def test_default(self):
p = TestPattern()
I = Matrix([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
self.assertTrue(matrix.equals(I, p.transform))
def test_inv5(self):
A = Matrix([[9, 3, 0, 9], [-5, -2, -6, -3], [-4, 9, 6, 4],
[-7, 6, 6, 2]])
B = Matrix([[-0.04074, -0.07778, 0.14444, -0.22222],
[-0.07778, 0.03333, 0.36667, -0.33333],
[-0.02901, -0.14630, -0.10926, 0.12963],
[0.17778, 0.06667, -0.26667, 0.33333]])
self.assertTrue(matrix.equals(A.inverse(), B))
def test_transform1(self):
pfrom = Point(0, 0, 0)
pto = Point(0, 0, -1)
vup = Vector(0, 1, 0)
t = view_transform(pfrom, pto, vup)
I = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
self.assertTrue(matrix.equals(I, t))
def test_inv4(self):
A = Matrix([[8, -5, 9, 2], [7, 5, 6, 1], [-6, 0, 9, 6],
[-3, 0, -9, -4]])
B = Matrix([[-0.15385, -0.15385, -0.28205, -0.53846],
[-0.07692, 0.12308, 0.02564, 0.03077],
[0.35897, 0.35897, 0.43590, 0.92308],
[-0.69231, -0.69231, -0.76923, -1.92308]])
self.assertTrue(matrix.equals(A.inverse(), B))
def test_transform2(self):
pfrom = Point(0, 0, 0)
pto = Point(0, 0, 1)
vup = Vector(0, 1, 0)
t = view_transform(pfrom, pto, vup)
s = scale(-1, 1, -1)
self.assertTrue(matrix.equals(s, t))
def test_camera1(self):
hsize = 160
vsize = 120
field_of_view = pi / 2
c = Camera(hsize, vsize, field_of_view)
self.assertEqual(hsize, c.hsize)
self.assertEqual(vsize, c.vsize)
self.assertEqual(field_of_view, pi / 2)
I = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
self.assertTrue(matrix.equals(c.transform, I))
def test_minor1(self):
A = Matrix([[3, 5, 0], [2, -1, 7], [6, -1, 5]])
B = A.submatrix(1, 0)
C = Matrix([[5, 0], [-1, 5]])
self.assertTrue(matrix.equals(A.submatrix(1, 0), C))
self.assertEqual(B.determinant(), 25)
self.assertEqual(A.minor(1, 0), 25)
def test_transform4(self):
pfrom = Point(1, 3, 2)
pto = Point(4, -2, 8)
vup = Vector(1, 1, 0)
t = view_transform(pfrom, pto, vup)
m = Matrix([[-0.50709, 0.50709, 0.67612, -2.36643],
[0.76772, 0.60609, 0.12122, -2.82843],
[-0.35857, 0.59761, -0.71714, 0.00000],
[0.00000, 0.00000, 0.00000, 1.00000]])
self.assertTrue(matrix.equals(m, t))
def test_inv3(self):
A = Matrix([[-5, 2, 6, -8], [1, -5, 1, 8], [7, 7, -6, -7],
[1, -3, 7, 4]])
B = A.inverse()
C = Matrix([[0.21805, 0.45113, 0.24060, -0.04511],
[-0.80827, -1.45677, -0.44361, 0.52068],
[-0.07895, -0.22368, -0.05263, 0.19737],
[-0.52256, -0.81391, -0.30075, 0.30639]])
self.assertEqual(A.determinant(), 532)
self.assertEqual(A.cofactor(2, 3), -160)
self.assertEqual(B[3][2], -160. / 532)
self.assertEqual(A.cofactor(3, 2), 105)
self.assertEqual(B[2][3], 105. / 532)
self.assertTrue(matrix.equals(B, C))
def test_transform2(self):
s = TestShape()
t = translate(2, 3, 4)
s.set_transform(t)
self.assertTrue(matrix.equals(s.transform, t))
def test_transform1(self):
s = TestShape()
I = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
self.assertTrue(matrix.equals(s.transform, I))
def test_transform1(self):
p = TestPattern()
p.set_pattern_transform(translate(1, 2, 3))
self.assertTrue(matrix.equals(p.transform, translate(1, 2, 3)))
def test_mul1(self):
A = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 8, 7, 6], [5, 4, 3, 2]])
B = Matrix([[-2, 1, 2, 3], [3, 2, 1, -1], [4, 3, 6, 5], [1, 2, 7, 8]])
C = Matrix([[20, 22, 50, 48], [44, 54, 114, 108], [40, 58, 110, 102],
[16, 26, 46, 42]])
self.assertTrue(matrix.equals(C, A * B))
def test_tranpose1(self):
A = Matrix([[0, 9, 3, 0], [9, 8, 0, 8], [1, 8, 5, 3], [0, 0, 5, 8]])
B = Matrix([[0, 9, 1, 0], [9, 8, 8, 0], [3, 0, 5, 5], [0, 8, 3, 8]])
self.assertTrue(matrix.equals(A.transpose(), B))
def test_subm3(self):
A = Matrix([[3, 5, 0], [2, -1, 7], [6, -1, 5]])
B = Matrix([[5, 0], [-1, 5]])
self.assertTrue(matrix.equals(A.submatrix(1, 0), B))
def test_subm2(self):
A = Matrix([[-6, 1, 1, 6], [-8, 5, 8, 6], [-1, 0, 8, 2],
[-7, 1, -1, 1]])
B = Matrix([[-6, 1, 6], [-8, 8, 6], [-7, -1, 1]])
self.assertTrue(matrix.equals(A.submatrix(2, 1), B))
def test_subm1(self):
A = Matrix([[1, 5, 0], [-3, 2, 7], [0, 6, -3]])
B = Matrix([[-3, 2], [0, 6]])
self.assertTrue(matrix.equals(A.submatrix(0, 2), B))
def test_create2(self):
A = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 8, 7, 6], [5, 4, 3, 2]])
B = Matrix([[2, 2, 3, 4], [5, 6, 7, 8], [9, 8, 7, 6], [5, 4, 3, 2]])
self.assertFalse(matrix.equals(A, B))
def test_transform3(self):
pfrom = Point(0, 0, 8)
pto = Point(0, 0, 0)
vup = Vector(0, 1, 0)
t = view_transform(pfrom, pto, vup)
self.assertTrue(matrix.equals(translate(0, 0, -8), t))
def test_inv6(self):
A = Matrix([[3, -9, 7, 3], [3, -8, 2, -9], [-4, 4, 4, 1],
[-6, 5, -1, 1]])
B = Matrix([[8, 2, 2, 2], [3, -1, 7, 0], [7, 0, 5, 4], [6, -2, 0, 5]])
C = A * B
self.assertTrue(matrix.equals(C * B.inverse(), A))
def test_default1(self):
s = GlassSphere()
self.assertTrue(matrix.equals(I(), s.transform))
self.assertEqual(s.material.transparency, 1.0)
self.assertEqual(s.material.refractive_index, 1.5)
def test_ide1(self):
I = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
A = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 8, 7, 6], [5, 4, 3, 2]])
self.assertTrue(matrix.equals(A, A * I))
