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Diffstat (limited to 'libs/cairo-1.16.0/src/cairo-spline.c')
| -rw-r--r-- | libs/cairo-1.16.0/src/cairo-spline.c | 424 |
1 files changed, 424 insertions, 0 deletions
diff --git a/libs/cairo-1.16.0/src/cairo-spline.c b/libs/cairo-1.16.0/src/cairo-spline.c new file mode 100644 index 0000000..44634fa --- /dev/null +++ b/libs/cairo-1.16.0/src/cairo-spline.c @@ -0,0 +1,424 @@ +/* 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., 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 University of Southern + * California. + * + * Contributor(s): + * Carl D. Worth <cworth@cworth.org> + */ + +#include "cairoint.h" + +#include "cairo-box-inline.h" +#include "cairo-slope-private.h" + +cairo_bool_t +_cairo_spline_intersects (const cairo_point_t *a, + const cairo_point_t *b, + const cairo_point_t *c, + const cairo_point_t *d, + const cairo_box_t *box) +{ + cairo_box_t bounds; + + if (_cairo_box_contains_point (box, a) || + _cairo_box_contains_point (box, b) || + _cairo_box_contains_point (box, c) || + _cairo_box_contains_point (box, d)) + { + return TRUE; + } + + bounds.p2 = bounds.p1 = *a; + _cairo_box_add_point (&bounds, b); + _cairo_box_add_point (&bounds, c); + _cairo_box_add_point (&bounds, d); + + if (bounds.p2.x <= box->p1.x || bounds.p1.x >= box->p2.x || + bounds.p2.y <= box->p1.y || bounds.p1.y >= box->p2.y) + { + return FALSE; + } + +#if 0 /* worth refining? */ + bounds.p2 = bounds.p1 = *a; + _cairo_box_add_curve_to (&bounds, b, c, d); + if (bounds.p2.x <= box->p1.x || bounds.p1.x >= box->p2.x || + bounds.p2.y <= box->p1.y || bounds.p1.y >= box->p2.y) + { + return FALSE; + } +#endif + + return TRUE; +} + +cairo_bool_t +_cairo_spline_init (cairo_spline_t *spline, + cairo_spline_add_point_func_t add_point_func, + void *closure, + const cairo_point_t *a, const cairo_point_t *b, + const cairo_point_t *c, const cairo_point_t *d) +{ + /* If both tangents are zero, this is just a straight line */ + if (a->x == b->x && a->y == b->y && c->x == d->x && c->y == d->y) + return FALSE; + + 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 + return FALSE; /* just treat this as a straight-line from a -> d */ + + /* XXX if the initial, final and vector are all equal, this is just a line */ + + return TRUE; +} + +static cairo_status_t +_cairo_spline_add_point (cairo_spline_t *spline, + const cairo_point_t *point, + const cairo_point_t *knot) +{ + cairo_point_t *prev; + cairo_slope_t slope; + + prev = &spline->last_point; + if (prev->x == point->x && prev->y == point->y) + return CAIRO_STATUS_SUCCESS; + + _cairo_slope_init (&slope, point, knot); + + spline->last_point = *point; + return spline->add_point_func (spline->closure, point, &slope); +} + +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; + + /* We are going to compute the distance (squared) between each of the the b + * and c control points and the segment a-b. The maximum of these two + * distances will be our approximation error. */ + + 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) { + /* Intersection point (px): + * px = p1 + u(p2 - p1) + * (p - px) ∙ (p2 - p1) = 0 + * Thus: + * u = ((p - p1) ∙ (p2 - p1)) / ∥p2 - p1∥²; + */ + + 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 cairo_status_t +_cairo_spline_decompose_into (cairo_spline_knots_t *s1, + double tolerance_squared, + cairo_spline_t *result) +{ + cairo_spline_knots_t s2; + cairo_status_t status; + + if (_cairo_spline_error_squared (s1) < tolerance_squared) + return _cairo_spline_add_point (result, &s1->a, &s1->b); + + _de_casteljau (s1, &s2); + + status = _cairo_spline_decompose_into (s1, tolerance_squared, result); + if (unlikely (status)) + return status; + + return _cairo_spline_decompose_into (&s2, tolerance_squared, result); +} + +cairo_status_t +_cairo_spline_decompose (cairo_spline_t *spline, double tolerance) +{ + cairo_spline_knots_t s1; + cairo_status_t status; + + s1 = spline->knots; + spline->last_point = s1.a; + status = _cairo_spline_decompose_into (&s1, tolerance * tolerance, spline); + if (unlikely (status)) + return status; + + return spline->add_point_func (spline->closure, + &spline->knots.d, &spline->final_slope); +} + +/* Note: this function is only good for computing bounds in device space. */ +cairo_status_t +_cairo_spline_bound (cairo_spline_add_point_func_t add_point_func, + void *closure, + const cairo_point_t *p0, const cairo_point_t *p1, + const cairo_point_t *p2, const cairo_point_t *p3) +{ + double x0, x1, x2, x3; + double y0, y1, y2, y3; + double a, b, c; + double t[4]; + int t_num = 0, i; + cairo_status_t status; + + x0 = _cairo_fixed_to_double (p0->x); + y0 = _cairo_fixed_to_double (p0->y); + x1 = _cairo_fixed_to_double (p1->x); + y1 = _cairo_fixed_to_double (p1->y); + x2 = _cairo_fixed_to_double (p2->x); + y2 = _cairo_fixed_to_double (p2->y); + x3 = _cairo_fixed_to_double (p3->x); + y3 = _cairo_fixed_to_double (p3->y); + + /* The spline can be written as a polynomial of the four points: + * + * (1-t)³p0 + 3t(1-t)²p1 + 3t²(1-t)p2 + t³p3 + * + * for 0≤t≤1. Now, the X and Y components of the spline follow the + * same polynomial but with x and y replaced for p. To find the + * bounds of the spline, we just need to find the X and Y bounds. + * To find the bound, we take the derivative and equal it to zero, + * and solve to find the t's that give the extreme points. + * + * Here is the derivative of the curve, sorted on t: + * + * 3t²(-p0+3p1-3p2+p3) + 2t(3p0-6p1+3p2) -3p0+3p1 + * + * Let: + * + * a = -p0+3p1-3p2+p3 + * b = p0-2p1+p2 + * c = -p0+p1 + * + * Gives: + * + * a.t² + 2b.t + c = 0 + * + * With: + * + * delta = b*b - a*c + * + * the extreme points are at -c/2b if a is zero, at (-b±√delta)/a if + * delta is positive, and at -b/a if delta is zero. + */ + +#define ADD(t0) \ + { \ + double _t0 = (t0); \ + if (0 < _t0 && _t0 < 1) \ + t[t_num++] = _t0; \ + } + +#define FIND_EXTREMES(a,b,c) \ + { \ + if (a == 0) { \ + if (b != 0) \ + ADD (-c / (2*b)); \ + } else { \ + double b2 = b * b; \ + double delta = b2 - a * c; \ + if (delta > 0) { \ + cairo_bool_t feasible; \ + double _2ab = 2 * a * b; \ + /* We are only interested in solutions t that satisfy 0<t<1 \ + * here. We do some checks to avoid sqrt if the solutions \ + * are not in that range. The checks can be derived from: \ + * \ + * 0 < (-b±√delta)/a < 1 \ + */ \ + if (_2ab >= 0) \ + feasible = delta > b2 && delta < a*a + b2 + _2ab; \ + else if (-b / a >= 1) \ + feasible = delta < b2 && delta > a*a + b2 + _2ab; \ + else \ + feasible = delta < b2 || delta < a*a + b2 + _2ab; \ + \ + if (unlikely (feasible)) { \ + double sqrt_delta = sqrt (delta); \ + ADD ((-b - sqrt_delta) / a); \ + ADD ((-b + sqrt_delta) / a); \ + } \ + } else if (delta == 0) { \ + ADD (-b / a); \ + } \ + } \ + } + + /* Find X extremes */ + a = -x0 + 3*x1 - 3*x2 + x3; + b = x0 - 2*x1 + x2; + c = -x0 + x1; + FIND_EXTREMES (a, b, c); + + /* Find Y extremes */ + a = -y0 + 3*y1 - 3*y2 + y3; + b = y0 - 2*y1 + y2; + c = -y0 + y1; + FIND_EXTREMES (a, b, c); + + status = add_point_func (closure, p0, NULL); + if (unlikely (status)) + return status; + + for (i = 0; i < t_num; i++) { + cairo_point_t p; + double x, y; + double t_1_0, t_0_1; + double t_2_0, t_0_2; + double t_3_0, t_2_1_3, t_1_2_3, t_0_3; + + t_1_0 = t[i]; /* t */ + t_0_1 = 1 - t_1_0; /* (1 - t) */ + + t_2_0 = t_1_0 * t_1_0; /* t * t */ + t_0_2 = t_0_1 * t_0_1; /* (1 - t) * (1 - t) */ + + t_3_0 = t_2_0 * t_1_0; /* t * t * t */ + t_2_1_3 = t_2_0 * t_0_1 * 3; /* t * t * (1 - t) * 3 */ + t_1_2_3 = t_1_0 * t_0_2 * 3; /* t * (1 - t) * (1 - t) * 3 */ + t_0_3 = t_0_1 * t_0_2; /* (1 - t) * (1 - t) * (1 - t) */ + + /* Bezier polynomial */ + x = x0 * t_0_3 + + x1 * t_1_2_3 + + x2 * t_2_1_3 + + x3 * t_3_0; + y = y0 * t_0_3 + + y1 * t_1_2_3 + + y2 * t_2_1_3 + + y3 * t_3_0; + + p.x = _cairo_fixed_from_double (x); + p.y = _cairo_fixed_from_double (y); + status = add_point_func (closure, &p, NULL); + if (unlikely (status)) + return status; + } + + return add_point_func (closure, p3, NULL); +} |