def test_intersection_at_one_point_in_nested_circles(self):
circle1 = Circle(Point(0, 0), 4)
circle2 = Circle(Point(2, 0), 2)
self.assertEqual(circle1.intersection(circle2), [Point(4, 0)])
circle1 = Circle(Point(0, 0), 4)
circle2 = Circle(Point(0, 2), 2)
self.assertEqual(circle1.intersection(circle2), [Point(0, 4)])
def test_intersection_at_one_point_with_not_nested_circles(self):
circle1 = Circle(Point(0, 0), 2)
circle2 = Circle(Point(3, 0), 1)
self.assertEqual(circle1.intersection(circle2), [Point(2, 0)])
circle1 = Circle(Point(0, 0), 2)
circle2 = Circle(Point(0, 3), 1)
self.assertEqual(circle1.intersection(circle2), [Point(0, 2)])
def test_intersection_with_circles_that_do_not_intersect(self):
# with not nested circles
circle1 = Circle(Point(0, 0), 2)
circle2 = Circle(Point(6, 6), 3)
self.assertEqual(circle1.intersection(circle2), [])
# with nested circles
circle3 = Circle(Point(0, 0), 4)
circle4 = Circle(Point(2, 0), 1)
self.assertEqual(circle3.intersection(circle4), [])
def test_intersection_at_two_points(self):
# with circles with centers at different x and different y
circle1 = Circle(Point(0, 0), 1)
circle2 = Circle(Point(1, 1), 1)
self.assertEqual(circle1.intersection(circle2),
[Point(1, 0), Point(0, 1)])
# with each center outside the other circle
circle1 = Circle(Point(-3, 0), 5)
circle2 = Circle(Point(3, 0), 5)
self.assertEqual(circle1.intersection(circle2),
[Point(0, 4), Point(0, -4)])
circle1 = Circle(Point(0, -3), 5)
circle2 = Circle(Point(0, 3), 5)
self.assertEqual(circle1.intersection(circle2),
[Point(4, 0), Point(-4, 0)])
# with each's center inside the other circle
circle1 = Circle(Point(0, 0), math.sqrt(65))
circle2 = Circle(Point(4, 0), 5)
self.assertAlmostEqual(
circle1.intersection(circle2),
[Point(7.0, 4.0, 0.0), Point(7.0, -4.0, 0.0)])
circle1 = Circle(Point(0, 0), math.sqrt(65))
circle2 = Circle(Point(0, 4), 5)
self.assertAlmostEqual(
circle1.intersection(circle2),
[Point(4.0, 7.0, 0.0), Point(-4.0, 7.0, 0.0)])
# with one center inside the other circle and the line that contains both intersection points containing one circle's center
circle1 = Circle(Point(0, 0), 5)
circle2 = Circle(Point(-4, 0), 3)
self.assertAlmostEqual(circle1.intersection(circle2),
[Point(-4, 3), Point(-4, -3)])
circle1 = Circle(Point(0, 0), 5)
circle2 = Circle(Point(0, -4), 3)
self.assertAlmostEqual(circle1.intersection(circle2),
[Point(3, -4), Point(-3, -4)])
# with each's center inside the other circle and the line that contains both intersection points separating both centers
circle1 = Circle(Point(0, 0), 3)
circle2 = Circle(Point(2, 0), 3)
self.assertAlmostEqual(
circle1.intersection(circle2),
[Point(1, math.sqrt(8)),
Point(1, -math.sqrt(8))])
# with one center in the perimeter of the other circle
circle1 = Circle(Point(0, 0), 1)
circle2 = Circle(Point(1, 0), 1)
self.assertAlmostEqual(circle1.intersection(circle2), [
Point(1.0 / 2, math.sqrt(3.0 / 4)),
Point(1.0 / 2, -math.sqrt(3.0 / 4))
])
circle1 = Circle(Point(0, 0), 1)
circle2 = Circle(Point(0, 1), 1)
self.assertAlmostEqual(circle1.intersection(circle2), [
Point(math.sqrt(3.0 / 4), 1.0 / 2),
Point(-math.sqrt(3.0 / 4), 1.0 / 2)
])
def points_at_linear_offset(self, reference_point, offset):
circle1 = Circle(self.center_point(), self.radius())
circle2 = Circle(reference_point, abs(offset))
intersections = circle1.intersection(circle2)
if circle1.almost_equal_to(circle2):
return [self]
return filter(lambda point: self.includes_point(point), intersections)
def test_intersection_with_concentric_circles(self):
circle1 = Circle(Point(3, 3), 6)
circle2 = Circle(Point(3, 3), 8)
self.assertEqual(circle1.intersection(circle2), [])
def test_intersection_between_equal_circles(self):
circle = Circle(Point(45, 7), 9)
self.assertEqual(circle.intersection(circle), [circle])