add cairo

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);
+}