def rotation_z(angle: float) -> Matrix:
result = identity(4)
result[0, 0] = math.cos(angle)
result[0, 1] = -math.sin(angle)
result[1, 0] = math.sin(angle)
result[1, 1] = math.cos(angle)
return result
def shearing(x_y: float, x_z: float, y_x: float, y_z: float, z_x: float,
z_y: float) -> Matrix:
result = identity(4)
result[0, 1] = x_y
result[0, 2] = x_z
result[1, 0] = y_x
result[1, 2] = y_z
result[2, 0] = z_x
result[2, 1] = z_y
return result
def check_attribute(context, var, att, expected):
if expected == "identity_matrix":
exp = identity(4) # type: Union[Matrix, float]
elif is_number(expected):
exp = float(expected)
elif expected == "true":
exp = True
elif expected == "false":
exp = False
else:
exp = context.variables[expected]
my_variable = context.variables[var]
if att == "count":
assert len(my_variable) == exp
elif isinstance(exp, float) or isinstance(exp, int):
assert equals(exp, getattr(my_variable, att))
else:
assert getattr(my_variable, att) == exp, f"{getattr(my_variable, att)} == {exp}"
def identity_pre(context, var):
matrix = context.variables[var]
identity_matrix = identity(matrix.num_rows)
assert identity_matrix * matrix == matrix
def check_equality(context, var_1, var_2):
matrix_1 = context.variables[var_1]
matrix_2 = identity(
4) if var_2 == "identity_matrix" else context.variables[var_2]
assert matrix_1 == matrix_2
def assign_identity_transpose(context, var):
identity_matrix = identity(4)
context.variables[var] = transpose(identity_matrix)
context.variables["identity_matrix"] = identity_matrix
def __init__(self) -> None:
self.origin = point(0, 0, 0)
self.radius = 1.0
self.transform = identity(4)
self.material = Material()
def translation(x: float, y: float, z: float) -> Matrix:
result = identity(4)
result[0, 3] = x
result[1, 3] = y
result[2, 3] = z
return result
def scaling(x: float, y: float, z: float) -> Matrix:
result = identity(4)
result[0, 0] = x
result[1, 1] = y
result[2, 2] = z
return result