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-rw-r--r--test/spline-decomposition.c471
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diff --git a/test/spline-decomposition.c b/test/spline-decomposition.c
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+++ b/test/spline-decomposition.c
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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);
+}
+
+static void
+_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;
+ 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 * v;
+ else
+ return cerr * v;
+}
+
+static void
+_offset_line_to (cairo_t *cr,
+ const point_t *p0,
+ const point_t *p1,
+ const point_t *p2,
+ const point_t *p3,
+ double offset)
+{
+ double dx, dy, v;
+
+ 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;
+ v = hypot (dx, dy);
+ if (v == 0) {
+ dx = p3->x - p0->x;
+ dy = p3->y - p0->y;
+ v = hypot (dx, dy);
+ }
+ }
+
+ if (v == 0) {
+ cairo_line_to (cr, p0->x, p0->y);
+ } else
+ cairo_line_to (cr, p0->x - offset * dy / v, p0->y + offset * dx / v);
+}
+
+static void
+_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);
+}
+
+static void
+_spline_decompose (const knots_t *knots,
+ double tolerance, double offset,
+ cairo_t *cr)
+{
+ 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);
+}
+
+static void
+_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;
+}
+
+static void
+thick_splines (cairo_t *cr, double offset)
+{
+ knots_t k;
+
+ cairo_save (cr);
+ cairo_translate (cr, 15, 15);
+
+ k = knots[0];
+
+ cairo_new_path (cr);
+ _spline_decompose (&k, .1, offset, cr);
+ _knots_reverse (&k);
+ _spline_decompose (&k, .1, offset, cr);
+ cairo_close_path (cr);
+ cairo_fill (cr);
+
+ cairo_translate (cr, 130, 0);
+
+ k = knots[1];
+
+ cairo_new_path (cr);
+ _spline_decompose (&k, .1, offset, cr);
+ _knots_reverse (&k);
+ _spline_decompose (&k, .1, offset, cr);
+ cairo_close_path (cr);
+ cairo_fill (cr);
+
+ cairo_translate (cr, 130, 0);
+
+ k = knots[2];
+
+ cairo_new_path (cr);
+ _spline_decompose (&k, .1, offset, cr);
+ _knots_reverse (&k);
+ _spline_decompose (&k, .1, offset, cr);
+ cairo_close_path (cr);
+ cairo_fill (cr);
+
+ cairo_translate (cr, -130 - 65, 130);
+
+ k = knots[3];
+
+ cairo_new_path (cr);
+ _spline_decompose (&k, .1, offset, cr);
+ _knots_reverse (&k);
+ _spline_decompose (&k, .1, offset, cr);
+ cairo_close_path (cr);
+ cairo_fill (cr);
+
+ cairo_translate (cr, 130, 0);
+
+ k = knots[4];
+
+ cairo_new_path (cr);
+ _spline_decompose (&k, .1, offset, cr);
+ _knots_reverse (&k);
+ _spline_decompose (&k, .1, offset, cr);
+ cairo_close_path (cr);
+ cairo_fill (cr);
+ cairo_restore (cr);
+}
+
+static void
+thin_splines (cairo_t *cr)
+{
+ cairo_save (cr);
+ cairo_translate (cr, 15, 15);
+
+ cairo_new_path (cr);
+ _spline_decompose (&knots[0], .1, 0, cr);
+ cairo_stroke (cr);
+
+ cairo_translate (cr, 130, 0);
+
+ cairo_new_path (cr);
+ _spline_decompose (&knots[1], .1, 0, cr);
+ cairo_stroke (cr);
+
+ cairo_translate (cr, 130, 0);
+
+ cairo_new_path (cr);
+ _spline_decompose (&knots[2], .1, 0, cr);
+ cairo_stroke (cr);
+
+ cairo_translate (cr, -130 - 65, 130);
+
+ cairo_new_path (cr);
+ _spline_decompose (&knots[3], .1, 0, cr);
+ cairo_stroke (cr);
+
+ cairo_translate (cr, 130, 0);
+
+ cairo_new_path (cr);
+ _spline_decompose (&knots[4], .1, 0, cr);
+ cairo_stroke (cr);
+ cairo_restore (cr);
+}
+#endif
+
+static void
+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));
+ cairo_stroke (cr);
+}
+
+static void
+stroke_splines (cairo_t *cr)
+{
+ double stroke_x0, stroke_x1, stroke_y0, stroke_y1;
+ double path_x0, path_x1, path_y0, path_y1;
+
+ cairo_save (cr);
+ cairo_translate (cr, 15, 15);
+
+ cairo_new_path (cr);
+ 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_stroke (cr);
+
+ 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);
+
+ cairo_translate (cr, 130, 0);
+
+ cairo_new_path (cr);
+ cairo_move_to (cr,
+ knots[1].a.x, knots[1].a.y);
+ cairo_curve_to (cr,
+ knots[1].b.x, knots[1].b.y,
+ knots[1].c.x, knots[1].c.y,
+ knots[1].d.x, knots[1].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_stroke (cr);
+
+ 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);
+
+ cairo_translate (cr, 130, 0);
+
+ cairo_new_path (cr);
+ cairo_move_to (cr,
+ knots[2].a.x, knots[2].a.y);
+ cairo_curve_to (cr,
+ knots[2].b.x, knots[2].b.y,
+ knots[2].c.x, knots[2].c.y,
+ knots[2].d.x, knots[2].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_stroke (cr);
+
+ 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);
+
+ cairo_translate (cr, -130 - 65, 130);
+
+ cairo_new_path (cr);
+ cairo_move_to (cr,
+ knots[3].a.x, knots[3].a.y);
+ cairo_curve_to (cr,
+ knots[3].b.x, knots[3].b.y,
+ knots[3].c.x, knots[3].c.y,
+ knots[3].d.x, knots[3].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_stroke (cr);
+
+ 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);
+
+ cairo_translate (cr, 130, 0);
+
+ cairo_new_path (cr);
+ cairo_move_to (cr,
+ knots[4].a.x, knots[4].a.y);
+ cairo_curve_to (cr,
+ knots[4].b.x, knots[4].b.y,
+ knots[4].c.x, knots[4].c.y,
+ knots[4].d.x, knots[4].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_stroke (cr);
+
+ 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);
+
+ cairo_restore (cr);
+}
+
+static cairo_test_status_t
+draw (cairo_t *cr, int width, int height)
+{
+ cairo_set_source_rgb (cr, 1, 1, 1);
+ cairo_paint (cr);
+
+#ifdef REFERENCE
+ cairo_set_source_rgb (cr, 0, 0, 0);
+ thick_splines (cr, 5);
+
+ cairo_set_source_rgb (cr, 1, 1, 1);
+ thin_splines (cr);
+#endif
+
+ /*
+ * 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);
+ cairo_set_source_rgb (cr, 0, 0, 0);
+ stroke_splines (cr);
+ cairo_set_line_width (cr, 2);
+ cairo_set_source_rgb (cr, 1, 1, 1);
+ stroke_splines (cr);
+
+ return CAIRO_TEST_SUCCESS;
+}
+
+CAIRO_TEST (spline_decomposition,
+ "Tests splines with various inflection points",
+ "stroke, spline", /* keywords */
+ NULL, /* requirements */
+ 390, 260,
+ NULL, draw)
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