forked from KolibriOS/kolibrios
369 lines
10 KiB
C
369 lines
10 KiB
C
/* cairo - a vector graphics library with display and print output
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*
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* Copyright © 2002 University of Southern California
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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 University of Southern
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* California.
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*
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* Contributor(s):
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* Carl D. Worth <cworth@cworth.org>
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*/
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#include "cairoint.h"
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#include "cairo-slope-private.h"
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cairo_bool_t
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_cairo_spline_init (cairo_spline_t *spline,
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cairo_spline_add_point_func_t add_point_func,
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void *closure,
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const cairo_point_t *a, const cairo_point_t *b,
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const cairo_point_t *c, const cairo_point_t *d)
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{
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spline->add_point_func = add_point_func;
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spline->closure = closure;
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spline->knots.a = *a;
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spline->knots.b = *b;
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spline->knots.c = *c;
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spline->knots.d = *d;
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if (a->x != b->x || a->y != b->y)
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_cairo_slope_init (&spline->initial_slope, &spline->knots.a, &spline->knots.b);
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else if (a->x != c->x || a->y != c->y)
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_cairo_slope_init (&spline->initial_slope, &spline->knots.a, &spline->knots.c);
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else if (a->x != d->x || a->y != d->y)
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_cairo_slope_init (&spline->initial_slope, &spline->knots.a, &spline->knots.d);
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else
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return FALSE;
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if (c->x != d->x || c->y != d->y)
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_cairo_slope_init (&spline->final_slope, &spline->knots.c, &spline->knots.d);
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else if (b->x != d->x || b->y != d->y)
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_cairo_slope_init (&spline->final_slope, &spline->knots.b, &spline->knots.d);
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else
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_cairo_slope_init (&spline->final_slope, &spline->knots.a, &spline->knots.d);
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return TRUE;
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}
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static cairo_status_t
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_cairo_spline_add_point (cairo_spline_t *spline, cairo_point_t *point)
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{
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cairo_point_t *prev;
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prev = &spline->last_point;
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if (prev->x == point->x && prev->y == point->y)
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return CAIRO_STATUS_SUCCESS;
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spline->last_point = *point;
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return spline->add_point_func (spline->closure, point);
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}
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static void
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_lerp_half (const cairo_point_t *a, const cairo_point_t *b, cairo_point_t *result)
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{
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result->x = a->x + ((b->x - a->x) >> 1);
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result->y = a->y + ((b->y - a->y) >> 1);
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}
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static void
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_de_casteljau (cairo_spline_knots_t *s1, cairo_spline_knots_t *s2)
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{
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cairo_point_t ab, bc, cd;
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cairo_point_t abbc, bccd;
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cairo_point_t final;
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_lerp_half (&s1->a, &s1->b, &ab);
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_lerp_half (&s1->b, &s1->c, &bc);
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_lerp_half (&s1->c, &s1->d, &cd);
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_lerp_half (&ab, &bc, &abbc);
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_lerp_half (&bc, &cd, &bccd);
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_lerp_half (&abbc, &bccd, &final);
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s2->a = final;
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s2->b = bccd;
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s2->c = cd;
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s2->d = s1->d;
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s1->b = ab;
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s1->c = abbc;
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s1->d = final;
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}
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/* Return an upper bound on the error (squared) that could result from
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* approximating a spline as a line segment connecting the two endpoints. */
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static double
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_cairo_spline_error_squared (const cairo_spline_knots_t *knots)
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{
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double bdx, bdy, berr;
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double cdx, cdy, cerr;
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/* We are going to compute the distance (squared) between each of the the b
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* and c control points and the segment a-b. The maximum of these two
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* distances will be our approximation error. */
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bdx = _cairo_fixed_to_double (knots->b.x - knots->a.x);
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bdy = _cairo_fixed_to_double (knots->b.y - knots->a.y);
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cdx = _cairo_fixed_to_double (knots->c.x - knots->a.x);
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cdy = _cairo_fixed_to_double (knots->c.y - knots->a.y);
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if (knots->a.x != knots->d.x || knots->a.y != knots->d.y) {
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/* Intersection point (px):
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* px = p1 + u(p2 - p1)
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* (p - px) ∙ (p2 - p1) = 0
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* Thus:
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* u = ((p - p1) ∙ (p2 - p1)) / ∥p2 - p1∥²;
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*/
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double dx, dy, u, v;
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dx = _cairo_fixed_to_double (knots->d.x - knots->a.x);
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dy = _cairo_fixed_to_double (knots->d.y - knots->a.y);
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v = dx * dx + dy * dy;
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u = bdx * dx + bdy * dy;
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if (u <= 0) {
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/* bdx -= 0;
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* bdy -= 0;
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*/
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} else if (u >= v) {
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bdx -= dx;
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bdy -= dy;
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} else {
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bdx -= u/v * dx;
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bdy -= u/v * dy;
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}
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u = cdx * dx + cdy * dy;
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if (u <= 0) {
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/* cdx -= 0;
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* cdy -= 0;
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*/
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} else if (u >= v) {
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cdx -= dx;
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cdy -= dy;
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} else {
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cdx -= u/v * dx;
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cdy -= u/v * dy;
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}
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}
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berr = bdx * bdx + bdy * bdy;
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cerr = cdx * cdx + cdy * cdy;
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if (berr > cerr)
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return berr;
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else
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return cerr;
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}
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static cairo_status_t
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_cairo_spline_decompose_into (cairo_spline_knots_t *s1, double tolerance_squared, cairo_spline_t *result)
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{
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cairo_spline_knots_t s2;
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cairo_status_t status;
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if (_cairo_spline_error_squared (s1) < tolerance_squared)
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return _cairo_spline_add_point (result, &s1->a);
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_de_casteljau (s1, &s2);
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status = _cairo_spline_decompose_into (s1, tolerance_squared, result);
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if (unlikely (status))
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return status;
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return _cairo_spline_decompose_into (&s2, tolerance_squared, result);
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}
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cairo_status_t
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_cairo_spline_decompose (cairo_spline_t *spline, double tolerance)
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{
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cairo_spline_knots_t s1;
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cairo_status_t status;
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s1 = spline->knots;
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spline->last_point = s1.a;
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status = _cairo_spline_decompose_into (&s1, tolerance * tolerance, spline);
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if (unlikely (status))
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return status;
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return _cairo_spline_add_point (spline, &spline->knots.d);
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}
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/* Note: this function is only good for computing bounds in device space. */
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cairo_status_t
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_cairo_spline_bound (cairo_spline_add_point_func_t add_point_func,
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void *closure,
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const cairo_point_t *p0, const cairo_point_t *p1,
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const cairo_point_t *p2, const cairo_point_t *p3)
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{
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double x0, x1, x2, x3;
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double y0, y1, y2, y3;
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double a, b, c;
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double t[4];
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int t_num = 0, i;
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cairo_status_t status;
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x0 = _cairo_fixed_to_double (p0->x);
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y0 = _cairo_fixed_to_double (p0->y);
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x1 = _cairo_fixed_to_double (p1->x);
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y1 = _cairo_fixed_to_double (p1->y);
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x2 = _cairo_fixed_to_double (p2->x);
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y2 = _cairo_fixed_to_double (p2->y);
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x3 = _cairo_fixed_to_double (p3->x);
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y3 = _cairo_fixed_to_double (p3->y);
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/* The spline can be written as a polynomial of the four points:
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*
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* (1-t)³p0 + 3t(1-t)²p1 + 3t²(1-t)p2 + t³p3
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*
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* for 0≤t≤1. Now, the X and Y components of the spline follow the
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* same polynomial but with x and y replaced for p. To find the
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* bounds of the spline, we just need to find the X and Y bounds.
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* To find the bound, we take the derivative and equal it to zero,
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* and solve to find the t's that give the extreme points.
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*
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* Here is the derivative of the curve, sorted on t:
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*
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* 3t²(-p0+3p1-3p2+p3) + 2t(3p0-6p1+3p2) -3p0+3p1
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*
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* Let:
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*
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* a = -p0+3p1-3p2+p3
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* b = p0-2p1+p2
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* c = -p0+p1
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*
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* Gives:
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*
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* a.t² + 2b.t + c = 0
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*
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* With:
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*
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* delta = b*b - a*c
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*
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* the extreme points are at -c/2b if a is zero, at (-b±√delta)/a if
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* delta is positive, and at -b/a if delta is zero.
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*/
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#define ADD(t0) \
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{ \
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double _t0 = (t0); \
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if (0 < _t0 && _t0 < 1) \
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t[t_num++] = _t0; \
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}
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#define FIND_EXTREMES(a,b,c) \
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{ \
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if (a == 0) { \
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if (b != 0) \
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ADD (-c / (2*b)); \
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} else { \
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double b2 = b * b; \
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double delta = b2 - a * c; \
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if (delta > 0) { \
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cairo_bool_t feasible; \
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double _2ab = 2 * a * b; \
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/* We are only interested in solutions t that satisfy 0<t<1 \
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* here. We do some checks to avoid sqrt if the solutions \
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* are not in that range. The checks can be derived from: \
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* \
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* 0 < (-b±√delta)/a < 1 \
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*/ \
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if (_2ab >= 0) \
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feasible = delta > b2 && delta < a*a + b2 + _2ab; \
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else if (-b / a >= 1) \
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feasible = delta < b2 && delta > a*a + b2 + _2ab; \
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else \
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feasible = delta < b2 || delta < a*a + b2 + _2ab; \
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\
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if (unlikely (feasible)) { \
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double sqrt_delta = sqrt (delta); \
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ADD ((-b - sqrt_delta) / a); \
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ADD ((-b + sqrt_delta) / a); \
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} \
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} else if (delta == 0) { \
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ADD (-b / a); \
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} \
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} \
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}
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/* Find X extremes */
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a = -x0 + 3*x1 - 3*x2 + x3;
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b = x0 - 2*x1 + x2;
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c = -x0 + x1;
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FIND_EXTREMES (a, b, c);
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/* Find Y extremes */
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a = -y0 + 3*y1 - 3*y2 + y3;
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b = y0 - 2*y1 + y2;
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c = -y0 + y1;
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FIND_EXTREMES (a, b, c);
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status = add_point_func (closure, p0);
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if (unlikely (status))
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return status;
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for (i = 0; i < t_num; i++) {
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cairo_point_t p;
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double x, y;
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double t_1_0, t_0_1;
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double t_2_0, t_0_2;
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double t_3_0, t_2_1_3, t_1_2_3, t_0_3;
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t_1_0 = t[i]; /* t */
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t_0_1 = 1 - t_1_0; /* (1 - t) */
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t_2_0 = t_1_0 * t_1_0; /* t * t */
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t_0_2 = t_0_1 * t_0_1; /* (1 - t) * (1 - t) */
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t_3_0 = t_2_0 * t_1_0; /* t * t * t */
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t_2_1_3 = t_2_0 * t_0_1 * 3; /* t * t * (1 - t) * 3 */
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t_1_2_3 = t_1_0 * t_0_2 * 3; /* t * (1 - t) * (1 - t) * 3 */
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t_0_3 = t_0_1 * t_0_2; /* (1 - t) * (1 - t) * (1 - t) */
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/* Bezier polynomial */
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x = x0 * t_0_3
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+ x1 * t_1_2_3
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+ x2 * t_2_1_3
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+ x3 * t_3_0;
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y = y0 * t_0_3
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+ y1 * t_1_2_3
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+ y2 * t_2_1_3
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+ y3 * t_3_0;
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p.x = _cairo_fixed_from_double (x);
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p.y = _cairo_fixed_from_double (y);
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status = add_point_func (closure, &p);
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if (unlikely (status))
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return status;
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}
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return add_point_func (closure, p3);
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}
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