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/*
* Copyright 2008 Chris Wilson
*
* Permission to use, copy, modify, distribute, and sell this software
* and its documentation for any purpose is hereby granted without
* fee, provided that the above copyright notice appear in all copies
* and that both that copyright notice and this permission notice
* appear in supporting documentation, and that the name of
* Chris Wilson not be used in advertising or publicity pertaining to
* distribution of the software without specific, written prior
* permission. Chris Wilson makes no representations about the
* suitability of this software for any purpose. It is provided "as
* is" without express or implied warranty.
* CHRIS WILSON DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS
* SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS, IN NO EVENT SHALL CHRIS WILSON BE LIABLE FOR ANY SPECIAL,
* INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
* RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR
* IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
* Author: Chris Wilson <chris@chris-wilson.co.uk>
*/
#include "cairo-test.h"
typedef struct _point {
double x,y;
} point_t;
typedef struct _knots {
point_t a,b,c,d;
} knots_t;
static knots_t knots[5] = {
{ {0, 0}, {0, 100}, {100, 100}, {100, 0} },
{ {0, 0}, {75, 100}, {25, 100}, {100, 0} },
{ {0, 0}, {100, 100}, {0, 100}, {100, 0} },
{ {0, 0}, {150, 100}, {-50, 100}, {100, 0} },
{ {0, 0}, {100, 200}, {0, -100}, {100, 100} },
};
#ifdef REFERENCE
static void
_lerp_half (const point_t *a, const point_t *b, point_t *result)
{
result->x = .5 * (a->x + b->x);
result->y = .5 * (a->y + b->y);
}
_de_casteljau (knots_t *k1, knots_t *k2)
point_t ab, bc, cd;
point_t abbc, bccd;
point_t final;
_lerp_half (&k1->a, &k1->b, &ab);
_lerp_half (&k1->b, &k1->c, &bc);
_lerp_half (&k1->c, &k1->d, &cd);
_lerp_half (&ab, &bc, &abbc);
_lerp_half (&bc, &cd, &bccd);
_lerp_half (&abbc, &bccd, &final);
k2->a = final;
k2->b = bccd;
k2->c = cd;
k2->d = k1->d;
k1->b = ab;
k1->c = abbc;
k1->d = final;
static double
_spline_error_squared (const knots_t *knots)
double bdx, bdy, berr;
double cdx, cdy, cerr;
double dx, dy, v;
/* Intersection point (px):
* px = p1 + u(p2 - p1)
* (p - px) ∙ (p2 - p1) = 0
* Thus:
* u = ((p - p1) ∙ (p2 - p1)) / ∥p2 - p1∥²;
bdx = knots->b.x - knots->a.x;
bdy = knots->b.y - knots->a.y;
cdx = knots->c.x - knots->a.x;
cdy = knots->c.y - knots->a.y;
dx = knots->d.x - knots->a.x;
dy = knots->d.y - knots->a.y;
v = dx * dx + dy * dy;
if (v != 0.) {
double u;
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;
/* cdx -= 0;
* cdy -= 0;
cdx -= dx;
cdy -= dy;
cdx -= u/v * dx;
cdy -= u/v * dy;
berr = bdx * bdx + bdy * bdy;
cerr = cdx * cdx + cdy * cdy;
if (berr > cerr)
return berr * v;
else
return cerr * v;
_offset_line_to (cairo_t *cr,
const point_t *p0,
const point_t *p1,
const point_t *p2,
const point_t *p3,
double offset)
dx = p1->x - p0->x;
dy = p1->y - p0->y;
v = hypot (dx, dy);
if (v == 0) {
dx = p2->x - p0->x;
dy = p2->y - p0->y;
dx = p3->x - p0->x;
dy = p3->y - p0->y;
cairo_line_to (cr, p0->x, p0->y);
} else
cairo_line_to (cr, p0->x - offset * dy / v, p0->y + offset * dx / v);
_spline_decompose_into (knots_t *k1,
double tolerance_squared,
double offset,
cairo_t *cr)
knots_t k2;
if (_spline_error_squared (k1) < tolerance_squared) {
_offset_line_to (cr, &k1->a, &k1->b, &k1->c, &k1->d, offset);
return;
_de_casteljau (k1, &k2);
_spline_decompose_into (k1, tolerance_squared, offset, cr);
_spline_decompose_into (&k2, tolerance_squared, offset, cr);
_spline_decompose (const knots_t *knots,
double tolerance, double offset,
knots_t k;
k = *knots;
_spline_decompose_into (&k, tolerance * tolerance, offset, cr);
_offset_line_to (cr, &knots->d, &knots->c, &knots->b, &knots->a, -offset);
_knots_reverse (knots_t *knots)
point_t tmp;
tmp = knots->a;
knots->a = knots->d;
knots->d = tmp;
tmp = knots->b;
knots->b = knots->c;
knots->c = tmp;
thick_splines (cairo_t *cr, double offset)
cairo_save (cr);
cairo_translate (cr, 15, 15);
k = knots[0];
cairo_new_path (cr);
_spline_decompose (&k, .1, offset, cr);
_knots_reverse (&k);
cairo_close_path (cr);
cairo_fill (cr);
cairo_translate (cr, 130, 0);
k = knots[1];
k = knots[2];
cairo_translate (cr, -130 - 65, 130);
k = knots[3];
k = knots[4];
cairo_restore (cr);
thin_splines (cairo_t *cr)
_spline_decompose (&knots[0], .1, 0, cr);
cairo_stroke (cr);
_spline_decompose (&knots[1], .1, 0, cr);
_spline_decompose (&knots[2], .1, 0, cr);
_spline_decompose (&knots[3], .1, 0, cr);
_spline_decompose (&knots[4], .1, 0, cr);
#endif
draw_bbox (cairo_t *cr, double x0, double y0, double x1, double y1)
cairo_rectangle (cr,
floor (x0) + .5, floor (y0) + .5,
ceil (x1) - floor (x0), ceil (y1) - floor (y0));
stroke_splines (cairo_t *cr)
double stroke_x0, stroke_x1, stroke_y0, stroke_y1;
double path_x0, path_x1, path_y0, path_y1;
cairo_move_to (cr,
knots[0].a.x, knots[0].a.y);
cairo_curve_to (cr,
knots[0].b.x, knots[0].b.y,
knots[0].c.x, knots[0].c.y,
knots[0].d.x, knots[0].d.y);
cairo_stroke_extents (cr, &stroke_x0, &stroke_y0, &stroke_x1, &stroke_y1);
cairo_path_extents (cr, &path_x0, &path_y0, &path_x1, &path_y1);
cairo_save (cr); {
cairo_set_line_width (cr, 1);
cairo_set_source_rgb (cr, 1, 0, 0);
draw_bbox (cr, stroke_x0, stroke_y0, stroke_x1, stroke_y1);
cairo_set_source_rgb (cr, 0, 0, 1);
draw_bbox (cr, path_x0, path_y0, path_x1, path_y1);
} cairo_restore (cr);
knots[1].a.x, knots[1].a.y);
knots[1].b.x, knots[1].b.y,
knots[1].c.x, knots[1].c.y,
knots[1].d.x, knots[1].d.y);
knots[2].a.x, knots[2].a.y);
knots[2].b.x, knots[2].b.y,
knots[2].c.x, knots[2].c.y,
knots[2].d.x, knots[2].d.y);
knots[3].a.x, knots[3].a.y);
knots[3].b.x, knots[3].b.y,
knots[3].c.x, knots[3].c.y,
knots[3].d.x, knots[3].d.y);
knots[4].a.x, knots[4].a.y);
knots[4].b.x, knots[4].b.y,
knots[4].c.x, knots[4].c.y,
knots[4].d.x, knots[4].d.y);
static cairo_test_status_t
draw (cairo_t *cr, int width, int height)
cairo_set_source_rgb (cr, 1, 1, 1);
cairo_paint (cr);
cairo_set_source_rgb (cr, 0, 0, 0);
thick_splines (cr, 5);
thin_splines (cr);
* Use a high tolerance to reduce dependence upon algorithm used for
* spline decomposition.
cairo_set_tolerance (cr, 0.001);
cairo_set_line_width (cr, 10);
stroke_splines (cr);
cairo_set_line_width (cr, 2);
return CAIRO_TEST_SUCCESS;
CAIRO_TEST (spline_decomposition,
"Tests splines with various inflection points",
"stroke, spline", /* keywords */
NULL, /* requirements */
390, 260,
NULL, draw)