On Tue, 31 Jan 2017 21:23:55 -0500, Joseph Fox-Rabinovitz <jfoxrabinov...@gmail.com> wrote:
> Could you show what you are doing to get the statement "However, I > cannot reproduce this matrix via composition; i.e. by multiplying the > underlying rotation matrices.". I would guess something involving the > `*` operator instead of `@`, but guessing probably won't help you > solve your issue. Sure, although composition is not something I can take credit for, as it's a well-described operation for generating linear transformations. It is the matrix multiplication of two or more transformation matrices. In the case of Euler transformations, it's matrices specifying rotations around 3 orthogonal axes by 3 given angles. I'm using `numpy.dot' to perform matrix multiplication on 2D arrays representing matrices. However, it's not obvious from the link I provided what particular rotation matrices are multiplied and in what order (i.e. what composition) is used to arrive at the Z1Y2X3 rotation matrix shown. Perhaps I'm not understanding the conventions used therein. This is one of my attempts at reproducing that rotation matrix via composition: ---<--------------------cut here---------------start------------------->--- import numpy as np angles = np.radians(np.array([30, 20, 10])) def z1y2x3(alpha, beta, gamma): """Z1Y2X3 rotation matrix given Euler angles""" return np.array([[np.cos(alpha) * np.cos(beta), np.cos(alpha) * np.sin(beta) * np.sin(gamma) - np.cos(gamma) * np.sin(alpha), np.sin(alpha) * np.sin(gamma) + np.cos(alpha) * np.cos(gamma) * np.sin(beta)], [np.cos(beta) * np.sin(alpha), np.cos(alpha) * np.cos(gamma) + np.sin(alpha) * np.sin(beta) * np.sin(gamma), np.cos(gamma) * np.sin(alpha) * np.sin(beta) - np.cos(alpha) * np.sin(gamma)], [-np.sin(beta), np.cos(beta) * np.sin(gamma), np.cos(beta) * np.cos(gamma)]]) euler_mat = z1y2x3(angles[0], angles[1], angles[2]) ## Now via composition def rotation_matrix(theta, axis, active=False): """Generate rotation matrix for a given axis Parameters ---------- theta: numeric, optional The angle (degrees) by which to perform the rotation. Default is 0, which means return the coordinates of the vector in the rotated coordinate system, when rotate_vectors=False. axis: int, optional Axis around which to perform the rotation (x=0; y=1; z=2) active: bool, optional Whether to return active transformation matrix. Returns ------- numpy.ndarray 3x3 rotation matrix """ theta = np.radians(theta) if axis == 0: R_theta = np.array([[1, 0, 0], [0, np.cos(theta), -np.sin(theta)], [0, np.sin(theta), np.cos(theta)]]) elif axis == 1: R_theta = np.array([[np.cos(theta), 0, np.sin(theta)], [0, 1, 0], [-np.sin(theta), 0, np.cos(theta)]]) else: R_theta = np.array([[np.cos(theta), -np.sin(theta), 0], [np.sin(theta), np.cos(theta), 0], [0, 0, 1]]) if active: R_theta = np.transpose(R_theta) return R_theta ## The rotations are given as active xmat = rotation_matrix(angles[2], 0, active=True) ymat = rotation_matrix(angles[1], 1, active=True) zmat = rotation_matrix(angles[0], 2, active=True) ## The operation seems to imply this composition euler_comp_mat = np.dot(xmat, np.dot(ymat, zmat)) ---<--------------------cut here---------------end--------------------->--- I believe the matrices `euler_mat' and `euler_comp_mat' should be the same, but they aren't, so it's unclear to me what particular composition is meant to produce the matrix specified by this Z1Y2X3 transformation. What am I missing? -- Seb _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org https://mail.scipy.org/mailman/listinfo/numpy-discussion