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+/** @file
+ * @brief Unit tests for Ellipse and related functions
+ * Uses the Google Testing Framework
+ *//*
+ * Authors:
+ * Krzysztof Kosiński <tweenk.pl@gmail.com>
+ *
+ * Copyright 2015 Authors
+ *
+ * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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.
+ */
+
+#include <iostream>
+#include <glib.h>
+
+#include <2geom/angle.h>
+#include <2geom/ellipse.h>
+#include <2geom/elliptical-arc.h>
+#include <memory>
+
+#include "testing.h"
+
+#ifndef M_SQRT2
+# define M_SQRT2 1.41421356237309504880
+#endif
+
+using namespace Geom;
+
+TEST(EllipseTest, Arcs) {
+ Ellipse e(Point(5,10), Point(5, 10), 0);
+
+ std::unique_ptr<EllipticalArc> arc1(e.arc(Point(5,0), Point(0,0), Point(0,10)));
+
+ EXPECT_EQ(arc1->initialPoint(), Point(5,0));
+ EXPECT_EQ(arc1->finalPoint(), Point(0,10));
+ EXPECT_EQ(arc1->boundsExact(), Rect::from_xywh(0,0,5,10));
+ EXPECT_EQ(arc1->center(), e.center());
+ EXPECT_EQ(arc1->largeArc(), false);
+ EXPECT_EQ(arc1->sweep(), false);
+
+ std::unique_ptr<EllipticalArc> arc1r(e.arc(Point(0,10), Point(0,0), Point(5,0)));
+
+ EXPECT_EQ(arc1r->boundsExact(), arc1->boundsExact());
+ EXPECT_EQ(arc1r->sweep(), true);
+ EXPECT_EQ(arc1r->largeArc(), false);
+
+ std::unique_ptr<EllipticalArc> arc2(e.arc(Point(5,0), Point(10,20), Point(0,10)));
+
+ EXPECT_EQ(arc2->boundsExact(), Rect::from_xywh(0,0,10,20));
+ EXPECT_EQ(arc2->largeArc(), true);
+ EXPECT_EQ(arc2->sweep(), true);
+
+ std::unique_ptr<EllipticalArc> arc2r(e.arc(Point(0,10), Point(10,20), Point(5,0)));
+
+ EXPECT_EQ(arc2r->boundsExact(), arc2->boundsExact());
+ EXPECT_EQ(arc2r->largeArc(), true);
+ EXPECT_EQ(arc2r->sweep(), false);
+
+ // exactly half arc
+ std::unique_ptr<EllipticalArc> arc3(e.arc(Point(5,0), Point(0,10), Point(5,20)));
+
+ EXPECT_EQ(arc3->boundsExact(), Rect::from_xywh(0,0,5,20));
+ EXPECT_EQ(arc3->largeArc(), false);
+ EXPECT_EQ(arc3->sweep(), false);
+
+ // inner point exactly at midpoint between endpoints
+ std::unique_ptr<EllipticalArc> arc4(e.arc(Point(5,0), Point(2.5,5), Point(0,10)));
+
+ EXPECT_EQ(arc4->initialPoint(), Point(5,0));
+ EXPECT_EQ(arc4->finalPoint(), Point(0,10));
+ EXPECT_EQ(arc4->boundsExact(), Rect::from_xywh(0,0,5,10));
+ EXPECT_EQ(arc4->largeArc(), false);
+ EXPECT_EQ(arc4->sweep(), false);
+
+ std::unique_ptr<EllipticalArc> arc4r(e.arc(Point(0,10), Point(2.5,5), Point(5,0)));
+
+ EXPECT_EQ(arc4r->initialPoint(), Point(0,10));
+ EXPECT_EQ(arc4r->finalPoint(), Point(5,0));
+ EXPECT_EQ(arc4r->boundsExact(), Rect::from_xywh(0,0,5,10));
+ EXPECT_EQ(arc4r->largeArc(), false);
+ EXPECT_EQ(arc4r->sweep(), true);
+}
+
+TEST(EllipseTest, AreNear) {
+ Ellipse e1(Point(5.000001,10), Point(5,10), Angle::from_degrees(45));
+ Ellipse e2(Point(5.000000,10), Point(5,10), Angle::from_degrees(225));
+ Ellipse e3(Point(4.999999,10), Point(10,5), Angle::from_degrees(135));
+ Ellipse e4(Point(5.000001,10), Point(10,5), Angle::from_degrees(315));
+
+ EXPECT_TRUE(are_near(e1, e2, 1e-5));
+ EXPECT_TRUE(are_near(e1, e3, 1e-5));
+ EXPECT_TRUE(are_near(e1, e4, 1e-5));
+
+ Ellipse c1(Point(20.000001,35.000001), Point(5.000001,4.999999), Angle::from_degrees(180.00001));
+ Ellipse c2(Point(19.999999,34.999999), Point(4.999999,5.000001), Angle::from_degrees(179.99999));
+ //std::cout << c1 << "\n" << c2 << std::endl;
+ EXPECT_TRUE(are_near(c1, c2, 2e-5));
+
+ EXPECT_FALSE(are_near(c1, e1, 1e-5));
+ EXPECT_FALSE(are_near(c2, e1, 1e-5));
+ EXPECT_FALSE(are_near(c1, e2, 1e-5));
+ EXPECT_FALSE(are_near(c2, e2, 1e-5));
+ EXPECT_FALSE(are_near(c1, e3, 1e-5));
+ EXPECT_FALSE(are_near(c2, e3, 1e-5));
+ EXPECT_FALSE(are_near(c1, e4, 1e-5));
+ EXPECT_FALSE(are_near(c2, e4, 1e-5));
+}
+
+TEST(EllipseTest, Transformations) {
+ Ellipse e(Point(5,10), Point(5,10), Angle::from_degrees(45));
+
+ Ellipse er = e * Rotate::around(Point(5,10), Angle::from_degrees(45));
+ Ellipse ercmp(Point(5,10), Point(5,10), Angle::from_degrees(90));
+ //std::cout << e << "\n" << er << "\n" << ercmp << std::endl;
+ EXPECT_TRUE(are_near(er, ercmp, 1e-12));
+
+ Ellipse eflip = e * Affine(Scale(-1,1));
+ Ellipse eflipcmp(Point(-5, 10), Point(5,10), Angle::from_degrees(135));
+ EXPECT_TRUE(are_near(eflip, eflipcmp, 1e-12));
+}
+
+TEST(EllipseTest, TimeAt) {
+ Ellipse e(Point(4, 17), Point(22, 34), 2);
+
+ for (unsigned i = 0; i < 100; ++i) {
+ Coord t = g_random_double_range(0, 2*M_PI);
+ Point p = e.pointAt(t);
+ Coord t2 = e.timeAt(p);
+ EXPECT_FLOAT_EQ(t, t2);
+ }
+}
+
+TEST(EllipseTest, LineIntersection) {
+ Ellipse e(Point(0, 0), Point(3, 2), 0);
+ Line l(Point(0, -2), Point(1, 0));
+
+ std::vector<ShapeIntersection> xs = e.intersect(l);
+
+ ASSERT_EQ(xs.size(), 2ul);
+
+ // due to numeric imprecision when evaluating Ellipse,
+ // the points may deviate by around 2e-16
+ EXPECT_NEAR(xs[0].point()[X], 0, 1e-15);
+ EXPECT_NEAR(xs[0].point()[Y], -2, 1e-15);
+ EXPECT_NEAR(xs[1].point()[X], 9./5, 1e-15);
+ EXPECT_NEAR(xs[1].point()[Y], 8./5, 1e-15);
+
+ EXPECT_intersections_valid(e, l, xs, 1e-15);
+}
+
+TEST(EllipseTest, EllipseIntersection) {
+ Ellipse e1;
+ Ellipse e2;
+ std::vector<ShapeIntersection> xs;
+
+ e1.set(Point(300, 300), Point(212, 70), -0.785);
+ e2.set(Point(250, 300), Point(230, 90), 1.321);
+ xs = e1.intersect(e2);
+ EXPECT_EQ(xs.size(), 4ul);
+ EXPECT_intersections_valid(e1, e2, xs, 1e-10);
+
+ e1.set(Point(0, 0), Point(1, 1), 0);
+ e2.set(Point(0, 1), Point(1, 1), 0);
+ xs = e1.intersect(e2);
+ EXPECT_EQ(xs.size(), 2ul);
+ EXPECT_intersections_valid(e1, e2, xs, 1e-10);
+
+ e1.set(Point(0, 0), Point(1, 1), 0);
+ e2.set(Point(1, 0), Point(1, 1), 0);
+ xs = e1.intersect(e2);
+ EXPECT_EQ(xs.size(), 2ul);
+ EXPECT_intersections_valid(e1, e2, xs, 1e-10);
+}
+
+TEST(EllipseTest, BezierIntersection) {
+ Ellipse e(Point(300, 300), Point(212, 70), -3.926);
+ D2<Bezier> b(Bezier(100, 300, 100, 500), Bezier(100, 100, 500, 500));
+
+ std::vector<ShapeIntersection> xs = e.intersect(b);
+
+ EXPECT_EQ(xs.size(), 2ul);
+ EXPECT_intersections_valid(e, b, xs, 6e-12);
+}
+
+TEST(EllipseTest, Coefficients) {
+ std::vector<Ellipse> es;
+ es.emplace_back(Point(-15,25), Point(10,15), Angle::from_degrees(45).radians0());
+ es.emplace_back(Point(-10,33), Point(40,20), M_PI);
+ es.emplace_back(Point(10,-33), Point(40,20), Angle::from_degrees(135).radians0());
+ es.emplace_back(Point(-10,-33), Point(50,10), Angle::from_degrees(330).radians0());
+
+ for (auto & i : es) {
+ Coord a, b, c, d, e, f;
+ i.coefficients(a, b, c, d, e, f);
+ Ellipse te(a, b, c, d, e, f);
+ EXPECT_near(i, te, 1e-10);
+ for (Coord t = -5; t < 5; t += 0.125) {
+ Point p = i.pointAt(t);
+ Coord eq = a*p[X]*p[X] + b*p[X]*p[Y] + c*p[Y]*p[Y]
+ + d*p[X] + e*p[Y] + f;
+ EXPECT_NEAR(eq, 0, 1e-10);
+ }
+ }
+}
+
+TEST(EllipseTest, UnitCircleTransform) {
+ std::vector<Ellipse> es;
+ es.emplace_back(Point(-15,25), Point(10,15), Angle::from_degrees(45));
+ es.emplace_back(Point(-10,33), Point(40,20), M_PI);
+ es.emplace_back(Point(10,-33), Point(40,20), Angle::from_degrees(135));
+ es.emplace_back(Point(-10,-33), Point(50,10), Angle::from_degrees(330));
+
+ for (auto & e : es) {
+ EXPECT_near(e.unitCircleTransform() * e.inverseUnitCircleTransform(), Affine::identity(), 1e-8);
+
+ for (Coord t = -1; t < 10; t += 0.25) {
+ Point p = e.pointAt(t);
+ p *= e.inverseUnitCircleTransform();
+ EXPECT_near(p.length(), 1., 1e-10);
+ p *= e.unitCircleTransform();
+ EXPECT_near(e.pointAt(t), p, 1e-10);
+ }
+ }
+}
+
+TEST(EllipseTest, PointAt) {
+ Ellipse a(Point(0,0), Point(10,20), 0);
+ EXPECT_near(a.pointAt(0), Point(10,0), 1e-10);
+ EXPECT_near(a.pointAt(M_PI/2), Point(0,20), 1e-10);
+ EXPECT_near(a.pointAt(M_PI), Point(-10,0), 1e-10);
+ EXPECT_near(a.pointAt(3*M_PI/2), Point(0,-20), 1e-10);
+
+ Ellipse b(Point(0,0), Point(10,20), M_PI/2);
+ EXPECT_near(b.pointAt(0), Point(0,10), 1e-10);
+ EXPECT_near(b.pointAt(M_PI/2), Point(-20,0), 1e-10);
+ EXPECT_near(b.pointAt(M_PI), Point(0,-10), 1e-10);
+ EXPECT_near(b.pointAt(3*M_PI/2), Point(20,0), 1e-10);
+}
+
+TEST(EllipseTest, UnitTangentAt) {
+ Ellipse a(Point(14,-7), Point(20,10), 0);
+ Ellipse b(Point(-77,23), Point(40,10), Angle::from_degrees(45));
+
+ EXPECT_near(a.unitTangentAt(0), Point(0,1), 1e-12);
+ EXPECT_near(a.unitTangentAt(M_PI/2), Point(-1,0), 1e-12);
+ EXPECT_near(a.unitTangentAt(M_PI), Point(0,-1), 1e-12);
+ EXPECT_near(a.unitTangentAt(3*M_PI/2), Point(1,0), 1e-12);
+
+ EXPECT_near(b.unitTangentAt(0), Point(-M_SQRT2/2, M_SQRT2/2), 1e-12);
+ EXPECT_near(b.unitTangentAt(M_PI/2), Point(-M_SQRT2/2, -M_SQRT2/2), 1e-12);
+ EXPECT_near(b.unitTangentAt(M_PI), Point(M_SQRT2/2, -M_SQRT2/2), 1e-12);
+ EXPECT_near(b.unitTangentAt(3*M_PI/2), Point(M_SQRT2/2, M_SQRT2/2), 1e-12);
+}
+
+TEST(EllipseTest, BoundsExact) {
+ std::vector<Ellipse> es;
+ es.emplace_back(Point(-15,25), Point(10,15), Angle::from_degrees(45));
+ es.emplace_back(Point(-10,33), Point(40,20), M_PI);
+ es.emplace_back(Point(10,-33), Point(40,20), Angle::from_degrees(111));
+ es.emplace_back(Point(-10,-33), Point(50,10), Angle::from_degrees(222));
+
+ // for reproducibility
+ g_random_set_seed(1234);
+
+ for (auto & e : es) {
+ Rect r = e.boundsExact();
+ for (unsigned j = 0; j < 10000; ++j) {
+ Coord t = g_random_double_range(-M_PI, M_PI);
+ EXPECT_TRUE(r.contains(e.pointAt(t)));
+ }
+ }
+
+ Ellipse e(Point(0,0), Point(10, 10), M_PI);
+ Rect bounds = e.boundsExact();
+ EXPECT_EQ(bounds, Rect(Point(-10,-10), Point(10,10)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(0)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(M_PI/2)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(M_PI)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(3*M_PI/2)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(2*M_PI)));
+
+ e = Ellipse(Point(0,0), Point(10, 10), M_PI/2);
+ bounds = e.boundsExact();
+ EXPECT_EQ(bounds, Rect(Point(-10,-10), Point(10,10)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(0)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(M_PI/2)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(M_PI)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(3*M_PI/2)));
+ EXPECT_TRUE(bounds.contains(e.pointAt(2*M_PI)));
+}
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