def __init__(self, origin, direction):
if not Tuple.is_point(origin):
raise ValueError("Expected Point as first argument: {}".format(
str(origin)))
if not Tuple.is_vector(direction):
raise ValueError("Expected Vector as second argument: {}".format(
str(direction)))
self.origin = origin
self.direction = direction
def test_identity(self):
m = Matrix(
vals=[[0, 1, 2, 4], [1, 2, 4, 8], [2, 4, 8, 16], [4, 8, 16, 32]])
i = Matrix.identity()
self.assertEqual(1.0, i[0, 0])
self.assertEqual(1.0, i[1, 1])
self.assertEqual(1.0, i[2, 2])
self.assertEqual(1.0, i[3, 3])
self.assertEqual(m * i, m)
t = Tuple(1, 2, 3, 4)
self.assertEqual(i * t, t)
def __mul__(self, other):
if isinstance(other, Matrix):
a, b = self, other
assert a.size == b.size
m = self._create(a.size)
for r in range(a.size):
for c in range(a.size):
m[r][c] = sum(a[r, i] * b[i, c] for i in range(a.size))
return Matrix(vals=m)
if isinstance(other, Tuple):
a, b = self, other
assert a.size == len(b)
t = [0.0] * a.size
for r in range(a.size):
t[r] = sum(a[r, i] * b[i] for i in range(a.size))
return Tuple(*t)
def test_tuple_multiplication(self):
m = Matrix(
vals=[[1, 2, 3, 4], [2, 4, 4, 2], [8, 6, 4, 1], [0, 0, 0, 1]])
t = Tuple(1, 2, 3, 1)
c = m * t
self.assertEqual(c, Tuple(18, 24, 33, 1))
def test_scalar_division(self):
a = Tuple(1, -2, 3, -4)
self.assertEqual(a / 2.0, Tuple(0.5, -1, 1.5, -2))
def test_scalar_multiplication(self):
a = Tuple(1, -2, 3, -4)
self.assertEqual(a * 3.5, Tuple(3.5, -7, 10.5, -14))
self.assertEqual(a * 0.5, Tuple(0.5, -1, 1.5, -2))
def test_negation(self):
a = Tuple(1, -2, 3, -4)
self.assertEqual(-a, Tuple(-1, 2, -3, 4))
def test_subtraction(self):
t1 = Tuple(3, -2, 5, 1)
t2 = Tuple(-2, 3, 1, 0)
self.assertEqual(t1 - t2, Tuple(5, -5, 4, 1))
def test_addition(self):
t1 = Tuple(3, -2, 5, 1)
t2 = Tuple(-2, 3, 1, 0)
self.assertEqual(t1 + t2, Tuple(1, 1, 6, 1))
def test_vector_tuple_equality(self):
a = Vector(4, -4, 3)
t = Tuple(4, -4, 3, 0)
self.assertEqual(a, t)
def test_point_tuple_equality(self):
p = Point(4, -4, 3)
t = Tuple(4, -4, 3, 1)
self.assertEqual(p, t)