/* 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) { free (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]; }