cairo_stroke_style_t *style)
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{
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if (style->dash) {
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free (style->dash);
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style->dash = NULL;
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}
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style->num_dashes = 0;
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VG (VALGRIND_MAKE_MEM_NOACCESS (style, sizeof (cairo_stroke_style_t)));
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}
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/*
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* For a stroke in the given style, compute the maximum distance
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* from the path that vertices could be generated. In the case
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* of rotation in the ctm, the distance will not be exact.
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*/
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void
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_cairo_stroke_style_max_distance_from_path (const cairo_stroke_style_t *style,
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const cairo_matrix_t *ctm,
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double *dx, double *dy)
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{
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double style_expansion = 0.5;
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if (style->line_cap == CAIRO_LINE_CAP_SQUARE)
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style_expansion = M_SQRT1_2;
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if (style->line_join == CAIRO_LINE_JOIN_MITER &&
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style_expansion < M_SQRT2 * style->miter_limit)
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{
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style_expansion = M_SQRT2 * style->miter_limit;
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}
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style_expansion *= style->line_width;
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*dx = style_expansion * hypot (ctm->xx, ctm->xy);
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*dy = style_expansion * hypot (ctm->yy, ctm->yx);
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}
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/*
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* Computes the period of a dashed stroke style.
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* Returns 0 for non-dashed styles.
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*/
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double
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_cairo_stroke_style_dash_period (const cairo_stroke_style_t *style)
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{
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double period;
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unsigned int i;
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period = 0.0;
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for (i = 0; i < style->num_dashes; i++)
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period += style->dash[i];
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if (style->num_dashes & 1)
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period *= 2.0;
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return period;
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}
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/*
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* Coefficient of the linear approximation (minimizing square difference)
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* of the surface covered by round caps
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*
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* This can be computed in the following way:
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* the area inside the circle with radius w/2 and the region -d/2 <= x <= d/2 is:
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* f(w,d) = 2 * integrate (sqrt (w*w/4 - x*x), x, -d/2, d/2)
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* The square difference to a generic linear approximation (c*d) in the range (0,w) would be:
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* integrate ((f(w,d) - c*d)^2, d, 0, w)
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* To minimize this difference it is sufficient to find a solution of the differential with
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* respect to c:
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* solve ( diff (integrate ((f(w,d) - c*d)^2, d, 0, w), c), c)
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* Which leads to c = 9/32*pi*w
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* Since we're not interested in the true area, but just in a coverage extimate,
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* we always divide the real area by the line width (w).
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* The same computation for square caps would be
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* f(w,d) = 2 * integrate(w/2, x, -d/2, d/2)
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* c = 1*w
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* but in this case it would not be an approximation, since f is already linear in d.
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*/
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#define ROUND_MINSQ_APPROXIMATION (9*M_PI/32)
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/*
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* Computes the length of the "on" part of a dashed stroke style,
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* taking into account also line caps.
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* Returns 0 for non-dashed styles.
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*/
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double
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_cairo_stroke_style_dash_stroked (const cairo_stroke_style_t *style)
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{
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double stroked, cap_scale;
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unsigned int i;
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switch (style->line_cap) {
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default: ASSERT_NOT_REACHED;
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case CAIRO_LINE_CAP_BUTT: cap_scale = 0.0; break;
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case CAIRO_LINE_CAP_ROUND: cap_scale = ROUND_MINSQ_APPROXIMATION; break;
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case CAIRO_LINE_CAP_SQUARE: cap_scale = 1.0; break;
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}
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stroked = 0.0;
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if (style->num_dashes & 1) {
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/* Each dash element is used both as on and as off. The order in which they are summed is
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* irrelevant, so sum the coverage of one dash element, taken both on and off at each iteration */
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for (i = 0; i < style->num_dashes; i++)
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stroked += style->dash[i] + cap_scale * MIN (style->dash[i], style->line_width);
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} else {
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/* Even (0, 2, ...) dashes are on and simply counted for the coverage, odd dashes are off, thus
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* their coverage is approximated based on the area covered by the caps of adjacent on dases. */
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for (i = 0; i < style->num_dashes; i+=2)
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stroked += style->dash[i] + cap_scale * MIN (style->dash[i+1], style->line_width);
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}
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return stroked;
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}
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/*
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* Verifies if _cairo_stroke_style_dash_approximate should be used to generate
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* an approximation of the dash pattern in the specified style, when used for
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* stroking a path with the given CTM and tolerance.
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* Always %FALSE for non-dashed styles.
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*/
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cairo_bool_t
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_cairo_stroke_style_dash_can_approximate (const cairo_stroke_style_t *style,
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const cairo_matrix_t *ctm,
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double tolerance)
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{
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double period;
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if (! style->num_dashes)
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return FALSE;
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period = _cairo_stroke_style_dash_period (style);
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return _cairo_matrix_transformed_circle_major_axis (ctm, period) < tolerance;
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}
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/*
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* Create a 2-dashes approximation of a dashed style, by making the "on" and "off"
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* parts respect the original ratio.
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*/
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void
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_cairo_stroke_style_dash_approximate (const cairo_stroke_style_t *style,
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const cairo_matrix_t *ctm,
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double tolerance,
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double *dash_offset,
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double *dashes,
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unsigned int *num_dashes)
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{
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double coverage, scale, offset;
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cairo_bool_t on = TRUE;
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unsigned int i = 0;
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coverage = _cairo_stroke_style_dash_stroked (style) / _cairo_stroke_style_dash_period (style);
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coverage = MIN (coverage, 1.0);
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scale = tolerance / _cairo_matrix_transformed_circle_major_axis (ctm, 1.0);
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/* We stop searching for a starting point as soon as the
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* offset reaches zero. Otherwise when an initial dash
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* segment shrinks to zero it will be skipped over. */
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offset = style->dash_offset;
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while (offset > 0.0 && offset >= style->dash[i]) {
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offset -= style->dash[i];
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on = !on;
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if (++i == style->num_dashes)
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i = 0;
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}
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*num_dashes = 2;
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/*
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* We want to create a new dash pattern with the same relative coverage,
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* but composed of just 2 elements with total length equal to scale.
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* Based on the formula in _cairo_stroke_style_dash_stroked:
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* scale * coverage = dashes[0] + cap_scale * MIN (dashes[1], line_width)
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* = MIN (dashes[0] + cap_scale * (scale - dashes[0]),
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* dashes[0] + cap_scale * line_width) =
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* = MIN (dashes[0] * (1 - cap_scale) + cap_scale * scale,
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* dashes[0] + cap_scale * line_width)
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*
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* Solving both cases we get:
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* dashes[0] = scale * (coverage - cap_scale) / (1 - cap_scale)
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* when scale - dashes[0] <= line_width
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* dashes[0] = scale * coverage - cap_scale * line_width
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* when scale - dashes[0] > line_width.
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*
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* Comparing the two cases we get:
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* second > first
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* second > scale * (coverage - cap_scale) / (1 - cap_scale)
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* second - cap_scale * second - scale * coverage + scale * cap_scale > 0
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* (scale * coverage - cap_scale * line_width) - cap_scale * second - scale * coverage + scale * cap_scale > 0
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* - line_width - second + scale > 0
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* scale - second > line_width
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* which is the condition for the second solution to be the valid one.
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* So when second > first, the second solution is the correct one (i.e.
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* the solution is always MAX (first, second).
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*/
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switch (style->line_cap) {
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default:
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ASSERT_NOT_REACHED;
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dashes[0] = 0.0;
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break;
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case CAIRO_LINE_CAP_BUTT:
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/* Simplified formula (substituting 0 for cap_scale): */
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dashes[0] = scale * coverage;
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break;
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case CAIRO_LINE_CAP_ROUND:
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dashes[0] = MAX(scale * (coverage - ROUND_MINSQ_APPROXIMATION) / (1.0 - ROUND_MINSQ_APPROXIMATION),
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scale * coverage - ROUND_MINSQ_APPROXIMATION * style->line_width);
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break;
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case CAIRO_LINE_CAP_SQUARE:
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/*
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* Special attention is needed to handle the case cap_scale == 1 (since the first solution
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* is either indeterminate or -inf in this case). Since dash lengths are always >=0, using
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* 0 as first solution always leads to the correct solution.
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*/
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dashes[0] = MAX(0.0, scale * coverage - style->line_width);
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break;
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}
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dashes[1] = scale - dashes[0];
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*dash_offset = on ? 0.0 : dashes[0];
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}
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