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annotate pytouhou/utils/maths.pyx @ 412:5fe6cd6ceb48

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Refactor the maths functions out of Renderer.
author Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
date Wed, 12 Jun 2013 18:30:08 +0200
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children 878273a984c4
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5fe6cd6ceb48 Refactor the maths functions out of Renderer.
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1 # -*- encoding: utf-8 -*-
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2 ##
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3 ## Copyright (C) 2013 Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
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4 ##
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5 ## This program is free software; you can redistribute it and/or modify
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6 ## it under the terms of the GNU General Public License as published
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7 ## by the Free Software Foundation; version 3 only.
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8 ##
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9 ## This program is distributed in the hope that it will be useful,
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10 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
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11 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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12 ## GNU General Public License for more details.
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13 ##
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14
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15 from math import radians
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16 from libc.math cimport tan
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17
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18 from .matrix cimport Matrix
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19 from .vector import Vector, normalize, cross, dot
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20
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21
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22 cpdef ortho_2d(left, right, bottom, top):
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23 mat = Matrix()
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24 data = mat.data
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25 data[0][0] = 2 / (right - left)
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26 data[1][1] = 2 / (top - bottom)
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27 data[2][2] = -1
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28 data[3][0] = -(right + left) / (right - left)
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29 data[3][1] = -(top + bottom) / (top - bottom)
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30 return mat
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31
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32
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33 cpdef look_at(eye, center, up):
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34 eye = Vector(eye)
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35 center = Vector(center)
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36 up = Vector(up)
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37
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38 f = normalize(center - eye)
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39 u = normalize(up)
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40 s = normalize(cross(f, u))
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41 u = cross(s, f)
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42
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43 return Matrix([[s[0], u[0], -f[0], 0],
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44 [s[1], u[1], -f[1], 0],
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45 [s[2], u[2], -f[2], 0],
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46 [-dot(s, eye), -dot(u, eye), dot(f, eye), 1]])
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47
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48
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49 cpdef perspective(fovy, aspect, z_near, z_far):
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50 top = tan(radians(fovy / 2)) * z_near
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51 bottom = -top
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52 left = -top * aspect
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53 right = top * aspect
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54
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55 mat = Matrix()
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56 data = mat.data
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57 data[0][0] = (2 * z_near) / (right - left)
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58 data[1][1] = (2 * z_near) / (top - bottom)
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59 data[2][2] = -(z_far + z_near) / (z_far - z_near)
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60 data[2][3] = -1
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61 data[3][2] = -(2 * z_far * z_near) / (z_far - z_near)
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62 data[3][3] = 0
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63 return mat
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64
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65
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66 cpdef setup_camera(dx, dy, dz):
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67 # Some explanations on the magic constants:
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68 # 192. = 384. / 2. = width / 2.
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69 # 224. = 448. / 2. = height / 2.
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70 # 835.979370 = 224./math.tan(math.radians(15)) = (height/2.)/math.tan(math.radians(fov/2))
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71 # This is so that objects on the (O, x, y) plane use pixel coordinates
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72 return look_at((192., 224., - 835.979370 * dz),
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73 (192. + dx, 224. - dy, 0.), (0., -1., 0.))