Mercurial > touhou

annotate pytouhou/utils/maths.pyx @ 422:52829ebe2561

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Refactor window management in its own class.
author Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
date Tue, 16 Jul 2013 21:07:15 +0200
parents 5fe6cd6ceb48
children 878273a984c4
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
412
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
1 # -*- encoding: utf-8 -*-
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
2 ##
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
3 ## Copyright (C) 2013 Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
4 ##
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
5 ## This program is free software; you can redistribute it and/or modify
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
6 ## it under the terms of the GNU General Public License as published
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
7 ## by the Free Software Foundation; version 3 only.
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
8 ##
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
9 ## This program is distributed in the hope that it will be useful,
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
10 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
11 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
12 ## GNU General Public License for more details.
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
13 ##
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
14
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
15 from math import radians
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
16 from libc.math cimport tan
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
17
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
18 from .matrix cimport Matrix
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
19 from .vector import Vector, normalize, cross, dot
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
20
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
21
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
22 cpdef ortho_2d(left, right, bottom, top):
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
23 mat = Matrix()
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
24 data = mat.data
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
25 data[0][0] = 2 / (right - left)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
26 data[1][1] = 2 / (top - bottom)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
27 data[2][2] = -1
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
28 data[3][0] = -(right + left) / (right - left)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
29 data[3][1] = -(top + bottom) / (top - bottom)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
30 return mat
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
31
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
32
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
33 cpdef look_at(eye, center, up):
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
34 eye = Vector(eye)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
35 center = Vector(center)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
36 up = Vector(up)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
37
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
38 f = normalize(center - eye)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
39 u = normalize(up)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
40 s = normalize(cross(f, u))
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
41 u = cross(s, f)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
42
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
43 return Matrix([[s[0], u[0], -f[0], 0],
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
44 [s[1], u[1], -f[1], 0],
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
45 [s[2], u[2], -f[2], 0],
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
46 [-dot(s, eye), -dot(u, eye), dot(f, eye), 1]])
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
47
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
48
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
49 cpdef perspective(fovy, aspect, z_near, z_far):
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
50 top = tan(radians(fovy / 2)) * z_near
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
51 bottom = -top
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
52 left = -top * aspect
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
53 right = top * aspect
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
54
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
55 mat = Matrix()
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
56 data = mat.data
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
57 data[0][0] = (2 * z_near) / (right - left)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
58 data[1][1] = (2 * z_near) / (top - bottom)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
59 data[2][2] = -(z_far + z_near) / (z_far - z_near)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
60 data[2][3] = -1
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
61 data[3][2] = -(2 * z_far * z_near) / (z_far - z_near)
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
62 data[3][3] = 0
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
63 return mat
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
64
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
65
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
66 cpdef setup_camera(dx, dy, dz):
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
67 # Some explanations on the magic constants:
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
68 # 192. = 384. / 2. = width / 2.
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
69 # 224. = 448. / 2. = height / 2.
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
70 # 835.979370 = 224./math.tan(math.radians(15)) = (height/2.)/math.tan(math.radians(fov/2))
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
71 # This is so that objects on the (O, x, y) plane use pixel coordinates
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
72 return look_at((192., 224., - 835.979370 * dz),
5fe6cd6ceb48 Refactor the maths functions out of Renderer.
Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
parents:
diff changeset
73 (192. + dx, 224. - dy, 0.), (0., -1., 0.))