Added Geometry2D unit tests

core/math/geometry_2d.h

@@ -145,6 +145,12 @@ public:
 		return p_segment[0] + n * d; // Inside.
 	}
 
+// Disable False Positives in MSVC compiler; we correctly check for 0 here to prevent a division by 0.
+// See: https://github.com/godotengine/godot/pull/44274
+#ifdef _MSC_VER
+#pragma warning(disable : 4723)
+#endif
+
 	static bool line_intersects_line(const Vector2 &p_from_a, const Vector2 &p_dir_a, const Vector2 &p_from_b, const Vector2 &p_dir_b, Vector2 &r_result) {
 		// See http://paulbourke.net/geometry/pointlineplane/
 
@@ -159,6 +165,11 @@ public:
 		return true;
 	}
 
+// Re-enable division by 0 warning
+#ifdef _MSC_VER
+#pragma warning(default : 4723)
+#endif
+
 	static bool segment_intersects_segment(const Vector2 &p_from_a, const Vector2 &p_to_a, const Vector2 &p_from_b, const Vector2 &p_to_b, Vector2 *r_result) {
 		Vector2 B = p_to_a - p_from_a;
 		Vector2 C = p_from_b - p_from_a;

tests/test_geometry_2d.h

@@ -0,0 +1,553 @@
+/*************************************************************************/
+/*  test_geometry_2d.h                                                   */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef TEST_GEOMETRY_2D_H
+#define TEST_GEOMETRY_2D_H
+
+#include "core/math/geometry_2d.h"
+#include "core/templates/vector.h"
+
+#include "thirdparty/doctest/doctest.h"
+
+namespace TestGeometry2D {
+
+TEST_CASE("[Geometry2D] Point in circle") {
+	CHECK(Geometry2D::is_point_in_circle(Vector2(0, 0), Vector2(0, 0), 1.0));
+
+	CHECK(Geometry2D::is_point_in_circle(Vector2(0, 0), Vector2(11.99, 0), 12));
+	CHECK(Geometry2D::is_point_in_circle(Vector2(-11.99, 0), Vector2(0, 0), 12));
+
+	CHECK_FALSE(Geometry2D::is_point_in_circle(Vector2(0, 0), Vector2(12.01, 0), 12));
+	CHECK_FALSE(Geometry2D::is_point_in_circle(Vector2(-12.01, 0), Vector2(0, 0), 12));
+
+	CHECK(Geometry2D::is_point_in_circle(Vector2(7, -42), Vector2(4, -40), 3.7));
+	CHECK_FALSE(Geometry2D::is_point_in_circle(Vector2(7, -42), Vector2(4, -40), 3.5));
+
+	// This tests points on the edge of the circle. They are treated as beeing inside the circle.
+	// In `is_point_in_triangle` and `is_point_in_polygon` they are treated as being outside, so in order the make
+	// the behaviour consistent this may change in the future (see issue #44717 and PR #44274).
+	CHECK(Geometry2D::is_point_in_circle(Vector2(1.0, 0.0), Vector2(0, 0), 1.0));
+	CHECK(Geometry2D::is_point_in_circle(Vector2(0.0, -1.0), Vector2(0, 0), 1.0));
+}
+
+TEST_CASE("[Geometry2D] Point in triangle") {
+	CHECK(Geometry2D::is_point_in_triangle(Vector2(0, 0), Vector2(-1, 1), Vector2(0, -1), Vector2(1, 1)));
+	CHECK_FALSE(Geometry2D::is_point_in_triangle(Vector2(-1.01, 1.0), Vector2(-1, 1), Vector2(0, -1), Vector2(1, 1)));
+
+	CHECK(Geometry2D::is_point_in_triangle(Vector2(3, 2.5), Vector2(1, 4), Vector2(3, 2), Vector2(5, 4)));
+	CHECK(Geometry2D::is_point_in_triangle(Vector2(-3, -2.5), Vector2(-1, -4), Vector2(-3, -2), Vector2(-5, -4)));
+	CHECK_FALSE(Geometry2D::is_point_in_triangle(Vector2(0, 0), Vector2(1, 4), Vector2(3, 2), Vector2(5, 4)));
+
+	// This tests points on the edge of the triangle. They are treated as beeing outside the triangle.
+	// In `is_point_in_circle` they are treated as being inside, so in order the make
+	// the behaviour consistent this may change in the future (see issue #44717 and PR #44274).
+	CHECK_FALSE(Geometry2D::is_point_in_triangle(Vector2(1, 1), Vector2(-1, 1), Vector2(0, -1), Vector2(1, 1)));
+	CHECK_FALSE(Geometry2D::is_point_in_triangle(Vector2(0, 1), Vector2(-1, 1), Vector2(0, -1), Vector2(1, 1)));
+}
+
+TEST_CASE("[Geometry2D] Point in polygon") {
+	Vector<Vector2> p;
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(0, 0), p));
+
+	p.push_back(Vector2(-88, 120));
+	p.push_back(Vector2(-74, -38));
+	p.push_back(Vector2(135, -145));
+	p.push_back(Vector2(425, 70));
+	p.push_back(Vector2(68, 112));
+	p.push_back(Vector2(-120, 370));
+	p.push_back(Vector2(-323, -145));
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(-350, 0), p));
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(-110, 60), p));
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(412, 96), p));
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(83, 130), p));
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(-320, -153), p));
+
+	CHECK(Geometry2D::is_point_in_polygon(Vector2(0, 0), p));
+	CHECK(Geometry2D::is_point_in_polygon(Vector2(-230, 0), p));
+	CHECK(Geometry2D::is_point_in_polygon(Vector2(130, -110), p));
+	CHECK(Geometry2D::is_point_in_polygon(Vector2(370, 55), p));
+	CHECK(Geometry2D::is_point_in_polygon(Vector2(-160, 190), p));
+
+	// This tests points on the edge of the polygon. They are treated as beeing outside the polygon.
+	// In `is_point_in_circle` they are treated as being inside, so in order the make
+	// the behaviour consistent this may change in the future (see issue #44717 and PR #44274).
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(68, 112), p));
+	CHECK_FALSE(Geometry2D::is_point_in_polygon(Vector2(-88, 120), p));
+}
+
+TEST_CASE("[Geometry2D] Polygon clockwise") {
+	Vector<Vector2> p;
+	CHECK_FALSE(Geometry2D::is_polygon_clockwise(p));
+
+	p.push_back(Vector2(5, -5));
+	p.push_back(Vector2(-1, -5));
+	p.push_back(Vector2(-5, -1));
+	p.push_back(Vector2(-1, 3));
+	p.push_back(Vector2(1, 5));
+	CHECK(Geometry2D::is_polygon_clockwise(p));
+
+	p.invert();
+	CHECK_FALSE(Geometry2D::is_polygon_clockwise(p));
+}
+
+TEST_CASE("[Geometry2D] Line intersection") {
+	Vector2 r;
+	CHECK(Geometry2D::line_intersects_line(Vector2(2, 0), Vector2(0, 1), Vector2(0, 2), Vector2(1, 0), r));
+	CHECK(r.is_equal_approx(Vector2(2, 2)));
+
+	CHECK(Geometry2D::line_intersects_line(Vector2(-1, 1), Vector2(1, -1), Vector2(4, 1), Vector2(-1, -1), r));
+	CHECK(r.is_equal_approx(Vector2(1.5, -1.5)));
+
+	CHECK(Geometry2D::line_intersects_line(Vector2(-1, 0), Vector2(-1, -1), Vector2(1, 0), Vector2(1, -1), r));
+	CHECK(r.is_equal_approx(Vector2(0, 1)));
+
+	CHECK_FALSE_MESSAGE(
+			Geometry2D::line_intersects_line(Vector2(-1, 1), Vector2(1, -1), Vector2(0, 1), Vector2(1, -1), r),
+			"Parallel lines should not intersect.");
+}
+
+TEST_CASE("[Geometry2D] Segment intersection.") {
+	Vector2 r;
+
+	CHECK(Geometry2D::segment_intersects_segment(Vector2(-1, 1), Vector2(1, -1), Vector2(1, 1), Vector2(-1, -1), &r));
+	CHECK(r.is_equal_approx(Vector2(0, 0)));
+
+	CHECK_FALSE(Geometry2D::segment_intersects_segment(Vector2(-1, 1), Vector2(1, -1), Vector2(1, 1), Vector2(0.1, 0.1), &r));
+	CHECK_FALSE_MESSAGE(
+			Geometry2D::segment_intersects_segment(Vector2(-1, 1), Vector2(1, -1), Vector2(0, 1), Vector2(1, -1), &r),
+			"Parallel segments should not intersect.");
+}
+
+TEST_CASE("[Geometry2D] Closest point to segment") {
+	Vector2 s[] = { Vector2(-4, -4), Vector2(4, 4) };
+	CHECK(Geometry2D::get_closest_point_to_segment(Vector2(4.1, 4.1), s).is_equal_approx(Vector2(4, 4)));
+	CHECK(Geometry2D::get_closest_point_to_segment(Vector2(-4.1, -4.1), s).is_equal_approx(Vector2(-4, -4)));
+	CHECK(Geometry2D::get_closest_point_to_segment(Vector2(-1, 1), s).is_equal_approx(Vector2(0, 0)));
+}
+
+TEST_CASE("[Geometry2D] Closest point to uncapped segment") {
+	Vector2 s[] = { Vector2(-4, -4), Vector2(4, 4) };
+	CHECK(Geometry2D::get_closest_point_to_segment_uncapped(Vector2(-1, 1), s).is_equal_approx(Vector2(0, 0)));
+	CHECK(Geometry2D::get_closest_point_to_segment_uncapped(Vector2(-4, -6), s).is_equal_approx(Vector2(-5, -5)));
+	CHECK(Geometry2D::get_closest_point_to_segment_uncapped(Vector2(4, 6), s).is_equal_approx(Vector2(5, 5)));
+}
+
+TEST_CASE("[Geometry2D] Closest points between segments") {
+	Vector2 c1, c2;
+	Geometry2D::get_closest_points_between_segments(Vector2(2, 2), Vector2(3, 3), Vector2(4, 4), Vector2(4, 5), c1, c2);
+	CHECK(c1.is_equal_approx(Vector2(3, 3)));
+	CHECK(c2.is_equal_approx(Vector2(4, 4)));
+
+	Geometry2D::get_closest_points_between_segments(Vector2(0, 1), Vector2(-2, -1), Vector2(0, 0), Vector2(2, -2), c1, c2);
+	CHECK(c1.is_equal_approx(Vector2(-0.5, 0.5)));
+	CHECK(c2.is_equal_approx(Vector2(0, 0)));
+
+	Geometry2D::get_closest_points_between_segments(Vector2(-1, 1), Vector2(1, -1), Vector2(1, 1), Vector2(-1, -1), c1, c2);
+	CHECK(c1.is_equal_approx(Vector2(0, 0)));
+	CHECK(c2.is_equal_approx(Vector2(0, 0)));
+}
+
+TEST_CASE("[Geometry2D] Make atlas") {
+	Vector<Point2i> result;
+	Size2i size;
+
+	Vector<Size2i> r;
+	r.push_back(Size2i(2, 2));
+	Geometry2D::make_atlas(r, result, size);
+	CHECK(size == Size2i(2, 2));
+	CHECK(result.size() == r.size());
+
+	r.clear();
+	result.clear();
+	r.push_back(Size2i(1, 2));
+	r.push_back(Size2i(3, 4));
+	r.push_back(Size2i(5, 6));
+	r.push_back(Size2i(7, 8));
+	Geometry2D::make_atlas(r, result, size);
+	CHECK(result.size() == r.size());
+}
+
+TEST_CASE("[Geometry2D] Polygon intersection") {
+	Vector<Point2> a;
+	Vector<Point2> b;
+	Vector<Vector<Point2>> r;
+
+	a.push_back(Point2(30, 60));
+	a.push_back(Point2(70, 5));
+	a.push_back(Point2(200, 40));
+	a.push_back(Point2(80, 200));
+
+	SUBCASE("[Geometry2D] Both polygons are empty") {
+		r = Geometry2D::intersect_polygons(Vector<Point2>(), Vector<Point2>());
+		CHECK_MESSAGE(r.is_empty(), "Both polygons are empty. The intersection should also be empty.");
+	}
+
+	SUBCASE("[Geometry2D] One polygon is empty") {
+		r = Geometry2D::intersect_polygons(a, b);
+		REQUIRE_MESSAGE(r.is_empty(), "One polygon is empty. The intersection should also be empty.");
+	}
+
+	SUBCASE("[Geometry2D] Basic intersection") {
+		b.push_back(Point2(200, 300));
+		b.push_back(Point2(90, 200));
+		b.push_back(Point2(50, 100));
+		b.push_back(Point2(200, 90));
+		r = Geometry2D::intersect_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 1, "The polygons should intersect each other with 1 resulting intersection polygon.");
+		REQUIRE_MESSAGE(r[0].size() == 3, "The resulting intersection polygon should have 3 vertices.");
+		CHECK(r[0][0].is_equal_approx(Point2(86.52174, 191.30436)));
+		CHECK(r[0][1].is_equal_approx(Point2(50, 100)));
+		CHECK(r[0][2].is_equal_approx(Point2(160.52632, 92.63157)));
+	}
+
+	SUBCASE("[Geometry2D] Intersection with one polygon beeing completly inside the other polygon") {
+		b.push_back(Point2(80, 100));
+		b.push_back(Point2(50, 50));
+		b.push_back(Point2(150, 50));
+		r = Geometry2D::intersect_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 1, "The polygons should intersect each other with 1 resulting intersection polygon.");
+		REQUIRE_MESSAGE(r[0].size() == 3, "The resulting intersection polygon should have 3 vertices.");
+		CHECK(r[0][0].is_equal_approx(b[0]));
+		CHECK(r[0][1].is_equal_approx(b[1]));
+		CHECK(r[0][2].is_equal_approx(b[2]));
+	}
+
+	SUBCASE("[Geometry2D] No intersection with 2 non-empty polygons") {
+		b.push_back(Point2(150, 150));
+		b.push_back(Point2(250, 100));
+		b.push_back(Point2(300, 200));
+		r = Geometry2D::intersect_polygons(a, b);
+		REQUIRE_MESSAGE(r.is_empty(), "The polygons should not intersect each other.");
+	}
+
+	SUBCASE("[Geometry2D] Intersection with 2 resulting polygons") {
+		a.clear();
+		a.push_back(Point2(70, 5));
+		a.push_back(Point2(140, 7));
+		a.push_back(Point2(100, 52));
+		a.push_back(Point2(170, 50));
+		a.push_back(Point2(60, 125));
+		b.push_back(Point2(70, 105));
+		b.push_back(Point2(115, 55));
+		b.push_back(Point2(90, 15));
+		b.push_back(Point2(160, 50));
+		r = Geometry2D::intersect_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 2, "The polygons should intersect each other with 2 resulting intersection polygons.");
+		REQUIRE_MESSAGE(r[0].size() == 4, "The resulting intersection polygon should have 4 vertices.");
+		CHECK(r[0][0].is_equal_approx(Point2(70, 105)));
+		CHECK(r[0][1].is_equal_approx(Point2(115, 55)));
+		CHECK(r[0][2].is_equal_approx(Point2(112.894737, 51.63158)));
+		CHECK(r[0][3].is_equal_approx(Point2(159.509537, 50.299728)));
+
+		REQUIRE_MESSAGE(r[1].size() == 3, "The intersection polygon should have 3 vertices.");
+		CHECK(r[1][0].is_equal_approx(Point2(119.692307, 29.846149)));
+		CHECK(r[1][1].is_equal_approx(Point2(107.706421, 43.33028)));
+		CHECK(r[1][2].is_equal_approx(Point2(90, 15)));
+	}
+}
+
+TEST_CASE("[Geometry2D] Merge polygons") {
+	Vector<Point2> a;
+	Vector<Point2> b;
+	Vector<Vector<Point2>> r;
+
+	a.push_back(Point2(225, 180));
+	a.push_back(Point2(160, 230));
+	a.push_back(Point2(20, 212));
+	a.push_back(Point2(50, 115));
+
+	SUBCASE("[Geometry2D] Both polygons are empty") {
+		r = Geometry2D::merge_polygons(Vector<Point2>(), Vector<Point2>());
+		REQUIRE_MESSAGE(r.is_empty(), "Both polygons are empty. The union should also be empty.");
+	}
+
+	SUBCASE("[Geometry2D] One polygon is empty") {
+		r = Geometry2D::merge_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 1, "One polygon is non-empty. There should be 1 resulting merged polygon.");
+		REQUIRE_MESSAGE(r[0].size() == 4, "The resulting merged polygon should have 4 vertices.");
+		CHECK(r[0][0].is_equal_approx(a[0]));
+		CHECK(r[0][1].is_equal_approx(a[1]));
+		CHECK(r[0][2].is_equal_approx(a[2]));
+		CHECK(r[0][3].is_equal_approx(a[3]));
+	}
+
+	SUBCASE("[Geometry2D] Basic merge with 2 polygons") {
+		b.push_back(Point2(180, 190));
+		b.push_back(Point2(60, 140));
+		b.push_back(Point2(160, 80));
+		r = Geometry2D::merge_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 1, "The merged polygons should result in 1 polygon.");
+		REQUIRE_MESSAGE(r[0].size() == 7, "The resulting merged polygon should have 7 vertices.");
+		CHECK(r[0][0].is_equal_approx(Point2(174.791077, 161.350967)));
+		CHECK(r[0][1].is_equal_approx(Point2(225, 180)));
+		CHECK(r[0][2].is_equal_approx(Point2(160, 230)));
+		CHECK(r[0][3].is_equal_approx(Point2(20, 212)));
+		CHECK(r[0][4].is_equal_approx(Point2(50, 115)));
+		CHECK(r[0][5].is_equal_approx(Point2(81.911758, 126.852943)));
+		CHECK(r[0][6].is_equal_approx(Point2(160, 80)));
+	}
+
+	SUBCASE("[Geometry2D] Merge with 2 resulting merged polygons (outline and hole)") {
+		b.push_back(Point2(180, 190));
+		b.push_back(Point2(140, 125));
+		b.push_back(Point2(60, 140));
+		b.push_back(Point2(160, 80));
+		r = Geometry2D::merge_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 2, "The merged polygons should result in 2 polygons.");
+
+		REQUIRE_MESSAGE(!Geometry2D::is_polygon_clockwise(r[0]), "The merged polygon (outline) should be counter-clockwise.");
+		REQUIRE_MESSAGE(r[0].size() == 7, "The resulting merged polygon (outline) should have 7 vertices.");
+		CHECK(r[0][0].is_equal_approx(Point2(174.791077, 161.350967)));
+		CHECK(r[0][1].is_equal_approx(Point2(225, 180)));
+		CHECK(r[0][2].is_equal_approx(Point2(160, 230)));
+		CHECK(r[0][3].is_equal_approx(Point2(20, 212)));
+		CHECK(r[0][4].is_equal_approx(Point2(50, 115)));
+		CHECK(r[0][5].is_equal_approx(Point2(81.911758, 126.852943)));
+		CHECK(r[0][6].is_equal_approx(Point2(160, 80)));
+
+		REQUIRE_MESSAGE(Geometry2D::is_polygon_clockwise(r[1]), "The resulting merged polygon (hole) should be clockwise.");
+		REQUIRE_MESSAGE(r[1].size() == 3, "The resulting merged polygon (hole) should have 3 vertices.");
+		CHECK(r[1][0].is_equal_approx(Point2(98.083069, 132.859421)));
+		CHECK(r[1][1].is_equal_approx(Point2(158.689453, 155.370377)));
+		CHECK(r[1][2].is_equal_approx(Point2(140, 125)));
+	}
+}
+
+TEST_CASE("[Geometry2D] Clip polygons") {
+	Vector<Point2> a;
+	Vector<Point2> b;
+	Vector<Vector<Point2>> r;
+
+	a.push_back(Point2(225, 180));
+	a.push_back(Point2(160, 230));
+	a.push_back(Point2(20, 212));
+	a.push_back(Point2(50, 115));
+
+	SUBCASE("[Geometry2D] Both polygons are empty") {
+		r = Geometry2D::clip_polygons(Vector<Point2>(), Vector<Point2>());
+		CHECK_MESSAGE(r.is_empty(), "Both polygons are empty. The clip should also be empty.");
+	}
+
+	SUBCASE("[Geometry2D] Basic clip with one result polygon") {
+		b.push_back(Point2(250, 170));
+		b.push_back(Point2(175, 270));
+		b.push_back(Point2(120, 260));
+		b.push_back(Point2(25, 80));
+		r = Geometry2D::clip_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 1, "The clipped polygons should result in 1 polygon.");
+		REQUIRE_MESSAGE(r[0].size() == 3, "The resulting clipped polygon should have 3 vertices.");
+		CHECK(r[0][0].is_equal_approx(Point2(100.102173, 222.298843)));
+		CHECK(r[0][1].is_equal_approx(Point2(20, 212)));
+		CHECK(r[0][2].is_equal_approx(Point2(47.588089, 122.798492)));
+	}
+
+	SUBCASE("[Geometry2D] Polygon b completely overlaps polygon a") {
+		b.push_back(Point2(250, 170));
+		b.push_back(Point2(175, 270));
+		b.push_back(Point2(10, 210));
+		b.push_back(Point2(55, 80));
+		r = Geometry2D::clip_polygons(a, b);
+		CHECK_MESSAGE(r.is_empty(), "Polygon 'b' completely overlaps polygon 'a'. This should result in no clipped polygons.");
+	}
+
+	SUBCASE("[Geometry2D] Polygon a completely overlaps polygon b") {
+		b.push_back(Point2(150, 200));
+		b.push_back(Point2(65, 190));
+		b.push_back(Point2(80, 140));
+		r = Geometry2D::clip_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 2, "Polygon 'a' completely overlaps polygon 'b'. This should result in 2 clipped polygons.");
+		REQUIRE_MESSAGE(r[0].size() == 4, "The resulting clipped polygon should have 4 vertices.");
+		REQUIRE_MESSAGE(!Geometry2D::is_polygon_clockwise(r[0]), "The resulting clipped polygon (outline) should be counter-clockwise.");
+		CHECK(r[0][0].is_equal_approx(a[0]));
+		CHECK(r[0][1].is_equal_approx(a[1]));
+		CHECK(r[0][2].is_equal_approx(a[2]));
+		CHECK(r[0][3].is_equal_approx(a[3]));
+		REQUIRE_MESSAGE(r[1].size() == 3, "The resulting clipped polygon should have 3 vertices.");
+		REQUIRE_MESSAGE(Geometry2D::is_polygon_clockwise(r[1]), "The resulting clipped polygon (hole) should be clockwise.");
+		CHECK(r[1][0].is_equal_approx(b[1]));
+		CHECK(r[1][1].is_equal_approx(b[0]));
+		CHECK(r[1][2].is_equal_approx(b[2]));
+	}
+}
+
+TEST_CASE("[Geometry2D] Exclude polygons") {
+	Vector<Point2> a;
+	Vector<Point2> b;
+	Vector<Vector<Point2>> r;
+
+	a.push_back(Point2(225, 180));
+	a.push_back(Point2(160, 230));
+	a.push_back(Point2(20, 212));
+	a.push_back(Point2(50, 115));
+
+	SUBCASE("[Geometry2D] Both polygons are empty") {
+		r = Geometry2D::exclude_polygons(Vector<Point2>(), Vector<Point2>());
+		CHECK_MESSAGE(r.is_empty(), "Both polygons are empty. The excluded polygon should also be empty.");
+	}
+
+	SUBCASE("[Geometry2D] One polygon is empty") {
+		r = Geometry2D::exclude_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 1, "One polygon is non-empty. There should be 1 resulting excluded polygon.");
+		REQUIRE_MESSAGE(r[0].size() == 4, "The resulting excluded polygon should have 4 vertices.");
+		CHECK(r[0][0].is_equal_approx(a[0]));
+		CHECK(r[0][1].is_equal_approx(a[1]));
+		CHECK(r[0][2].is_equal_approx(a[2]));
+		CHECK(r[0][3].is_equal_approx(a[3]));
+	}
+
+	SUBCASE("[Geometry2D] Exclude with 2 resulting polygons (outline and hole)") {
+		b.push_back(Point2(140, 160));
+		b.push_back(Point2(150, 220));
+		b.push_back(Point2(40, 200));
+		b.push_back(Point2(60, 140));
+		r = Geometry2D::exclude_polygons(a, b);
+		REQUIRE_MESSAGE(r.size() == 2, "There should be 2 resulting excluded polygons (outline and hole).");
+		REQUIRE_MESSAGE(r[0].size() == 4, "The resulting excluded polygon should have 4 vertices.");
+		REQUIRE_MESSAGE(!Geometry2D::is_polygon_clockwise(r[0]), "The resulting excluded polygon (outline) should be counter-clockwise.");
+		CHECK(r[0][0].is_equal_approx(a[0]));
+		CHECK(r[0][1].is_equal_approx(a[1]));
+		CHECK(r[0][2].is_equal_approx(a[2]));
+		CHECK(r[0][3].is_equal_approx(a[3]));
+		REQUIRE_MESSAGE(r[1].size() == 4, "The resulting excluded polygon should have 4 vertices.");
+		REQUIRE_MESSAGE(Geometry2D::is_polygon_clockwise(r[1]), "The resulting excluded polygon (hole) should be clockwise.");
+		CHECK(r[1][0].is_equal_approx(Point2(40, 200)));
+		CHECK(r[1][1].is_equal_approx(Point2(150, 220)));
+		CHECK(r[1][2].is_equal_approx(Point2(140, 160)));
+		CHECK(r[1][3].is_equal_approx(Point2(60, 140)));
+	}
+}
+
+TEST_CASE("[Geometry2D] Intersect polyline with polygon") {
+	Vector<Vector2> l;
+	Vector<Vector2> p;
+	Vector<Vector<Point2>> r;
+
+	l.push_back(Vector2(100, 90));
+	l.push_back(Vector2(120, 250));
+
+	p.push_back(Vector2(225, 180));
+	p.push_back(Vector2(160, 230));
+	p.push_back(Vector2(20, 212));
+	p.push_back(Vector2(50, 115));
+
+	SUBCASE("[Geometry2D] Both line and polygon are empty") {
+		r = Geometry2D::intersect_polyline_with_polygon(Vector<Vector2>(), Vector<Vector2>());
+		CHECK_MESSAGE(r.is_empty(), "Both line and polygon are empty. The intersection line should also be empty.");
+	}
+
+	SUBCASE("[Geometry2D] Line is non-empty and polygon is empty") {
+		r = Geometry2D::intersect_polyline_with_polygon(l, Vector<Vector2>());
+		CHECK_MESSAGE(r.is_empty(), "The polygon is empty while the line is non-empty. The intersection line should be empty.");
+	}
+
+	SUBCASE("[Geometry2D] Basic intersection with 1 resulting intersection line") {
+		r = Geometry2D::intersect_polyline_with_polygon(l, p);
+		REQUIRE_MESSAGE(r.size() == 1, "There should be 1 resulting intersection line.");
+		REQUIRE_MESSAGE(r[0].size() == 2, "The resulting intersection line should have 2 vertices.");
+		CHECK(r[0][0].is_equal_approx(Vector2(105.711609, 135.692886)));
+		CHECK(r[0][1].is_equal_approx(Vector2(116.805809, 224.446457)));
+	}
+
+	SUBCASE("[Geometry2D] Complex intersection with 2 resulting intersection lines") {
+		l.clear();
+		l.push_back(Vector2(100, 90));
+		l.push_back(Vector2(190, 255));
+		l.push_back(Vector2(135, 260));
+		l.push_back(Vector2(57, 200));
+		l.push_back(Vector2(50, 170));
+		l.push_back(Vector2(15, 155));
+		r = Geometry2D::intersect_polyline_with_polygon(l, p);
+		REQUIRE_MESSAGE(r.size() == 2, "There should be 2 resulting intersection lines.");
+		REQUIRE_MESSAGE(r[0].size() == 2, "The resulting intersection line should have 2 vertices.");
+		CHECK(r[0][0].is_equal_approx(Vector2(129.804565, 144.641693)));
+		CHECK(r[0][1].is_equal_approx(Vector2(171.527084, 221.132996)));
+		REQUIRE_MESSAGE(r[1].size() == 4, "The resulting intersection line should have 4 vertices.");
+		CHECK(r[1][0].is_equal_approx(Vector2(83.15609, 220.120087)));
+		CHECK(r[1][1].is_equal_approx(Vector2(57, 200)));
+		CHECK(r[1][2].is_equal_approx(Vector2(50, 170)));
+		CHECK(r[1][3].is_equal_approx(Vector2(34.980492, 163.563065)));
+	}
+}
+
+TEST_CASE("[Geometry2D] Clip polyline with polygon") {
+	Vector<Vector2> l;
+	Vector<Vector2> p;
+	Vector<Vector<Point2>> r;
+
+	l.push_back(Vector2(70, 140));
+	l.push_back(Vector2(160, 320));
+
+	p.push_back(Vector2(225, 180));
+	p.push_back(Vector2(160, 230));
+	p.push_back(Vector2(20, 212));
+	p.push_back(Vector2(50, 115));
+
+	SUBCASE("[Geometry2D] Both line and polygon are empty") {
+		r = Geometry2D::clip_polyline_with_polygon(Vector<Vector2>(), Vector<Vector2>());
+		CHECK_MESSAGE(r.is_empty(), "Both line and polygon are empty. The clipped line should also be empty.");
+	}
+
+	SUBCASE("[Geometry2D] Polygon is empty and line is non-empty") {
+		r = Geometry2D::clip_polyline_with_polygon(l, Vector<Vector2>());
+		REQUIRE_MESSAGE(r.size() == 1, "There should be 1 resulting clipped line.");
+		REQUIRE_MESSAGE(r[0].size() == 2, "The resulting clipped line should have 2 vertices.");
+		CHECK(r[0][0].is_equal_approx(l[0]));
+		CHECK(r[0][1].is_equal_approx(l[1]));
+	}
+
+	SUBCASE("[Geometry2D] Basic clip with 1 resulting clipped line") {
+		r = Geometry2D::clip_polyline_with_polygon(l, p);
+		REQUIRE_MESSAGE(r.size() == 1, "There should be 1 resulting clipped line.");
+		REQUIRE_MESSAGE(r[0].size() == 2, "The resulting clipped line should have 2 vertices.");
+		CHECK(r[0][0].is_equal_approx(Vector2(111.908401, 223.816803)));
+		CHECK(r[0][1].is_equal_approx(Vector2(160, 320)));
+	}
+
+	SUBCASE("[Geometry2D] Complex clip with 2 resulting clipped lines") {
+		l.clear();
+		l.push_back(Vector2(55, 70));
+		l.push_back(Vector2(50, 190));
+		l.push_back(Vector2(120, 165));
+		l.push_back(Vector2(122, 250));
+		l.push_back(Vector2(160, 320));
+		r = Geometry2D::clip_polyline_with_polygon(l, p);
+		REQUIRE_MESSAGE(r.size() == 2, "There should be 2 resulting clipped lines.");
+		REQUIRE_MESSAGE(r[0].size() == 3, "The resulting clipped line should have 3 vertices.");
+		CHECK(r[0][0].is_equal_approx(Vector2(160, 320)));
+		CHECK(r[0][1].is_equal_approx(Vector2(122, 250)));
+		CHECK(r[0][2].is_equal_approx(Vector2(121.412682, 225.038757)));
+		REQUIRE_MESSAGE(r[1].size() == 2, "The resulting clipped line should have 2 vertices.");
+		CHECK(r[1][0].is_equal_approx(Vector2(53.07737, 116.143021)));
+		CHECK(r[1][1].is_equal_approx(Vector2(55, 70)));
+	}
+}
+} // namespace TestGeometry2D
+
+#endif // TEST_GEOMETRY_2D_H

tests/test_main.cpp

@@ -43,6 +43,7 @@
 #include "test_curve.h"
 #include "test_expression.h"
 #include "test_file_access.h"
+#include "test_geometry_2d.h"
 #include "test_gradient.h"
 #include "test_gui.h"
 #include "test_json.h"