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/* cairo - a vector graphics library with display and print output
*
* Copyright © 2002 University of Southern California
*
* 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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>
*/
#include "cairoint.h"
cairo_bool_t
_cairo_spline_init (cairo_spline_t *spline,
void (*add_point_func) (void*, const cairo_point_t *),
void *closure,
const cairo_point_t *a, const cairo_point_t *b,
const cairo_point_t *c, const cairo_point_t *d)
{
spline->add_point_func = add_point_func;
spline->closure = closure;
spline->knots.a = *a;
spline->knots.b = *b;
spline->knots.c = *c;
spline->knots.d = *d;
if (a->x != b->x || a->y != b->y)
_cairo_slope_init (&spline->initial_slope, &spline->knots.a, &spline->knots.b);
else if (a->x != c->x || a->y != c->y)
_cairo_slope_init (&spline->initial_slope, &spline->knots.a, &spline->knots.c);
else if (a->x != d->x || a->y != d->y)
_cairo_slope_init (&spline->initial_slope, &spline->knots.a, &spline->knots.d);
else
return FALSE;
if (c->x != d->x || c->y != d->y)
_cairo_slope_init (&spline->final_slope, &spline->knots.c, &spline->knots.d);
else if (b->x != d->x || b->y != d->y)
_cairo_slope_init (&spline->final_slope, &spline->knots.b, &spline->knots.d);
else
_cairo_slope_init (&spline->final_slope, &spline->knots.a, &spline->knots.d);
return TRUE;
}
void
_cairo_spline_fini (cairo_spline_t *spline)
{
}
static void
_cairo_spline_add_point (cairo_spline_t *spline, const cairo_point_t *point)
{
cairo_point_t *prev;
prev = &spline->last_point;
if (prev->x == point->x && prev->y == point->y)
return;
spline->add_point_func (spline->closure, point);
spline->last_point = *point;
}
static void
_lerp_half (const cairo_point_t *a, const cairo_point_t *b, cairo_point_t *result)
{
result->x = a->x + ((b->x - a->x) >> 1);
result->y = a->y + ((b->y - a->y) >> 1);
}
static void
_de_casteljau (cairo_spline_knots_t *s1, cairo_spline_knots_t *s2)
{
cairo_point_t ab, bc, cd;
cairo_point_t abbc, bccd;
cairo_point_t final;
_lerp_half (&s1->a, &s1->b, &ab);
_lerp_half (&s1->b, &s1->c, &bc);
_lerp_half (&s1->c, &s1->d, &cd);
_lerp_half (&ab, &bc, &abbc);
_lerp_half (&bc, &cd, &bccd);
_lerp_half (&abbc, &bccd, &final);
s2->a = final;
s2->b = bccd;
s2->c = cd;
s2->d = s1->d;
s1->b = ab;
s1->c = abbc;
s1->d = final;
}
/* Return an upper bound on the error (squared) that could result from
* approximating a spline as a line segment connecting the two endpoints. */
static double
_cairo_spline_error_squared (const cairo_spline_knots_t *knots)
{
double bdx, bdy, berr;
double cdx, cdy, cerr;
/* Intersection point (px):
* px = p1 + u(p2 - p1)
* (p - px) ∙ (p2 - p1) = 0
* Thus:
* u = ((p - p1) ∙ (p2 - p1)) / ∥p2 - p1∥²;
*/
bdx = _cairo_fixed_to_double (knots->b.x - knots->a.x);
bdy = _cairo_fixed_to_double (knots->b.y - knots->a.y);
cdx = _cairo_fixed_to_double (knots->c.x - knots->a.x);
cdy = _cairo_fixed_to_double (knots->c.y - knots->a.y);
if (knots->a.x != knots->d.x || knots->a.y != knots->d.y) {
double dx, dy, u, v;
dx = _cairo_fixed_to_double (knots->d.x - knots->a.x);
dy = _cairo_fixed_to_double (knots->d.y - knots->a.y);
v = dx * dx + dy * dy;
u = bdx * dx + bdy * dy;
if (u <= 0) {
/* bdx -= 0;
* bdy -= 0;
*/
} else if (u >= v) {
bdx -= dx;
bdy -= dy;
} else {
bdx -= u/v * dx;
bdy -= u/v * dy;
}
u = cdx * dx + cdy * dy;
if (u <= 0) {
/* cdx -= 0;
* cdy -= 0;
*/
} else if (u >= v) {
cdx -= dx;
cdy -= dy;
} else {
cdx -= u/v * dx;
cdy -= u/v * dy;
}
}
berr = bdx * bdx + bdy * bdy;
cerr = cdx * cdx + cdy * cdy;
if (berr > cerr)
return berr;
else
return cerr;
}
static void
_cairo_spline_decompose_into (cairo_spline_knots_t *s1, double tolerance_squared, cairo_spline_t *result)
{
cairo_spline_knots_t s2;
if (_cairo_spline_error_squared (s1) < tolerance_squared)
return _cairo_spline_add_point (result, &s1->a);
_de_casteljau (s1, &s2);
_cairo_spline_decompose_into (s1, tolerance_squared, result);
_cairo_spline_decompose_into (&s2, tolerance_squared, result);
}
void
_cairo_spline_decompose (cairo_spline_t *spline, double tolerance)
{
cairo_spline_knots_t s1;
s1 = spline->knots;
spline->last_point = s1.a;
_cairo_spline_decompose_into (&s1, tolerance * tolerance, spline);
_cairo_spline_add_point (spline, &spline->knots.d);
}
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