matrix.py

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)