File size: 3,492 Bytes
2d5f249
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144

# -*- 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: [email protected]

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