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| # -*- coding: utf-8 -*- | |
| # Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. (MPG) is | |
| # holder of all proprietary rights on this computer program. | |
| # You can only use this computer program if you have closed | |
| # a license agreement with MPG or you get the right to use the computer | |
| # program from someone who is authorized to grant you that right. | |
| # Any use of the computer program without a valid license is prohibited and | |
| # liable to prosecution. | |
| # | |
| # Copyright©2019 Max-Planck-Gesellschaft zur Förderung | |
| # der Wissenschaften e.V. (MPG). acting on behalf of its Max Planck Institute | |
| # for Intelligent Systems. All rights reserved. | |
| # | |
| # Contact: ps-license@tuebingen.mpg.de | |
| import numpy as np | |
| def vec3(x, y, z): | |
| return np.array([x, y, z], dtype=np.float32) | |
| def radians(v): | |
| return np.radians(v) | |
| def identity(): | |
| return np.identity(4, dtype=np.float32) | |
| def empty(): | |
| return np.zeros([4, 4], dtype=np.float32) | |
| def magnitude(v): | |
| return np.linalg.norm(v) | |
| def normalize(v): | |
| m = magnitude(v) | |
| return v if m == 0 else v / m | |
| def dot(u, v): | |
| return np.sum(u * v) | |
| def cross(u, v): | |
| res = vec3(0, 0, 0) | |
| res[0] = u[1] * v[2] - u[2] * v[1] | |
| res[1] = u[2] * v[0] - u[0] * v[2] | |
| res[2] = u[0] * v[1] - u[1] * v[0] | |
| return res | |
| # below functions can be optimized | |
| def translate(m, v): | |
| res = np.copy(m) | |
| res[:, 3] = m[:, 0] * v[0] + m[:, 1] * v[1] + m[:, 2] * v[2] + m[:, 3] | |
| return res | |
| def rotate(m, angle, v): | |
| a = angle | |
| c = np.cos(a) | |
| s = np.sin(a) | |
| axis = normalize(v) | |
| temp = (1 - c) * axis | |
| rot = empty() | |
| rot[0][0] = c + temp[0] * axis[0] | |
| rot[0][1] = temp[0] * axis[1] + s * axis[2] | |
| rot[0][2] = temp[0] * axis[2] - s * axis[1] | |
| rot[1][0] = temp[1] * axis[0] - s * axis[2] | |
| rot[1][1] = c + temp[1] * axis[1] | |
| rot[1][2] = temp[1] * axis[2] + s * axis[0] | |
| rot[2][0] = temp[2] * axis[0] + s * axis[1] | |
| rot[2][1] = temp[2] * axis[1] - s * axis[0] | |
| rot[2][2] = c + temp[2] * axis[2] | |
| res = empty() | |
| res[:, 0] = m[:, 0] * rot[0][0] + m[:, 1] * rot[0][1] + m[:, 2] * rot[0][2] | |
| res[:, 1] = m[:, 0] * rot[1][0] + m[:, 1] * rot[1][1] + m[:, 2] * rot[1][2] | |
| res[:, 2] = m[:, 0] * rot[2][0] + m[:, 1] * rot[2][1] + m[:, 2] * rot[2][2] | |
| res[:, 3] = m[:, 3] | |
| return res | |
| def perspective(fovy, aspect, zNear, zFar): | |
| tanHalfFovy = np.tan(fovy / 2) | |
| res = empty() | |
| res[0][0] = 1 / (aspect * tanHalfFovy) | |
| res[1][1] = 1 / (tanHalfFovy) | |
| res[2][3] = -1 | |
| res[2][2] = -(zFar + zNear) / (zFar - zNear) | |
| res[3][2] = -(2 * zFar * zNear) / (zFar - zNear) | |
| return res.T | |
| def ortho(left, right, bottom, top, zNear, zFar): | |
| # res = np.ones([4, 4], dtype=np.float32) | |
| res = identity() | |
| res[0][0] = 2 / (right - left) | |
| res[1][1] = 2 / (top - bottom) | |
| res[2][2] = -2 / (zFar - zNear) | |
| res[3][0] = -(right + left) / (right - left) | |
| res[3][1] = -(top + bottom) / (top - bottom) | |
| res[3][2] = -(zFar + zNear) / (zFar - zNear) | |
| return res.T | |
| def lookat(eye, center, up): | |
| f = normalize(center - eye) | |
| s = normalize(cross(f, up)) | |
| u = cross(s, f) | |
| res = identity() | |
| res[0][0] = s[0] | |
| res[1][0] = s[1] | |
| res[2][0] = s[2] | |
| res[0][1] = u[0] | |
| res[1][1] = u[1] | |
| res[2][1] = u[2] | |
| res[0][2] = -f[0] | |
| res[1][2] = -f[1] | |
| res[2][2] = -f[2] | |
| res[3][0] = -dot(s, eye) | |
| res[3][1] = -dot(u, eye) | |
| res[3][2] = -dot(f, eye) | |
| return res.T | |
| def transform(d, m): | |
| return np.dot(m, d.T).T | |