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_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))
assert v3.is_similar_mag(v3.mag(v * s), s * v3.mag(v))
assert v3.is_similar_mag(v3.mag(s * v), 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))
assert v3.is_similar_vector(v * -s, -(v * s))
assert v3.is_similar_vector(-s * v, -(s * v))
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)) assert v3.is_similar_mag(v3.mag(v*s), s*v3.mag(v)) assert v3.is_similar_mag(v3.mag(s*v), 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)) assert v3.is_similar_vector(v*-s, -(v*s)) assert v3.is_similar_vector(-s*v, -(s*v))
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_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)