def test_matrix_combination():
n = 4
x = v3.random_vector()
y1 = v3.vector(x)
matrix = v3.identity()
for i in range(4):
r_matrix = v3.random_matrix()
y1 = v3.transform(r_matrix, y1)
matrix = v3.combine(r_matrix, matrix)
y2 = v3.transform(matrix, x)
assert v3.is_similar_vector(y1, y2)
def test_matrix_combination():
n = 4
x = v3.random_vector()
y1 = v3.vector(x)
matrix = v3.identity()
for i in range(4):
r_matrix = v3.random_matrix()
y1 = v3.transform(r_matrix, y1)
matrix = v3.combine(r_matrix, matrix)
y2 = v3.transform(matrix, x)
assert v3.is_similar_vector(y1, y2)
def test_orthogonality():
x = v3.vector(v3.random_mag(), 0, 0)
y = v3.vector(0, v3.random_mag(), 0)
z = v3.vector(0, 0, v3.random_mag())
ry_x = v3.transform(v3.rotation(y, v3.radians(90)), x)
assert v3.is_similar_vector(v3.norm(ry_x), -v3.norm(z))
assert v3.is_similar_mag(v3.mag(ry_x), v3.mag(x))
ry_z = v3.transform(v3.rotation(y, v3.radians(90)), z)
assert v3.is_similar_vector(v3.norm(ry_z), v3.norm(x))
cross_x_y = v3.cross(x, y)
assert v3.is_similar_vector(v3.norm(cross_x_y), v3.norm(z))
assert v3.is_similar_mag(0, v3.dot(cross_x_y, x))
assert v3.is_similar_mag(0, v3.dot(cross_x_y, y))
cross_y_x = v3.cross(y, x)
assert v3.is_similar_vector(v3.norm(cross_y_x), -v3.norm(z))
def test_orthogonality(): x = v3.vector(v3.random_mag(), 0, 0) y = v3.vector(0, v3.random_mag(), 0) z = v3.vector(0, 0, v3.random_mag()) ry_x = v3.transform(v3.rotation(y, v3.radians(90)), x) assert v3.is_similar_vector(v3.norm(ry_x), -v3.norm(z)) assert v3.is_similar_mag(v3.mag(ry_x), v3.mag(x)) ry_z = v3.transform(v3.rotation(y, v3.radians(90)), z) assert v3.is_similar_vector(v3.norm(ry_z), v3.norm(x)) cross_x_y = v3.cross(x, y) assert v3.is_similar_vector(v3.norm(cross_x_y), v3.norm(z)) assert v3.is_similar_mag(0, v3.dot(cross_x_y, x)) assert v3.is_similar_mag(0, v3.dot(cross_x_y, y)) cross_y_x = v3.cross(y, x) assert v3.is_similar_vector(v3.norm(cross_y_x), -v3.norm(z))
def test_rotation():
x = v3.random_vector()
y = v3.transform(v3.random_rotation(), x)
assert v3.is_similar_mag(v3.mag(x), v3.mag(y))
def test_translation():
x = v3.vector(v3.random_mag(), 0, 0)
y = v3.vector(0, v3.random_mag(), 0)
x_and_y = v3.transform(v3.translation(y), x)
assert v3.is_similar_vector(x_and_y, x + y)
def test_rotation(): x = v3.random_vector() y = v3.transform(v3.random_rotation(), x) assert v3.is_similar_mag(v3.mag(x), v3.mag(y))
def test_translation(): x = v3.vector(v3.random_mag(), 0, 0) y = v3.vector(0, v3.random_mag(), 0) x_and_y = v3.transform(v3.translation(y), x) assert v3.is_similar_vector(x_and_y, x+y)