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diff --git a/Build/source/libs/cairo/cairo-1.12.8/src/cairo-spline.c b/Build/source/libs/cairo/cairo-1.12.8/src/cairo-spline.c
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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., 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);
+}
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