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Diffstat (limited to 'src/3rdparty/2geom/tests/ellipse-test.cpp')
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diff --git a/src/3rdparty/2geom/tests/ellipse-test.cpp b/src/3rdparty/2geom/tests/ellipse-test.cpp new file mode 100644 index 0000000..2720398 --- /dev/null +++ b/src/3rdparty/2geom/tests/ellipse-test.cpp @@ -0,0 +1,311 @@ +/** @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))); +} |