def test_init_circle(self):
circle = ConstructionCircle((0., 0.), 5)
point = circle.point_at(HALF_PI)
self.assertAlmostEqual(point[0], 0., 3)
self.assertAlmostEqual(point[1], 5., 3)
point = circle.point_at(HALF_PI / 2)
self.assertAlmostEqual(point[0], 3.5355, 3)
self.assertAlmostEqual(point[1], 3.5355, 3)
def test_init_circle():
circle = ConstructionCircle((0., 0.), 5)
point = circle.point_at(HALF_PI)
assert isclose(point[0], 0., abs_tol=1e-4)
assert isclose(point[1], 5., abs_tol=1e-4)
point = circle.point_at(HALF_PI / 2)
assert isclose(point[0], 3.5355, abs_tol=1e-4)
assert isclose(point[1], 3.5355, abs_tol=1e-4)
def test_intersect_ray_pass(self):
circle = ConstructionCircle((10., 10.), 3)
ray1_hor = ConstructionRay((10., 15.), angle=0)
ray2_hor = ConstructionRay((10., 5.), angle=0)
ray1_vert = ConstructionRay((5., 10.), angle=HALF_PI)
ray2_vert = ConstructionRay((15., 10.), angle=-HALF_PI)
ray3 = ConstructionRay((13.24, 14.95), angle=0.3992)
self.assertFalse(circle.intersect_ray(ray1_hor))
self.assertFalse(circle.intersect_ray(ray2_hor))
self.assertFalse(circle.intersect_ray(ray1_vert))
self.assertFalse(circle.intersect_ray(ray2_vert))
self.assertFalse(circle.intersect_ray(ray3))
def test_intersect_circle_intersect():
def check_intersection(m, p1, p2, abs_tol=1e-4):
p1 = Vec2(p1)
p2 = Vec2(p2)
circle2 = ConstructionCircle(m, 1.5)
points = circle1.intersect_circle(circle2, abs_tol=abs_tol)
assert len(points) == 2
a, b = points
result1 = is_close_points(a, p1, abs_tol=abs_tol) and is_close_points(
b, p2, abs_tol=abs_tol)
result2 = is_close_points(a, p2, abs_tol=abs_tol) and is_close_points(
b, p1, abs_tol=abs_tol)
return result1 or result2
circle1 = ConstructionCircle((40, 20), 5)
assert check_intersection((46., 20.), (44.8958, 21.0153),
(44.8958, 18.9847)) is True
assert check_intersection((44., 20.), (44.8438, 21.2402),
(44.8438, 18.7598)) is True
assert check_intersection((40., 26.), (38.9847, 24.8958),
(41.0153, 24.8958)) is True
assert check_intersection((40., 24.), (38.7598, 24.8438),
(41.2402, 24.8438)) is True
assert check_intersection((34., 20.), (35.1042, 18.9847),
(35.1042, 21.0153)) is True
# assert check_intersection( (36.,20.), (35.1563, 18.7598), (35.1563, 21.2402)))
assert check_intersection((40., 14.), (38.9847, 15.1042),
(41.0153, 15.1042)) is True
assert check_intersection((40., 14.), (38.9847, 15.1042),
(41.0153, 15.1042)) is True
assert check_intersection((36.8824, 17.4939), (35.4478, 17.9319),
(37.0018, 15.9987)) is True
assert check_intersection((35.3236, 16.2408), (35.5481, 17.7239),
(36.8203, 16.1413)) is True
def test_create_3P(self):
p1 = (3., 3.)
p2 = (5., 7.)
p3 = (12., 5.)
circle = ConstructionCircle.from_3p(p1, p2, p3)
self.assertAlmostEqual(circle.center[0], 7.6875, 4)
self.assertAlmostEqual(circle.center[1], 3.15625, 4)
self.assertAlmostEqual(circle.radius, 4.6901, 4)
def test_create_3P():
p1 = (3., 3.)
p2 = (5., 7.)
p3 = (12., 5.)
circle = ConstructionCircle.from_3p(p1, p2, p3)
assert isclose(circle.center[0], 7.6875, abs_tol=1e-4)
assert isclose(circle.center[1], 3.15625, abs_tol=1e-4)
assert isclose(circle.radius, 4.6901, abs_tol=1e-4)
def test_intersect_ray_intersect(self):
circle = ConstructionCircle((10., 10.), 3)
ray_vert = ConstructionRay((8.5, 10.), angle=HALF_PI)
cross_points = circle.intersect_ray(ray_vert)
self.assertEqual(len(cross_points), 2)
p1, p2 = cross_points
if p1[1] > p2[1]: p1, p2 = p2, p1
self.assertTrue(is_close_points(p1, (8.5, 7.4019), abs_tol=1e-4))
self.assertTrue(is_close_points(p2, (8.5, 12.5981), abs_tol=1e-4))
ray_hor = ConstructionRay((10, 8.5), angle=0.)
cross_points = circle.intersect_ray(ray_hor)
self.assertEqual(len(cross_points), 2)
p1, p2 = cross_points
if p1[0] > p2[0]: p1, p2 = p2, p1
self.assertTrue(is_close_points(p1, (7.4019, 8.5), abs_tol=1e-4))
self.assertTrue(is_close_points(p2, (12.5981, 8.5), abs_tol=1e-4))
ray_slope = ConstructionRay((5, 5), (16, 12))
cross_points = circle.intersect_ray(ray_slope)
self.assertEqual(len(cross_points), 2)
p1, p2 = cross_points
if p1[0] > p2[0]: p1, p2 = p2, p1
self.assertTrue(is_close_points(p1, (8.64840, 7.3217), abs_tol=1e-4))
self.assertTrue(is_close_points(p2, (12.9986, 10.0900), abs_tol=1e-4))
# ray with slope through midpoint
ray_slope = ConstructionRay((10, 10), angle=HALF_PI / 2)
cross_points = circle.intersect_ray(ray_slope)
self.assertEqual(len(cross_points), 2)
p1, p2 = cross_points
if p1[0] > p2[0]: p1, p2 = p2, p1
# print (p1[0], p1[1], p2[0], p2[1])
self.assertTrue(is_close_points(p1, (7.8787, 7.8787), abs_tol=1e-4))
self.assertTrue(is_close_points(p2, (12.1213, 12.1213), abs_tol=1e-4))
# horizontal ray through midpoint
ray_hor = ConstructionRay((10, 10), angle=0)
cross_points = circle.intersect_ray(ray_hor)
self.assertEqual(len(cross_points), 2)
p1, p2 = cross_points
if p1[0] > p2[0]: p1, p2 = p2, p1
# print (p1[0], p1[1], p2[0], p2[1])
self.assertTrue(is_close_points(p1, (7, 10), abs_tol=1e-5))
self.assertTrue(is_close_points(p2, (13, 10), abs_tol=1e-5))
# vertical ray through midpoint
ray_vert = ConstructionRay((10, 10), angle=HALF_PI)
cross_points = circle.intersect_ray(ray_vert)
self.assertEqual(len(cross_points), 2)
p1, p2 = cross_points
if p1[1] > p2[1]: p1, p2 = p2, p1
# print (p1[0], p1[1], p2[0], p2[1])
self.assertTrue(is_close_points(p1, (10, 7), abs_tol=1e-5))
self.assertTrue(is_close_points(p2, (10, 13), abs_tol=1e-5))
def test_intersect_circle_pass():
M1 = (30, 30)
M2 = (40, 40)
M3 = (30.3, 30.3)
circle1 = ConstructionCircle(M1, 5)
circle2 = ConstructionCircle(M1, 3)
circle3 = ConstructionCircle(M2, 3)
circle4 = ConstructionCircle(M3, 3)
cross_points = circle1.intersect_circle(circle2)
assert len(cross_points) == 0
cross_points = circle2.intersect_circle(circle3)
assert len(cross_points) == 0
cross_points = circle1.intersect_circle(circle4)
assert len(cross_points) == 0
def test_intersect_circle_pass(self):
M1 = (30, 30)
M2 = (40, 40)
M3 = (30.3, 30.3)
circle1 = ConstructionCircle(M1, 5)
circle2 = ConstructionCircle(M1, 3)
circle3 = ConstructionCircle(M2, 3)
circle4 = ConstructionCircle(M3, 3)
cross_points = circle1.intersect_circle(circle2)
self.assertFalse(cross_points)
cross_points = circle2.intersect_circle(circle3)
self.assertFalse(cross_points)
cross_points = circle1.intersect_circle(circle4)
self.assertFalse(cross_points)
def check_intersection(m, p1, p2, abs_tol=1e-4):
p1 = Vec2(p1)
p2 = Vec2(p2)
circle2 = ConstructionCircle(m, 1.5)
points = circle1.intersect_circle(circle2, abs_tol=abs_tol)
self.assertEqual(len(points), 2)
a, b = points
result1 = is_close_points(a, p1, abs_tol=abs_tol) and is_close_points(b, p2, abs_tol=abs_tol)
result2 = is_close_points(a, p2, abs_tol=abs_tol) and is_close_points(b, p1, abs_tol=abs_tol)
return result1 or result2
def test_tangent(self):
circle = ConstructionCircle((0., 0.), 5.)
tangent = circle.tangent(HALF_PI / 2)
self.assertAlmostEqual(tangent._slope, -1, 4)
tangent = circle.tangent(-HALF_PI / 2)
self.assertAlmostEqual(tangent._slope, 1, 4)
tangent = circle.tangent(0)
self.assertTrue(tangent._is_vertical)
tangent = circle.tangent(HALF_PI)
self.assertTrue(tangent._is_horizontal)
def test_tangent():
circle = ConstructionCircle((0., 0.), 5.)
tangent = circle.tangent(HALF_PI / 2)
assert isclose(tangent._slope, -1, abs_tol=1e-4)
tangent = circle.tangent(-HALF_PI / 2)
assert isclose(tangent._slope, 1, abs_tol=1e-4)
tangent = circle.tangent(0)
assert tangent._is_vertical is True
tangent = circle.tangent(HALF_PI)
assert tangent._is_horizontal is True
def test_intersect_circle_touch(self):
def check_touch(m, t, abs_tol=1e-9):
circle2 = ConstructionCircle(m, 1.5)
points = circle1.intersect_circle(circle2, 4)
self.assertEqual(len(points), 1)
return is_close_points(points[0], Vec2(t), abs_tol=abs_tol)
circle1 = ConstructionCircle((20, 20), 5)
self.assertTrue(check_touch((26.5, 20.), (25., 20.)))
self.assertTrue(check_touch((20., 26.5), (20., 25.)))
self.assertTrue(check_touch((13.5, 20.), (15., 20.)))
self.assertTrue(check_touch((20., 13.5), (20., 15.)))
self.assertTrue(check_touch((14.9339, 15.9276), (16.1030, 16.8674), abs_tol=1e-4))
self.assertTrue(check_touch((23.5, 20.), (25., 20.)))
self.assertTrue(check_touch((20., 23.5), (20., 25.)))
self.assertTrue(check_touch((16.5, 20.), (15., 20.)))
self.assertTrue(check_touch((20., 16.5), (20., 15.)))
self.assertTrue(check_touch((17.2721, 17.8071), (16.1030, 16.8673), abs_tol=1e-4))
def test_intersect_ray_touch(self):
def test_touch(testnum, x, y, _angle, abs_tol=1e-6):
result = True
ray = ConstructionRay((x, y), angle=_angle)
points = circle.intersect_ray(ray, abs_tol=abs_tol)
if len(points) != 1:
result = False
else:
point = points[0]
# print ("{0}: x= {1:.{places}f} y= {2:.{places}f} : x'= {3:.{places}f} y' = {4:.{places}f}".format(testnum, x, y, point[0], point[1], places=places))
if not isclose(point[0], x, abs_tol=abs_tol):
result = False
if not isclose(point[1], y, abs_tol=abs_tol):
result = False
return result
circle = ConstructionCircle((10., 10.), 3)
self.assertTrue(test_touch(1, 10., 13., 0))
self.assertTrue(test_touch(2, 10., 7., 0))
self.assertTrue(test_touch(3, 7., 10., HALF_PI))
self.assertTrue(test_touch(4, 13., 10., -HALF_PI))
self.assertTrue(test_touch(5, 8.8341, 12.7642, 0.3991568, abs_tol=1e-4))
def test_within():
circle = ConstructionCircle((0., 0.), 5)
p1 = (3., 2.)
p2 = (4., 5.)
assert circle.inside(p1) is True
assert circle.inside(p2) is False
def test_within(self):
circle = ConstructionCircle((0., 0.), 5)
p1 = (3., 2.)
p2 = (4., 5.)
self.assertTrue(circle.inside(p1))
self.assertFalse(circle.inside(p2))
def check_touch(m, t, abs_tol=1e-9):
circle2 = ConstructionCircle(m, 1.5)
points = circle1.intersect_circle(circle2, 4)
self.assertEqual(len(points), 1)
return is_close_points(points[0], Vec2(t), abs_tol=abs_tol)