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)) 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))
cross_y_x = v3.cross(y, x)
assert v3.is_similar_vector(v3.norm(cross_y_x), -v3.norm(z))
def test_vector_algebra(): a = v3.random_vector() assert v3.is_similar_vector(a, +a) b = v3.random_vector() a_add_b = a+b assert v3.is_similar_vector(a_add_b - b, a) a_sub_b = a-b assert v3.is_similar_vector(a_sub_b + b, a) s = v3.random_mag() v = v3.random_vector() assert v3.is_similar_mag(v3.mag(v3.scale(v, s)), s*v3.mag(v)) s = v3.random_mag() v = v3.random_vector() assert v3.is_similar_vector(v3.scale(v, -s), -v3.scale(v, s))
def test_vector_algebra():
a = v3.random_vector()
assert v3.is_similar_vector(a, +a)
b = v3.random_vector()
a_add_b = a + b
assert v3.is_similar_vector(a_add_b - b, a)
a_sub_b = a - b
assert v3.is_similar_vector(a_sub_b + b, a)
s = v3.random_mag()
v = v3.random_vector()
assert v3.is_similar_mag(v3.mag(v3.scale(v, s)), s * v3.mag(v))
s = v3.random_mag()
v = v3.random_vector()
assert v3.is_similar_vector(v3.scale(v, -s), -v3.scale(v, s))
def get_orientate(self, tangent, up, scale):
"""
Transform stretches the length to the length of tangent and
the radius to scale.
"""
return v3.combine(get_xy_face_transform(tangent, up, scale),
v3.scaling_matrix(1.0, 1.0,
v3.mag(tangent) / scale))
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_rotation():
x = v3.random_vector()
y = v3.transform(v3.random_rotation(), x)
assert v3.is_similar_mag(v3.mag(x), v3.mag(y))