VoxelEngine/MatrixStuff/Transformations.py

import math as math
import numpy as np


def lookAt(eyeX, eyeY, eyeZ, cX, cY, cZ, upX, upY, upZ):
    F = np.matrix([cX - eyeX, cY - eyeY, cZ - eyeZ])
    UP = np.matrix([upX, upY, upZ])
    f = F / math.sqrt(np.sum(np.square(F)))
    UP = UP / math.sqrt(np.sum(np.square(UP)))
    s = np.cross(f, UP)
    u = np.cross((s / math.sqrt(np.sum(np.square(s)))), f)
    mat = np.matrix([
        [s[0, 0], s[0, 1], s[0, 2], 0],
        [u[0, 0], u[0, 1], u[0, 2], 0],
        [-f[0, 0], -f[0, 1], -f[0, 2], 0],
        [0, 0, 0, 1]
    ])

    return np.transpose(mat)


def orthogonalMatrix(r, l, t, b, f, n):
    mat = np.matrix([
        [2 / (r - l), 0, 0, -(r + l) / (r - l)],
        [0, 2 / (t - b), 0, -(t + b) / (t - b)],
        [0, 0, -2 / (f - n), -(f + n) / (f - n)],
        [0, 0, 0, 1]
    ])

    return np.transpose(mat)


def perspectiveMatrix(fovy, aspect, znear, zfar):
    fovy_rads = fovy * math.pi / 180
    f = math.cos(fovy_rads / 2.0) / math.sin(fovy_rads / 2.0)
    a = (zfar + znear) / (znear - zfar)
    b = (2 * zfar * znear) / (znear - zfar)

    mat = np.matrix([[f / aspect, 0, 0, 0],
                     [0, f, 0, 0],
                     [0, 0, a, b],
                     [0, 0, -1, 0]], np.float32)

    return np.transpose(mat)


def translate(x, y, z):
    mat = np.matrix([[1, 0, 0, x],
                     [0, 1, 0, y],
                     [0, 0, 1, z],
                     [0, 0, 0, 1]], np.float32)

    return np.transpose(mat)


def rotate(x, y, z, d4=False):
    if not d4:
        mat = np.matrix([[1, 0, 0], [0, math.cos(x), -math.sin(x)], [0, math.sin(x), math.cos(x)]], np.float32)
        mat = mat * np.matrix([[math.cos(y), 0, -math.sin(y)], [0, 1, 0], [math.sin(y), 0, math.cos(y)]], np.float32)
        mat = mat * np.matrix([[math.cos(z), -math.sin(z), 0], [math.sin(z), math.cos(z), 0], [0, 0, 1]], np.float32)
    else:
        mat = np.matrix(
            [[1, 0, 0, 0], [0, math.cos(x), -math.sin(x), 0], [0, math.sin(x), math.cos(x), 0], [0, 0, 0, 1]],
            np.float32)
        mat = mat * np.matrix(
            [[math.cos(y), 0, -math.sin(y), 0], [0, 1, 0, 0], [math.sin(y), 0, math.cos(y), 0], [0, 0, 0, 1]],
            np.float32)
        mat = mat * np.matrix(
            [[math.cos(z), -math.sin(z), 0, 0], [math.sin(z), math.cos(z), 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
            np.float32)
    return np.transpose(mat)