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| # Copyright 2016 The TensorFlow Authors All Rights Reserved. | |
| # | |
| # Licensed under the Apache License, Version 2.0 (the "License"); | |
| # you may not use this file except in compliance with the License. | |
| # You may obtain a copy of the License at | |
| # | |
| # http://www.apache.org/licenses/LICENSE-2.0 | |
| # | |
| # Unless required by applicable law or agreed to in writing, software | |
| # distributed under the License is distributed on an "AS IS" BASIS, | |
| # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
| # See the License for the specific language governing permissions and | |
| # limitations under the License. | |
| # ============================================================================== | |
| """Utilities for generating and applying rotation matrices. | |
| """ | |
| import numpy as np | |
| ANGLE_EPS = 0.001 | |
| def normalize(v): | |
| return v / np.linalg.norm(v) | |
| def get_r_matrix(ax_, angle): | |
| ax = normalize(ax_) | |
| if np.abs(angle) > ANGLE_EPS: | |
| S_hat = np.array( | |
| [[0.0, -ax[2], ax[1]], [ax[2], 0.0, -ax[0]], [-ax[1], ax[0], 0.0]], | |
| dtype=np.float32) | |
| R = np.eye(3) + np.sin(angle)*S_hat + \ | |
| (1-np.cos(angle))*(np.linalg.matrix_power(S_hat, 2)) | |
| else: | |
| R = np.eye(3) | |
| return R | |
| def r_between(v_from_, v_to_): | |
| v_from = normalize(v_from_) | |
| v_to = normalize(v_to_) | |
| ax = normalize(np.cross(v_from, v_to)) | |
| angle = np.arccos(np.dot(v_from, v_to)) | |
| return get_r_matrix(ax, angle) | |
| def rotate_camera_to_point_at(up_from, lookat_from, up_to, lookat_to): | |
| inputs = [up_from, lookat_from, up_to, lookat_to] | |
| for i in range(4): | |
| inputs[i] = normalize(np.array(inputs[i]).reshape((-1,))) | |
| up_from, lookat_from, up_to, lookat_to = inputs | |
| r1 = r_between(lookat_from, lookat_to) | |
| new_x = np.dot(r1, np.array([1, 0, 0]).reshape((-1, 1))).reshape((-1)) | |
| to_x = normalize(np.cross(lookat_to, up_to)) | |
| angle = np.arccos(np.dot(new_x, to_x)) | |
| if angle > ANGLE_EPS: | |
| if angle < np.pi - ANGLE_EPS: | |
| ax = normalize(np.cross(new_x, to_x)) | |
| flip = np.dot(lookat_to, ax) | |
| if flip > 0: | |
| r2 = get_r_matrix(lookat_to, angle) | |
| elif flip < 0: | |
| r2 = get_r_matrix(lookat_to, -1. * angle) | |
| else: | |
| # Angle of rotation is too close to 180 degrees, direction of rotation | |
| # does not matter. | |
| r2 = get_r_matrix(lookat_to, angle) | |
| else: | |
| r2 = np.eye(3) | |
| return np.dot(r2, r1) | |