Convert between different ways of describing a camera

cameraConv.py

import numpy as np
from scipy.linalg import rq


def getKRC(P):
    # https://ksimek.github.io/2012/08/14/decompose/
    # P = [M|-MC]
    M = P[:,:3]
    
    # camera position
    C = -np.linalg.inv(M).dot(P[:,3])

    # intrinsic matix and extrinsic (rotaition) matrix
    K, R = rq(M) # this decomposition is not unique so we make diagonal elements (focal lengths) positive
    sign = np.diag(np.sign(np.diag(K)))
    K = K.dot(sign)
    R = sign.dot(R)

    return K, R, C


# todo
#def changeCooordinateSystem(A, transition=T):


def projectionToLookAt(P):
    # conversion to a different coordinate system
    # todo: extract it from here
    t = np.array([[1.0, 0, 0, 0], [0, -1.0, 0, 0], [0, 0, -1.0, 0], [0, 0, 0, 1]])
    P = P.dot(t)
    
    K, R, C = getKRC(P)
    
    # position is the camera position in world coordinates
    position = C.T

    # look_at is the object camera looks at
    direction = np.array([0, 0, -1.0]).T 
    direction = R.dot(direction)
    look_at = position + direction
    
    # up is just up
    up = np.array([0.0, 1.0, 0.0])

    # fov = 2 arctan (x / (2 f))
    # note here K[0,2] is already x/2
    fov = np.rad2deg(2 * np.arctan2(K[0,2], K[0,0]))
    
    return position, look_at, up, fov