transformations.py

# coding=utf-8
"""
Daniel Calderon, CC3501, 2019-1
Transformation matrices for computer graphics
v2.0
"""

import numpy as np


def identity():
    return np.identity(4, dtype=np.float32)


def uniformScale(s):
    return np.array([
        [s, 0, 0, 0],
        [0, s, 0, 0],
        [0, 0, s, 0],
        [0, 0, 0, 1]], dtype=np.float32)


def scale(sx, sy, sz):
    return np.array([
        [sx, 0, 0, 0],
        [0, sy, 0, 0],
        [0, 0, sz, 0],
        [0, 0, 0, 1]], dtype=np.float32)


def rotationX(theta):
    sin_theta = np.sin(theta)
    cos_theta = np.cos(theta)

    return np.array([
        [1, 0, 0, 0],
        [0, cos_theta, -sin_theta, 0],
        [0, sin_theta, cos_theta, 0],
        [0, 0, 0, 1]], dtype=np.float32)


def rotationY(theta):
    sin_theta = np.sin(theta)
    cos_theta = np.cos(theta)

    return np.array([
        [cos_theta, 0, sin_theta, 0],
        [0, 1, 0, 0],
        [-sin_theta, 0, cos_theta, 0],
        [0, 0, 0, 1]], dtype=np.float32)


def rotationZ(theta):
    sin_theta = np.sin(theta)
    cos_theta = np.cos(theta)

    return np.array([
        [cos_theta, -sin_theta, 0, 0],
        [sin_theta, cos_theta, 0, 0],
        [0, 0, 1, 0],
        [0, 0, 0, 1]], dtype=np.float32)


def rotationA(theta, axis):
    s = np.sin(theta)
    c = np.cos(theta)

    assert axis.shape == (3,)

    x = axis[0]
    y = axis[1]
    z = axis[2]

    return np.array([
        # First row
        [c + (1 - c) * x * x,
         (1 - c) * x * y - s * z,
         (1 - c) * x * z + s * y,
         0],
        # Second row
        [(1 - c) * x * y + s * z,
         c + (1 - c) * y * y,
         (1 - c) * y * z - s * x,
         0],
        # Third row
        [(1 - c) * x * z - s * y,
         (1 - c) * y * z + s * x,
         c + (1 - c) * z * z,
         0],
        # Fourth row
        [0, 0, 0, 1]], dtype=np.float32)


def translate(tx, ty, tz):
    return np.array([
        [1, 0, 0, tx],
        [0, 1, 0, ty],
        [0, 0, 1, tz],
        [0, 0, 0, 1]], dtype=np.float32)


def shearing(xy, yx, xz, zx, yz, zy):
    return np.array([
        [1, xy, xz, 0],
        [yx, 1, yz, 0],
        [zx, zy, 1, 0],
        [0, 0, 0, 1]], dtype=np.float32)


def matmul(mats):
    out = mats[0]
    for i in range(1, len(mats)):
        out = np.matmul(out, mats[i])

    return out


def frustum(left, right, bottom, top, near, far):
    r_l = right - left
    t_b = top - bottom
    f_n = far - near
    return np.array([
        [2 * near / r_l,
         0,
         (right + left) / r_l,
         0],
        [0,
         2 * near / t_b,
         (top + bottom) / t_b,
         0],
        [0,
         0,
         -(far + near) / f_n,
         -2 * near * far / f_n],
        [0,
         0,
         -1,
         0]], dtype=np.float32)


def perspective(fovy, aspect, near, far):
    halfHeight = np.tan(np.pi * fovy / 360) * near
    halfWidth = halfHeight * aspect
    return frustum(-halfWidth, halfWidth, -halfHeight, halfHeight, near, far)


def ortho(left, right, bottom, top, near, far):
    r_l = right - left
    t_b = top - bottom
    f_n = far - near
    return np.array([
        [2 / r_l,
         0,
         0,
         -(right + left) / r_l],
        [0,
         2 / t_b,
         0,
         -(top + bottom) / t_b],
        [0,
         0,
         -2 / f_n,
         -(far + near) / f_n],
        [0,
         0,
         0,
         1]], dtype=np.float32)


def lookAt(eye, at, up):
    forward = (at - eye)
    forward = forward / np.linalg.norm(forward)

    side = np.cross(forward, up)
    side = side / np.linalg.norm(side)

    newUp = np.cross(side, forward)
    newUp = newUp / np.linalg.norm(newUp)

    return np.array([
        [side[0], side[1], side[2], -np.dot(side, eye)],
        [newUp[0], newUp[1], newUp[2], -np.dot(newUp, eye)],
        [-forward[0], -forward[1], -forward[2], np.dot(forward, eye)],
        [0, 0, 0, 1]
    ], dtype=np.float32)