Add Circle.intersect() (#235)

* circle intersect

* fix test

* slightly faster formula

* better docs, added a test

* added a comment, fixed missing newline

* use more permissive comparisons

* fix docs a bit

docs/circle.rst

@@ -404,4 +404,20 @@ Circle Methods
         as the original `Circle` object. The function takes no arguments and returns the
         new `Circle` object.
 
-      .. ## Circle.copy ##
+      .. ## Circle.copy ##
+
+    .. method:: intersect
+
+        | :sl:`finds intersections between the circle and another shape`
+        | :sg:`intersect(Circle) -> list[Tuple[float, float]]`
+
+        Returns a list of intersection points between the circle and another shape.
+        The other shape must be a `Circle` object.
+        If the circle does not intersect or has infinite intersections, an empty list is returned.
+
+        .. note::
+            The shape argument must be an instance of the `Circle` class.
+            Passing a tuple or list of coordinates representing the shape is not supported,
+            as the type of shape cannot be determined from coordinates alone.
+
+      .. ## Circle.intersect ##

docs/geometry.rst

@@ -70,6 +70,8 @@ performing transformations and checking for collisions with other objects.
 
     as_rect: Returns the smallest rectangle that contains the circle.
 
+    intersect: Finds intersections between the circle and another shape.
+
 Additionally to these, the circle shape can also be used as a collider for the ``geometry.raycast`` function.
 
 Line

geometry.pyi

@@ -208,6 +208,7 @@ class Circle:
     def rotate_ip(
         self, angle: float, rotation_point: Coordinate = Circle.center
     ) -> None: ...
+    def intersect(self, other: Circle) -> List[Tuple[float, float]]: ...
 
 class Polygon:
     vertices: List[Coordinate]

src_c/circle.c

@@ -732,6 +732,28 @@ pg_circle_collidelistall(pgCircleObject *self, PyObject *arg)
     return ret;
 }
 
+static PyObject *
+pg_circle_intersect(pgCircleObject *self, PyObject *arg)
+{
+    pgCircleBase *scirc = &self->circle;
+
+    /* max number of intersections when supporting: Circle (2), */
+    double intersections[4];
+    int num = 0;
+
+    if (pgCircle_Check(arg)) {
+        pgCircleBase *other = &pgCircle_AsCircle(arg);
+        num = pgIntersection_CircleCircle(scirc, other, intersections);
+    }
+    else {
+        PyErr_Format(PyExc_TypeError, "Argument must be a CircleType, got %s",
+                     Py_TYPE(arg)->tp_name);
+        return NULL;
+    }
+
+    return pg_PointList_FromArrayDouble(intersections, num * 2);
+}
+
 static struct PyMethodDef pg_circle_methods[] = {
     {"collidecircle", (PyCFunction)pg_circle_collidecircle, METH_FASTCALL,
      NULL},
@@ -752,6 +774,7 @@ static struct PyMethodDef pg_circle_methods[] = {
     {"copy", (PyCFunction)pg_circle_copy, METH_NOARGS, NULL},
     {"rotate", (PyCFunction)pg_circle_rotate, METH_FASTCALL, NULL},
     {"rotate_ip", (PyCFunction)pg_circle_rotate_ip, METH_FASTCALL, NULL},
+    {"intersect", (PyCFunction)pg_circle_intersect, METH_O, NULL},
     {NULL, NULL, 0, NULL}};
 
 /* numeric functions */

src_c/collisions.c

@@ -588,3 +588,48 @@ pgRaycast_LineCircle(pgLineBase *line, pgCircleBase *circle, double max_t,
 
     return 1;
 }
+
+static int
+pgIntersection_CircleCircle(pgCircleBase *A, pgCircleBase *B,
+                            double *intersections)
+{
+    double dx = B->x - A->x;
+    double dy = B->y - A->y;
+    double d2 = dx * dx + dy * dy;
+    double r_sum = A->r + B->r;
+    double r_diff = A->r - B->r;
+    double r_sum2 = r_sum * r_sum;
+    double r_diff2 = r_diff * r_diff;
+
+    if (d2 > r_sum2 || d2 < r_diff2) {
+        return 0;
+    }
+
+    if (double_compare(d2, 0) && double_compare(A->r, B->r)) {
+        return 0;
+    }
+
+    double d = sqrt(d2);
+    double a = (d2 + A->r * A->r - B->r * B->r) / (2 * d);
+    double h = sqrt(A->r * A->r - a * a);
+
+    double xm = A->x + a * (dx / d);
+    double ym = A->y + a * (dy / d);
+
+    double xs1 = xm + h * (dy / d);
+    double ys1 = ym - h * (dx / d);
+    double xs2 = xm - h * (dy / d);
+    double ys2 = ym + h * (dx / d);
+
+    if (double_compare(d2, r_sum2) || double_compare(d2, r_diff2)) {
+        intersections[0] = xs1;
+        intersections[1] = ys1;
+        return 1;
+    }
+
+    intersections[0] = xs1;
+    intersections[1] = ys1;
+    intersections[2] = xs2;
+    intersections[3] = ys2;
+    return 2;
+}

src_c/include/collisions.h

@@ -48,5 +48,8 @@ pgCollision_PolygonLine(pgPolygonBase *, pgLineBase *, int);
 static int
 pgCollision_CirclePolygon(pgCircleBase *, pgPolygonBase *, int);
 
+static int
+pgIntersection_CircleCircle(pgCircleBase *A, pgCircleBase *B,
+                            double *intersections);
 
 #endif /* ~_PG_COLLISIONS_H */

src_c/include/geometry.h

@@ -147,4 +147,12 @@ PG_FREEPOLY_COND(pgPolygonBase *poly, int was_sequence)
     }
 }
 
+static int
+double_compare(double a, double b)
+{
+    /* Uses both a fixed epsilon and an adaptive epsilon */
+    const double e = 1e-6;
+    return fabs(a - b) < e || fabs(a - b) <= e * MAX(fabs(a), fabs(b));
+}
+
 #endif /* ~_GEOMETRY_H */

test/test_circle.py

@@ -1,12 +1,10 @@
-import unittest
-
 import math
+import unittest
 from math import sqrt
 
-from pygame import Vector2, Vector3
-from pygame import Rect
-
 from geometry import Circle, Line, Polygon, regular_polygon
+from pygame import Rect
+from pygame import Vector2, Vector3
 
 E_T = "Expected True, "
 E_F = "Expected False, "
@@ -1482,6 +1480,61 @@ def test_collidelistall(self):
         for objects, expected in zip([circles, rects, lines, polygons], expected):
             self.assertEqual(c.collidelistall(objects), expected)
 
+    def test_intersect_argtype(self):
+        """Tests if the function correctly handles incorrect types as parameters"""
+
+        invalid_types = (None, "1", (1,), 1, (1, 2, 3), True, False)
+
+        c = Circle(10, 10, 4)
+
+        for value in invalid_types:
+            with self.assertRaises(TypeError):
+                c.intersect(value)
+
+    def test_intersect_argnum(self):
+        """Tests if the function correctly handles incorrect number of parameters"""
+        c = Circle(10, 10, 4)
+
+        circles = [(Circle(10, 10, 4) for _ in range(100))]
+        for size in range(len(circles)):
+            with self.assertRaises(TypeError):
+                c.intersect(*circles[:size])
+
+    def test_intersect_return_type(self):
+        """Tests if the function returns the correct type"""
+        c = Circle(10, 10, 4)
+
+        objects = [
+            Circle(10, 10, 4),
+            Circle(10, 10, 400),
+            Circle(10, 10, 1),
+            Circle(15, 10, 10),
+        ]
+
+        for object in objects:
+            self.assertIsInstance(c.intersect(object), list)
+
+    def test_intersect(self):
+
+        # Circle
+        c = Circle(10, 10, 4)
+        c2 = Circle(10, 10, 2)
+        c3 = Circle(100, 100, 1)
+        c3_1 = Circle(10, 10, 400)
+        c4 = Circle(16, 10, 7)
+        c5 = Circle(18, 10, 4)
+
+        for circle in [c, c2, c3, c3_1]:
+            self.assertEqual(c.intersect(circle), [])
+
+        # intersecting circle
+        self.assertEqual(
+            [(10.25, 6.007820144332172), (10.25, 13.992179855667828)], c.intersect(c4)
+        )
+
+        # touching
+        self.assertEqual([(14.0, 10.0)], c.intersect(c5))
+
 
 if __name__ == "__main__":
     unittest.main()