File size: 3,975 Bytes
f92c150 |
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 |
import copy
import ctypes
import math
def copy_matrix(matrix):
return copy.deepcopy(matrix) # we need to use deepcopy since we're dealing with 2D arrays
clean_matrix = [[0.0 for x in range(4)] for x in range(4)]
identity_matrix = copy_matrix(clean_matrix)
identity_matrix[0][0] = 1.0
identity_matrix[1][1] = 1.0
identity_matrix[2][2] = 1.0
identity_matrix[3][3] = 1.0
def multiply_matrices(x_matrix, y_matrix):
result_matrix = copy_matrix(clean_matrix)
for i in range(4):
for j in range(4):
result_matrix[i][j] = \
(x_matrix[0][j] * y_matrix[i][0]) + \
(x_matrix[1][j] * y_matrix[i][1]) + \
(x_matrix[2][j] * y_matrix[i][2]) + \
(x_matrix[3][j] * y_matrix[i][3])
return result_matrix
class Matrix:
def __init__(self, base = None):
if type(base) == Matrix: self.data = copy_matrix(base.data)
elif type(base) == list: self.data = copy_matrix(base)
else: self.data = copy_matrix(clean_matrix)
def load_identity(self):
self.data = copy_matrix(identity_matrix)
def __mul__(self, matrix):
return Matrix(multiply_matrices(self.data, matrix.data))
def __imul__(self, matrix):
self.data = multiply_matrices(self.data, matrix.data)
def scale(self, x, y, z):
for i in range(4): self.data[0][i] *= x
for i in range(4): self.data[1][i] *= y
for i in range(4): self.data[2][i] *= z
def translate(self, x, y, z):
for i in range(4):
self.data[3][i] = self.data[3][i] + (self.data[0][i] * x + self.data[1][i] * y + self.data[2][i] * z)
def rotate(self, angle, x, y, z):
magnitude = math.sqrt(x * x + y * y + z * z)
x /= -magnitude
y /= -magnitude
z /= -magnitude
sin_angle = math.sin(angle)
cos_angle = math.cos(angle)
one_minus_cos = 1.0 - cos_angle
xx = x * x
yy = y * y
zz = z * z
xy = x * y
yz = y * z
zx = z * x
xs = x * sin_angle
ys = y * sin_angle
zs = z * sin_angle
rotation_matrix = copy_matrix(clean_matrix)
rotation_matrix[0][0] = (one_minus_cos * xx) + cos_angle
rotation_matrix[0][1] = (one_minus_cos * xy) - zs
rotation_matrix[0][2] = (one_minus_cos * zx) + ys
rotation_matrix[1][0] = (one_minus_cos * xy) + zs
rotation_matrix[1][1] = (one_minus_cos * yy) + cos_angle
rotation_matrix[1][2] = (one_minus_cos * yz) - xs
rotation_matrix[2][0] = (one_minus_cos * zx) - ys
rotation_matrix[2][1] = (one_minus_cos * yz) + xs
rotation_matrix[2][2] = (one_minus_cos * zz) + cos_angle
rotation_matrix[3][3] = 1.0
self.data = multiply_matrices(self.data, rotation_matrix)
def rotate_2d(self, x, y):
self.rotate(x, 0, 1.0, 0)
self.rotate(-y, math.cos(x), 0, math.sin(x))
def frustum(self, left, right, bottom, top, near, far):
deltax = right - left
deltay = top - bottom
deltaz = far - near
frustum_matrix = copy_matrix(clean_matrix)
frustum_matrix[0][0] = 2 * near / deltax
frustum_matrix[1][1] = 2 * near / deltay
frustum_matrix[2][0] = (right + left) / deltax
frustum_matrix[2][1] = (top + bottom) / deltay
frustum_matrix[2][2] = -(near + far) / deltaz
frustum_matrix[2][3] = -1.0
frustum_matrix[3][2] = -2 * near * far / deltaz
self.data = multiply_matrices(self.data, frustum_matrix)
def perspective(self, fovy, aspect, near, far):
frustum_y = math.tan(math.radians(fovy) / 2)
frustum_x = frustum_y * aspect
self.frustum(-frustum_x * near, frustum_x * near, -frustum_y * near, frustum_y * near, near, far)
def orthographic(self, left, right, bottom, top, near, far):
deltax = right - left
deltay = top - bottom
deltaz = far - near
orthographic_matrix = copy_matrix(identity_matrix)
orthographic_matrix[0][0] = 2.0 / deltax
orthographic_matrix[3][0] = -(right + left) / deltax
orthographic_matrix[1][1] = 2.0 / deltay
orthographic_matrix[3][1] = -(top + bottom) / deltay
orthographic_matrix[2][2] = 2.0 / deltax
orthographic_matrix[3][2] = -(near + far) / deltaz
self.data = multiply_matrices(self.data, orthographic_matrix)
|