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Diffstat (limited to 'tests/elliptical-arc-test.cpp')
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diff --git a/tests/elliptical-arc-test.cpp b/tests/elliptical-arc-test.cpp new file mode 100644 index 0000000..1f6eff7 --- /dev/null +++ b/tests/elliptical-arc-test.cpp @@ -0,0 +1,275 @@ +/** @file + * @brief Unit tests for EllipticalArc. + * 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 "testing.h" +#include <2geom/elliptical-arc.h> +#include <glib.h> + +using namespace Geom; + +TEST(EllipticalArcTest, PointAt) { + EllipticalArc a(Point(0,0), Point(10,20), M_PI/2, false, true, Point(-40,0)); + EXPECT_near(a.pointAt(0), a.initialPoint(), 1e-14); + EXPECT_near(a.pointAt(1), a.finalPoint(), 1e-14); + EXPECT_near(a.pointAt(0.5), Point(-20,10), 1e-14); + + EllipticalArc b(Point(0,0), Point(10,20), 0, false, true, Point(-40,0)); + EXPECT_near(b.pointAt(0), b.initialPoint(), 1e-14); + EXPECT_near(b.pointAt(1), b.finalPoint(), 1e-14); + EXPECT_near(b.pointAt(0.5), Point(-20,40), 1e-14); + + EllipticalArc c(Point(200,0), Point(40,20), Angle::from_degrees(90), false, false, Point(200,100)); + EXPECT_near(c.pointAt(0), c.initialPoint(), 1e-13); + EXPECT_near(c.pointAt(1), c.finalPoint(), 1e-13); + EXPECT_near(c.pointAt(0.5), Point(175, 50), 1e-13); +} + +TEST(EllipticalArc, Transform) { + EllipticalArc a(Point(0,0), Point(10,20), M_PI/2, false, true, Point(-40,0)); + EllipticalArc b(Point(-40,0), Point(10,20), M_PI/2, false, true, Point(0,0)); + EllipticalArc c = a; + Affine m = Rotate::around(Point(-20,0), M_PI); + c.transform(m); + + for (unsigned i = 0; i <= 100; ++i) { + Coord t = i/100.; + EXPECT_near(c.pointAt(t), b.pointAt(t), 1e-12); + EXPECT_near(a.pointAt(t)*m, c.pointAt(t), 1e-12); + } +} + +TEST(EllipticalArcTest, Duplicate) { + EllipticalArc a(Point(0,0), Point(10,20), M_PI/2, true, false, Point(-40,0)); + EllipticalArc *b = static_cast<EllipticalArc*>(a.duplicate()); + EXPECT_EQ(a, *b); + delete b; +} + +TEST(EllipticalArcTest, LineSegmentIntersection) { + std::vector<CurveIntersection> r1; + EllipticalArc a3(Point(0,0), Point(5,1.5), 0, true, true, Point(0,2)); + LineSegment ls(Point(0,5), Point(7,-3)); + r1 = a3.intersect(ls); + EXPECT_EQ(r1.size(), 2u); + EXPECT_intersections_valid(a3, ls, r1, 1e-10); + + g_random_set_seed(0xB747A380); + // Test with randomized arcs and segments. + for (size_t _ = 0; _ < 10'000; _++) { + auto arc = EllipticalArc({g_random_double_range(1.0, 5.0), 0.0}, + {g_random_double_range(6.0, 8.0), g_random_double_range(2.0, 7.0)}, + g_random_double_range(-0.5, 0.5), true, g_random_boolean(), + {g_random_double_range(-5.0, -1.0), 0.0}); + Coord x = g_random_double_range(15, 30); + Coord y = g_random_double_range(10, 20); + auto seg = LineSegment(Point(-x, y), Point(x, -y)); + auto xings = arc.intersect(seg); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(arc, seg, xings, 1e-12); + } + + // Test with degenerate arcs + EllipticalArc x_squash_pos{{3.0, 0.0}, {3.0, 2.0}, 0, true, true, {-3.0, 0.0}}; + EllipticalArc x_squash_neg{{3.0, 0.0}, {3.0, 2.0}, 0, true, false, {-3.0, 0.0}}; + auto const squash_to_x = Scale(1.0, 0.0); + x_squash_pos *= squash_to_x; // squash to X axis interval [-3, 3]. + x_squash_neg *= squash_to_x; + + for (size_t _ = 0; _ < 10'000; _++) { + auto seg = LineSegment(Point(g_random_double_range(-3.0, 3.0), g_random_double_range(-3.0, -1.0)), + Point(g_random_double_range(-3.0, 3.0), g_random_double_range(1.0, 3.0))); + auto xings = x_squash_pos.intersect(seg); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(x_squash_pos, seg, xings, 1e-12); + + std::unique_ptr<Curve> rev{x_squash_pos.reverse()}; + xings = rev->intersect(seg); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(*rev, seg, xings, 1e-12); + + xings = x_squash_neg.intersect(seg); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(x_squash_neg, seg, xings, 1e-12); + + rev.reset(x_squash_neg.reverse()); + xings = rev->intersect(seg); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(*rev, seg, xings, 1e-12); + } + + // Now test with an arc squashed to the Y-axis. + EllipticalArc y_squash_pos{{0.0, -2.0}, {3.0, 2.0}, 0, true, true, {0.0, 2.0}}; + EllipticalArc y_squash_neg{{0.0, -2.0}, {3.0, 2.0}, 0, true, false, {0.0, 2.0}}; + auto const squash_to_y = Scale(0.0, 1.0); + y_squash_pos *= squash_to_y; // Y-axis interval [-2, 2]. + y_squash_neg *= squash_to_y; + + for (size_t _ = 0; _ < 10'000; _++) { + auto seg = LineSegment(Point(g_random_double_range(-3.0, -1.0), g_random_double_range(-2.0, 2.0)), + Point(g_random_double_range(1.0, 3.0), g_random_double_range(-2.0, 2.0))); + auto xings = y_squash_pos.intersect(seg, 1e-10); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(y_squash_pos, seg, xings, 1e-12); + + std::unique_ptr<Curve> rev{y_squash_pos.reverse()}; + xings = rev->intersect(seg, 1e-12); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(*rev, seg, xings, 1e-12); + + xings = y_squash_neg.intersect(seg, 1e-12); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(y_squash_neg, seg, xings, 1e-12); + + rev.reset(y_squash_neg.reverse()); + xings = rev->intersect(seg, 1e-12); + EXPECT_EQ(xings.size(), 1u); + EXPECT_intersections_valid(*rev, seg, xings, 1e-12); + } + + // Test whether the coincidence between the common endpoints of an + // arc and a segment is correctly detected as an intersection. + { + Point const from{1, 0}; + Point const to{0.30901699437494745, 0.9510565162951535}; + auto arc = EllipticalArc(from, {1, 1}, 0, false, true, to); + auto seg = LineSegment({0, 0}, to); + auto xings = arc.intersect(seg); + ASSERT_EQ(xings.size(), 1); + EXPECT_TRUE(are_near(xings[0].point(), to, 1e-12)); + EXPECT_TRUE(are_near(xings[0].first, 1.0, 1e-24)); + EXPECT_TRUE(are_near(xings[0].second, 1.0, 1e-24)); + + auto seg2 = LineSegment(Point{1, 1}, from); + xings = arc.intersect(seg2); + ASSERT_EQ(xings.size(), 1); + EXPECT_TRUE(are_near(xings[0].point(), from, 1e-12)); + EXPECT_TRUE(are_near(xings[0].first, 0.0, 1e-24)); + EXPECT_TRUE(are_near(xings[0].second, 1.0, 1e-24)); + } +} + +TEST(EllipticalArcTest, ArcIntersection) { + std::vector<CurveIntersection> r1, r2; + + EllipticalArc a1(Point(0,0), Point(6,3), 0.1, false, false, Point(10,0)); + EllipticalArc a2(Point(0,2), Point(6,3), -0.1, false, true, Point(10,2)); + r1 = a1.intersect(a2); + EXPECT_EQ(r1.size(), 2u); + EXPECT_intersections_valid(a1, a2, r1, 1e-10); + + EllipticalArc a3(Point(0,0), Point(5,1.5), 0, true, true, Point(0,2)); + EllipticalArc a4(Point(3,5), Point(5,1.5), M_PI/2, true, true, Point(5,0)); + r2 = a3.intersect(a4); + EXPECT_EQ(r2.size(), 3u); + EXPECT_intersections_valid(a3, a4, r2, 1e-10); + + // Make sure intersections are found between two identical arcs on the unit circle. + EllipticalArc const upper(Point(1, 0), Point(1, 1), 0, true, true, Point(-1, 0)); + auto self_intersect = upper.intersect(upper); + EXPECT_EQ(self_intersect.size(), 2u); + + // Make sure intersections are found between overlapping arcs. + EllipticalArc const right(Point(0, -1), Point(1, 1), 0, true, true, Point(0, 1)); + auto quartering_overlap_xings = right.intersect(upper); + EXPECT_EQ(quartering_overlap_xings.size(), 2u); + + // Make sure intersecections are found between an arc and its sub-arc. + EllipticalArc const middle(upper.pointAtAngle(0.25 * M_PI), Point(1, 1), 0, true, true, upper.pointAtAngle(-0.25 * M_PI)); + EXPECT_EQ(middle.intersect(upper).size(), 2u); + + // Make sure intersections are NOT found between non-overlapping sub-arcs of the same circle. + EllipticalArc const arc1{Point(1, 0), Point(1, 1), 0, true, true, Point(0, 1)}; + EllipticalArc const arc2{Point(-1, 0), Point(1, 1), 0, true, true, Point(0, -1)}; + EXPECT_EQ(arc1.intersect(arc2).size(), 0u); + + // Overlapping sub-arcs but on an Ellipse with different rays. + EllipticalArc const eccentric{Point(2, 0), Point(2, 1), 0, true, true, Point(-2, 0)}; + EllipticalArc const subarc{eccentric.pointAtAngle(0.8), Point(2, 1), 0, true, true, eccentric.pointAtAngle(2)}; + EXPECT_EQ(eccentric.intersect(subarc).size(), 2u); + + // Check intersection times for two touching arcs. + EllipticalArc const lower{Point(-1, 0), Point(1, 1), 0, false, true, Point(0, -1)}; + auto expected_neg_x = upper.intersect(lower); + ASSERT_EQ(expected_neg_x.size(), 1); + auto const &left_pt = expected_neg_x[0]; + EXPECT_EQ(left_pt.point(), Point(-1, 0)); + EXPECT_DOUBLE_EQ(left_pt.first, 1.0); // Expect (-1, 0) reached at the end of upper + EXPECT_DOUBLE_EQ(left_pt.second, 0.0); // Expect (-1, 0) passed at the start of lower +} + +TEST(EllipticalArcTest, BezierIntersection) { + std::vector<CurveIntersection> r1, r2; + + EllipticalArc a3(Point(0,0), Point(1.5,5), M_PI/2, true, true, Point(0,2)); + CubicBezier bez1(Point(0,3), Point(7,3), Point(0,-1), Point(7,-1)); + r1 = a3.intersect(bez1); + EXPECT_EQ(r1.size(), 2u); + EXPECT_intersections_valid(a3, bez1, r1, 1e-10); + + EllipticalArc a4(Point(3,5), Point(5,1.5), 3*M_PI/2, true, true, Point(5,5)); + CubicBezier bez2(Point(0,5), Point(10,-4), Point(10,5), Point(0,-4)); + r2 = a4.intersect(bez2); + EXPECT_EQ(r2.size(), 4u); + EXPECT_intersections_valid(a4, bez2, r2, 1e-10); +} + +TEST(EllipticalArcTest, ExpandToTransformedTest) +{ + auto test_curve = [] (EllipticalArc const &c) { + constexpr int N = 50; + for (int i = 0; i < N; i++) { + auto angle = 2 * M_PI * i / N; + auto transform = Affine(Rotate(angle)) * Scale(0.9, 1.2); + + auto copy = std::unique_ptr<Curve>(c.duplicate()); + *copy *= transform; + auto box1 = copy->boundsExact(); + + auto pt = c.initialPoint() * transform; + auto box2 = Rect(pt, pt); + c.expandToTransformed(box2, transform); + + for (auto i : { X, Y }) { + EXPECT_NEAR(box1[i].min(), box2[i].min(), 2e-15); + EXPECT_NEAR(box1[i].max(), box2[i].max(), 2e-15); + } + } + }; + + test_curve(EllipticalArc(Point(0, 0), 1.0, 2.0, 0.0, false, false, Point(1, 1))); + test_curve(EllipticalArc(Point(0, 0), 3.0, 2.0, M_PI / 6, false, false, Point(1, 1))); + test_curve(EllipticalArc(Point(0, 0), 1.0, 2.0, M_PI / 5, true, true, Point(1, 1))); + test_curve(EllipticalArc(Point(1, 0), 1.0, 0.0, M_PI / 5, false, false, Point(1, 1))); + test_curve(EllipticalArc(Point(1, 0), 0.0, 0.0, 0.0, false, false, Point(2, 0))); + test_curve(EllipticalArc(Point(1, 0), 0.0, 0.0, 0.0, false, false, Point(1, 0))); +} |