Add methods to generate random points within a circle and a ring

core/math/2d/geometry/goost_geometry_2d.cpp

@@ -400,3 +400,22 @@ Vector<Point2> GoostGeometry2D::circle(real_t p_radius, real_t p_max_error) {
 
 	return regular_polygon(vertex_count, p_radius); // vertex count == edge count
 }
+
+Vector2 GoostGeometry2D::rand_point_in_circle(real_t p_radius) {
+	real_t r = Math::sqrt(Math::random(0.0, 1.0)) * p_radius;
+	real_t t = Math::random(0.0, 1.0) * Math_TAU;
+	return Vector2(r * Math::cos(t), r * Math::sin(t));
+}
+
+Vector2 GoostGeometry2D::rand_point_on_circle(real_t p_radius) {
+	real_t t = Math::random(0.0, 1.0) * Math_TAU;
+	return Vector2(p_radius * Math::cos(t), p_radius * Math::sin(t));
+}
+
+Vector2 GoostGeometry2D::rand_point_in_ring(real_t p_min_radius, real_t p_max_radius) {
+	const double r2_max = p_max_radius * p_max_radius;
+	const double r2_min = p_min_radius * p_min_radius;
+	real_t r = Math::sqrt(Math::random(0.0, 1.0) * (r2_max - r2_min) + r2_min);
+	real_t t = Math::random(0.0, 1.0) * Math_TAU;
+	return Vector2(r * Math::cos(t), r * Math::sin(t));
+}

core/math/2d/geometry/goost_geometry_2d.h

@@ -84,6 +84,11 @@ class GoostGeometry2D {
 	static Vector<Point2> regular_polygon(int p_edge_count, real_t p_size);
 	static Vector<Point2> circle(real_t p_radius, real_t p_max_error = 0.25);
 
+	/* Random methods */
+	static Vector2 rand_point_in_circle(real_t p_radius);
+	static Vector2 rand_point_on_circle(real_t p_radius);
+	static Vector2 rand_point_in_ring(real_t p_min_radius, real_t p_max_radius);
+
 public:
 	static void initialize();
 	static void finalize();

core/math/2d/geometry/goost_geometry_2d_bind.cpp

@@ -360,6 +360,18 @@ Vector<Point2> _GoostGeometry2D::circle(real_t p_radius, real_t p_max_error) con
 	return GoostGeometry2D::circle(p_radius, p_max_error);
 }
 
+Vector2 _GoostGeometry2D::rand_point_in_circle(real_t p_radius) const {
+	return GoostGeometry2D::rand_point_in_circle(p_radius);
+}
+
+Vector2 _GoostGeometry2D::rand_point_on_circle(real_t p_radius) const {
+	return GoostGeometry2D::rand_point_on_circle(p_radius);
+}
+
+Vector2 _GoostGeometry2D::rand_point_in_ring(real_t p_min_radius, real_t p_max_radius) const {
+	return GoostGeometry2D::rand_point_in_ring(p_min_radius, p_max_radius);
+}
+
 void _GoostGeometry2D::_bind_methods() {
 	ClassDB::bind_method(D_METHOD("merge_polygons", "polygon_a", "polygon_b", "params"), &_GoostGeometry2D::merge_polygons, DEFVAL(Variant()));
 	ClassDB::bind_method(D_METHOD("clip_polygons", "polygon_a", "polygon_b", "params"), &_GoostGeometry2D::clip_polygons, DEFVAL(Variant()));
@@ -405,6 +417,10 @@ void _GoostGeometry2D::_bind_methods() {
 	ClassDB::bind_method(D_METHOD("regular_polygon", "sides", "size"), &_GoostGeometry2D::regular_polygon, DEFVAL(64.0));
 	ClassDB::bind_method(D_METHOD("circle", "radius", "max_error"), &_GoostGeometry2D::circle, DEFVAL(0.25));
 
+	ClassDB::bind_method(D_METHOD("rand_point_in_circle", "radius"), &_GoostGeometry2D::rand_point_in_circle);
+	ClassDB::bind_method(D_METHOD("rand_point_on_circle", "radius"), &_GoostGeometry2D::rand_point_on_circle);
+	ClassDB::bind_method(D_METHOD("rand_point_in_ring", "min_radius", "max_radius"), &_GoostGeometry2D::rand_point_in_ring);
+
 	BIND_ENUM_CONSTANT(OPERATION_NONE);
 	BIND_ENUM_CONSTANT(OPERATION_UNION);
 	BIND_ENUM_CONSTANT(OPERATION_DIFFERENCE);

core/math/2d/geometry/goost_geometry_2d_bind.h

@@ -76,6 +76,10 @@ class _GoostGeometry2D : public Object {
 	Vector<Point2> regular_polygon(int p_edge_count, real_t p_size) const;
 	Vector<Point2> circle(real_t p_radius, real_t p_max_error) const;
 
+	Vector2 rand_point_in_circle(real_t p_radius) const;
+	Vector2 rand_point_on_circle(real_t p_radius) const;
+	Vector2 rand_point_in_ring(real_t p_min_radius, real_t p_max_radius) const;
+
 	_GoostGeometry2D();
 };
 

doc/GoostGeometry2D.xml

@@ -417,6 +417,45 @@
 				Returns the total length of the segments representing the polyline. See also [method polygon_perimeter].
 			</description>
 		</method>
+		<method name="rand_point_in_circle" qualifiers="const">
+			<return type="Vector2">
+			</return>
+			<argument index="0" name="radius" type="float">
+			</argument>
+			<description>
+				Returns a random point uniformly distributed within a circle, such that [method Geometry.is_point_in_circle] shall return [code]true[/code] given the same [code]radius[/code].
+				This method is faster than [method rand_point_in_ring] and equivalent to:
+				[codeblock]
+				GoostGeometry2D.rand_point_in_ring(0.0, radius)
+				[/codeblock]
+			</description>
+		</method>
+		<method name="rand_point_in_ring" qualifiers="const">
+			<return type="Vector2">
+			</return>
+			<argument index="0" name="min_radius" type="float">
+			</argument>
+			<argument index="1" name="max_radius" type="float">
+			</argument>
+			<description>
+				Returns a random point uniformly distributed within the ring's area confined by inner (hole) and outer (boundary) circles as specified with [code]min_radius[/code] and [code]max_radius[/code] respectively.
+				The method can be used to generate points distributed strictly on the circle's boundary if [code]min_radius == max_radius[/code] which is equivalent to [method rand_point_on_circle].
+			</description>
+		</method>
+		<method name="rand_point_on_circle" qualifiers="const">
+			<return type="Vector2">
+			</return>
+			<argument index="0" name="radius" type="float">
+			</argument>
+			<description>
+				Returns a random point uniformly distributed strictly [b]on[/b] the circle's boundary.
+				This method is faster than [method rand_point_in_ring] with the following equivalent code:
+				[codeblock]
+				GoostGeometry2D.rand_point_in_ring(radius, radius)
+				[/codeblock]
+				[b]Note[/b]: the point may slightly deviate from the actual circle's boundary due to floating point error accumulation.
+			</description>
+		</method>
 		<method name="regular_polygon" qualifiers="const">
 			<return type="PoolVector2Array">
 			</return>

tests/project/goost/core/math/2d/geometry/test_geometry_2d.gd

@@ -303,3 +303,27 @@ func test_regular_polygon():
 func test_circle():
 	solution = GoostGeometry2D.circle(SIZE, 0.25)
 	assert_eq(solution.size(), 32)
+
+
+func test_rand_point_in_circle():
+	var max_radius = 10.0
+	for i in 100:
+		var point = GoostGeometry2D.rand_point_in_circle(max_radius)
+		assert_true(Geometry.is_point_in_circle(point, Vector2(), max_radius))
+		assert_lt(point.length(), max_radius)
+
+
+func test_rand_point_on_circle():
+	var max_radius = 50.0
+	for i in 100:
+		var point = GoostGeometry2D.rand_point_on_circle(max_radius)
+		assert_true(is_equal_approx(point.length(), max_radius))
+
+
+func test_rand_point_in_ring():
+	var min_radius = 10.0
+	var max_radius = 100.0
+	for i in 100:
+		var point = GoostGeometry2D.rand_point_in_ring(min_radius, max_radius)
+		assert_lt(point.length(), max_radius)
+		assert_gt(point.length(), min_radius)