def test_vertices():
circle = ConstructionCircle((0, 0), 1.0)
vertices = list(circle.vertices([0, math.pi * 0.5, math.pi, math.pi * 1.5]))
assert vertices[0].isclose((1, 0))
assert vertices[1].isclose((0, 1))
assert vertices[2].isclose((-1, 0))
assert vertices[3].isclose((0, -1))
def test_init_circle():
circle = ConstructionCircle((0.0, 0.0), 5)
point = circle.point_at(HALF_PI)
assert isclose(point[0], 0.0, abs_tol=1e-4)
assert isclose(point[1], 5.0, 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():
circle = ConstructionCircle((10.0, 10.0), 3)
ray1_hor = ConstructionRay((10.0, 15.0), angle=0)
ray2_hor = ConstructionRay((10.0, 5.0), angle=0)
ray1_vert = ConstructionRay((5.0, 10.0), angle=HALF_PI)
ray2_vert = ConstructionRay((15.0, 10.0), angle=-HALF_PI)
ray3 = ConstructionRay((13.24, 14.95), angle=0.3992)
assert len(circle.intersect_ray(ray1_hor)) == 0
assert len(circle.intersect_ray(ray2_hor)) == 0
assert len(circle.intersect_ray(ray1_vert)) == 0
assert len(circle.intersect_ray(ray2_vert)) == 0
assert len(circle.intersect_ray(ray3)) == 0
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():
p1 = (3.0, 3.0)
p2 = (5.0, 7.0)
p3 = (12.0, 5.0)
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():
circle = ConstructionCircle((10., 10.), 3)
ray_vert = ConstructionRay((8.5, 10.), angle=HALF_PI)
cross_points = circle.intersect_ray(ray_vert)
assert len(cross_points) == 2
p1, p2 = cross_points
if p1[1] > p2[1]: p1, p2 = p2, p1
assert is_close_points(p1, (8.5, 7.4019), abs_tol=1e-4) is True
assert is_close_points(p2, (8.5, 12.5981), abs_tol=1e-4) is True
ray_hor = ConstructionRay((10, 8.5), angle=0.)
cross_points = circle.intersect_ray(ray_hor)
assert len(cross_points) == 2
p1, p2 = cross_points
if p1[0] > p2[0]: p1, p2 = p2, p1
assert is_close_points(p1, (7.4019, 8.5), abs_tol=1e-4) is True
assert is_close_points(p2, (12.5981, 8.5), abs_tol=1e-4) is True
ray_slope = ConstructionRay((5, 5), (16, 12))
cross_points = circle.intersect_ray(ray_slope)
assert len(cross_points) == 2
p1, p2 = cross_points
if p1[0] > p2[0]: p1, p2 = p2, p1
assert is_close_points(p1, (8.64840, 7.3217), abs_tol=1e-4) is True
assert is_close_points(p2, (12.9986, 10.0900), abs_tol=1e-4) is True
# ray with slope through midpoint
ray_slope = ConstructionRay((10, 10), angle=HALF_PI / 2)
cross_points = circle.intersect_ray(ray_slope)
assert 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])
assert is_close_points(p1, (7.8787, 7.8787), abs_tol=1e-4) is True
assert is_close_points(p2, (12.1213, 12.1213), abs_tol=1e-4) is True
# horizontal ray through midpoint
ray_hor = ConstructionRay((10, 10), angle=0)
cross_points = circle.intersect_ray(ray_hor)
assert 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])
assert is_close_points(p1, (7, 10), abs_tol=1e-5) is True
assert is_close_points(p2, (13, 10), abs_tol=1e-5) is True
# vertical ray through midpoint
ray_vert = ConstructionRay((10, 10), angle=HALF_PI)
cross_points = circle.intersect_ray(ray_vert)
assert 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])
assert is_close_points(p1, (10, 7), abs_tol=1e-5) is True
assert is_close_points(p2, (10, 13), abs_tol=1e-5) is True
def test_cicles_do_not_intersect():
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 circle_3p(self, data: bytes):
bs = ByteStream(data)
attribs = self._build_dxf_attribs()
p1 = Vec3(bs.read_vertex())
p2 = Vec3(bs.read_vertex())
p3 = Vec3(bs.read_vertex())
circle = ConstructionCircle.from_3p(p1, p2, p3)
attribs['center'] = circle.center
attribs['radius'] = circle.radius
return self._factory('CIRCLE', dxfattribs=attribs)
def intersection(master: ConstructionLine, slaver: ConstructionArc):
res = intersection_seg_arc(slaver.center.x, slaver.center.y, slaver.radius,
master.start.x, master.start.y, master.end.x,
master.end.y)
if res == None or len(res) == 0:
return None
elif len(res) == 2:
tmp = ConstructionCircle(slaver.center, slaver.radius)
IntPointAng = Angle.from_rad(get_point_angle(tmp, res[0],
res[1])).to_degrees()
if slaver.start_angle <= slaver.end_angle and (
slaver.start_angle <= IntPointAng
and IntPointAng <= slaver.end_angle):
return res[0], res[1]
elif slaver.end_angle <= slaver.start_angle and not (
slaver.end_angle <= IntPointAng
and IntPointAng <= slaver.start_angle):
return res[0], res[1]
else:
tmp = ConstructionCircle(slaver.center, slaver.radius)
IntPointAng = Angle.from_rad(get_point_angle(tmp, res[0],
res[1])).to_degrees()
if slaver.start_angle <= slaver.end_angle and (
slaver.start_angle <= IntPointAng
and IntPointAng <= slaver.end_angle):
return res[0], res[1]
elif slaver.end_angle <= slaver.start_angle and not (
slaver.end_angle <= IntPointAng
and IntPointAng <= slaver.start_angle):
return res[0], res[1]
IntPointAng = Angle.from_rad(get_point_angle(tmp, res[2],
res[3])).to_degrees()
if slaver.start_angle <= slaver.end_angle and (
slaver.start_angle <= IntPointAng
and IntPointAng <= slaver.end_angle):
return res[2], res[3]
elif slaver.end_angle <= slaver.start_angle and not (
slaver.end_angle <= IntPointAng
and IntPointAng <= slaver.start_angle):
return res[2], res[3]
return None
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
def test_tangent():
circle = ConstructionCircle((0.0, 0.0), 5.0)
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_ray_touch():
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((10.0, 10.0), 3)
assert test_touch(1, 10.0, 13.0, 0) is True
assert test_touch(2, 10.0, 7.0, 0) is True
assert test_touch(3, 7.0, 10.0, HALF_PI) is True
assert test_touch(4, 13.0, 10.0, -HALF_PI) is True
assert test_touch(5, 8.8341, 12.7642, 0.3991568, abs_tol=1e-4) is True
def test_intersect_circle_touch():
def check_touch(m, t, abs_tol=1e-9):
circle2 = ConstructionCircle(m, 1.5)
points = circle1.intersect_circle(circle2, 4)
assert len(points) == 1
return is_close_points(points[0], Vec2(t), abs_tol=abs_tol)
circle1 = ConstructionCircle((20, 20), 5)
assert check_touch((26.5, 20.), (25., 20.)) is True
assert check_touch((20., 26.5), (20., 25.)) is True
assert check_touch((13.5, 20.), (15., 20.)) is True
assert check_touch((20., 13.5), (20., 15.)) is True
assert check_touch((14.9339, 15.9276),
(16.1030, 16.8674), abs_tol=1e-4) is True
assert check_touch((23.5, 20.), (25., 20.)) is True
assert check_touch((20., 23.5), (20., 25.)) is True
assert check_touch((16.5, 20.), (15., 20.)) is True
assert check_touch((20., 16.5), (20., 15.)) is True
assert check_touch((17.2721, 17.8071),
(16.1030, 16.8673), abs_tol=1e-4) is True
def test_intersect_line_in_two_points(start, end):
circle = ConstructionCircle((0, 0), 1.0)
assert len(circle.intersect_line(ConstructionLine(start, end))) == 2
def test_intersect_line_in_one_point(start, end):
"""The intersection calculation itself is based on intersect_ray() and is
already tested.
"""
circle = ConstructionCircle((0, 0), 1.0)
assert len(circle.intersect_line(ConstructionLine(start, end))) == 1
def test_within():
circle = ConstructionCircle((0.0, 0.0), 5)
p1 = (3.0, 2.0)
p2 = (4.0, 5.0)
assert circle.inside(p1) is True
assert circle.inside(p2) is False
def check_touch(m, t, abs_tol=1e-9):
circle2 = ConstructionCircle(m, 1.5)
points = circle1.intersect_circle(circle2, 4)
assert len(points) == 1
return is_close_points(points[0], Vec2(t), abs_tol=abs_tol)
def test_flattening():
circle = ConstructionCircle((0, 0), 1.0)
vertices = list(circle.flattening(0.01))
assert len(vertices) == 24
assert vertices[0].isclose(vertices[-1]), "expected closed polygon"
def test_arc_does_not_intersect_circle(c, r):
arc = ConstructionArc((0, 0), 1, -90, 90)
assert len(arc.intersect_circle(ConstructionCircle(c, r))) == 0
def circle(self):
return ConstructionCircle((10.0, 10.0), 3)
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_two_circles_touching_at_one_point(center, point):
circle1 = ConstructionCircle((20, 20), 5)
circle2 = ConstructionCircle(center, 1.5)
points = circle1.intersect_circle(circle2)
assert len(points) == 1
return points[0].isclose(point, abs_tol=1e-9)
def test_arc_intersect_circle_in_two_points(c, r):
arc = ConstructionArc((0, 0), 1, -90, 90)
assert len(arc.intersect_circle(ConstructionCircle(c, r))) == 2
