def represent_in_local_coordinates(self, point):
"""Represents a point in the frame's local coordinate system.
Parameters
----------
point : :obj:`list` of :obj:`float`
A point in world XY.
Returns
-------
:obj:`list` of :obj:`float`
A point in the local coordinate system of the frame.
Examples
--------
>>> f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> pw1 = [2, 2, 2]
>>> pf = f.represent_in_local_coordinates(pw1)
>>> pw2 = f.represent_in_global_coordinates(pf)
>>> allclose(pw1, pw2)
True
"""
pt = Point(*subtract_vectors(point, self.point))
T = inverse(matrix_from_basis_vectors(self.xaxis, self.yaxis))
pt.transform(T)
return pt
def represent_in_global_coordinates(self, point):
"""Represents a point from local coordinates in the world coordinate system.
Parameters
----------
point : :obj:`list` of :obj:`float`
A point in local coordinates.
Returns
-------
:obj:`list` of :obj:`float`
A point in the world coordinate system.
Examples
--------
>>> f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> pw1 = [2, 2, 2]
>>> pf = f.represent_in_local_coordinates(pw1)
>>> pw2 = f.represent_in_global_coordinates(pf)
>>> allclose(pw1, pw2)
True
"""
T = matrix_from_frame(self)
pt = Point(*point)
pt.transform(T)
return pt
f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f)
Tinv = T.inverse()
I = Transformation()
print(I == T * Tinv)
f1 = Frame([2, 2, 2], [0.12, 0.58, 0.81], [-0.80, 0.53, -0.26])
f2 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame_to_frame(f1, f2)
f1.transform(T)
print(f1 == f2)
f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f)
p = Point(0, 0, 0)
p.transform(T)
print(allclose(f.point, p))
f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f1)
points = [[1.0, 1.0, 1.0], [1.68, 1.68, 1.27], [0.33, 1.73, 0.85]]
points = transform_points(points, T)
trans1 = [1, 2, 3]
angle1 = [-2.142, 1.141, -0.142]
scale1 = [0.123, 2, 0.5]
T = matrix_from_translation(trans1)
R = matrix_from_euler_angles(angle1)
S = matrix_from_scale_factors(scale1)
M = multiply_matrices(multiply_matrices(T, R), S)
# M = compose_matrix(scale1, None, angle1, trans1, None)