def test_area(self):
A = Point3D(0, 0, 2)
B = Point3D(0, 1, 2)
C = Point3D(1, 0, 2)
triangle = Triangle3D(A, B, C)
self.assertEqual(triangle.area, 0.5)
def test_vector_from_point_sub_point(self):
A = Point3D(1, 2, 3)
B = Point3D(6, 5, 4)
V = B - A
self.assertEqual(V.x, 5)
self.assertEqual(V.y, 3)
self.assertEqual(V.z, 1)
def test_point_projection_on_horizontal_plane(self):
"""
M(0.5,0.5,1.)
+
| ^ z
|
x B(1,0,0) | A(0,0,0)
< +------|--------------+
/ | /
/ + /
/ P(0.5,0.5,0) /
+---------------------+ C(0,1,0)
y
"""
A = Point3D(0, 0, 0)
B = Point3D(1, 0, 0)
C = Point3D(0, 1, 0)
P = Point3D(0.5, 0.5, 0)
M = Point3D(0.5, 0.5, 1)
plane = Plane(point=P, normal=M-P)
projection = plane.project_point(M)
self.assertAlmostEqual(projection.x, P.x)
self.assertAlmostEqual(projection.y, P.y)
self.assertAlmostEqual(projection.z, P.z)
def test_point_projection_on_vertical_plane(self):
"""
^ z
+ C(0,0,1)
/ |
/ |
/ |
M(0.5,0.5,0.5) x + P |
x---------------<----|---+ + A(0,0,0)
| /
| /
| /
+ B(0,1,0)
y
"""
A = Point3D(0,0,0)
B = Point3D(0,1,0)
C = Point3D(0,0,1)
P = Point3D(0. , 0.5, 0.5)
M = Point3D(0.5, 0.5, 0.5)
plane = Plane(point=P, normal=M-P)
projection = plane.project_point(M)
self.assertAlmostEqual(projection.x, P.x)
self.assertAlmostEqual(projection.y, P.y)
self.assertAlmostEqual(projection.z, P.z)
def test_create_segment(self):
A = Point3D(1,2,3)
B = Point3D(6,5,3)
segment = Segment3D(A,B)
self.assertEqual(segment.B.y, 5)
segment.B.y = 3
self.assertEqual(segment.B.y, 3)
segment.B = Point3D(-1, -2, -3)
self.assertEqual(segment.B.y, -2)
def test_to_cylindrical(self):
A = Point3D(2, 0, 0.5)
P = A.to_cylindrical()
self.assertAlmostEqual(P.r, 2)
self.assertAlmostEqual(P.theta, 0)
self.assertEqual(P.z, 0.5)
A = Point3D(0, 2, 0.5)
P = A.to_cylindrical()
self.assertAlmostEqual(P.r, 2.)
self.assertAlmostEqual(P.theta, pi / 2)
self.assertEqual(P.z, 0.5)
def test_triangle_and_segment_are_parallel(self):
A = Point3D(0, 0, 0)
B = Point3D(1, 0, 0)
C = Point3D(0, 1, 0)
triangle = Triangle3D(A, B, C)
S = Point3D(0., 0.5, 1)
T = Point3D(0.5, 0., 1)
segment = Segment3D(S, T)
with self.assertRaisesRegex(ValueError, 'There is no intersection'):
intersec3d_triangle_segment(triangle, segment)
def test_no_intersection(self):
A = Point3D(0, 0, 0)
B = Point3D(1, 0, 0)
C = Point3D(0, 1, 0)
triangle = Triangle3D(A, B, C)
S = Point3D(0.25, 0.25, -1)
T = Point3D(0.25, 0.25, -0.5)
segment = Segment3D(S, T)
with self.assertRaisesRegex(ValueError, 'There is no intersection'):
intersec3d_triangle_segment(triangle, segment)
def test_triangle_and_segment_are_in_same_plane(self):
A = Point3D(0, 0, 0)
B = Point3D(1, 0, 0)
C = Point3D(0, 1, 0)
triangle = Triangle3D(A, B, C)
S = Point3D(0., 0.5, 0)
T = Point3D(0.5, 0., 0)
segment = Segment3D(S, T)
msg = 'Triangle and segment are in the same plane'
with self.assertRaisesRegex(ValueError, msg):
intersec3d_triangle_segment(triangle, segment)
def test_triangle_is_a_point(self):
A = Point3D(0, 0, 0)
B = Point3D(0, 0, 0)
C = Point3D(0, 0, 0)
triangle = Triangle3D(A, B, C)
S = Point3D(0.25, 0.25, -1)
T = Point3D(0.25, 0.25, 1)
segment = Segment3D(S, T)
msg = 'Triangle is degenerated \(a segment or point\)'
with self.assertRaisesRegex(ValueError, msg):
intersec3d_triangle_segment(triangle, segment)
def test_normal(self):
A = Point3D(3, 0, 0)
B = Point3D(0, 6, 0)
C = Point3D(0, 0, 9)
triangle = Triangle3D(A, B, C)
E = triangle.center
self.assertAlmostEqual(E.x, 1.)
self.assertAlmostEqual(E.y, 2.)
self.assertAlmostEqual(E.z, 3.)
def test_symetric_point(self):
A = Point3D(0, 0, 0)
B = Point3D(0, 1, 0)
C = Point3D(1, 0, 0)
triangle = Triangle3D(A, B, C)
P = Point3D(1, 2, -3)
S = triangle.symetric_point(P)
self.assertEqual(S.x, 1)
self.assertEqual(S.y, 2)
self.assertEqual(S.z, 3)
def test_create_triangle(self):
A = Point3D(0, 0, 0)
B = Point3D(0, 1, 0)
C = Point3D(1, 0, 0)
triangle = Triangle3D(A, B, C)
self.assertEqual(triangle.B.y, 1)
# Change coordiante.
triangle.B.y = 3
self.assertEqual(triangle.B.y, 3)
# Change point.
triangle.B = Point3D(-1, -2, -3)
self.assertEqual(triangle.B.y, -2)
def test_creation(self):
A = Point3D(0, 0, 0)
B = Point3D(1, 0, 0)
C = Point3D(0, 1, 0)
P = Point3D(0.5, 0.5, 0)
M = Point3D(0.5, 0.5, 1)
normal = M - P
plane = Plane(point=P, normal=normal)
self.assertEqual(plane.point.x, 0.5)
self.assertEqual(plane.normal.z, 1)
def test_intersection_in_triangle(self):
"""
C T y ^
| - / | z
| I - |/
A--/--------B +-----> x
S
"""
A = Point3D(0, 0, 0)
B = Point3D(1, 0, 0)
C = Point3D(0, 1, 0)
triangle = Triangle3D(A, B, C)
S = Point3D(0.25, 0.25, -1)
T = Point3D(0.25, 0.25, 1)
segment = Segment3D(S, T)
I = intersec3d_triangle_segment(triangle, segment)
self.assertEqual(I.x, 0.25)
self.assertEqual(I.y, 0.25)
self.assertEqual(I.z, 0.)
def test_property_x(self):
A = Point3D(1, 2, 3)
self.assertEqual(A.x, 1)
A.x = 10
self.assertEqual(A.x, 10)
def test_str(self):
A = Point3D(3, 2, 1)
expected_string = "Point3D(3.0, 2.0, 1.0)"
string = str(A)
self.assertEqual(string, expected_string)
def test_distance(self):
A = Point3D(3, 2, 1)
B = Point3D(4, 3, 2)
dist = A.distance(B)
expected_dist = sqrt(3.)
self.assertAlmostEqual(dist, expected_dist)
def test_index(self):
A = Point3D(1, 2, 3)
self.assertEqual(A.index, 0)
B = Point3D(1, 2, 3, index=8)
self.assertEqual(B.index, 8)
def setUp(self):
self.A = Point3D(1, 1, 2)
self.B = Point3D(6, 0, 1)
self.C = Point3D(7, 3, 3)
self.T = Triangle3D(self.A, self.B, self.C)