import torch
import math

def getProjectionMatrix(znear, zfar, fovX, fovY):
    tanHalfFovY = math.tan((fovY / 2))
    tanHalfFovX = math.tan((fovX / 2))

    top = tanHalfFovY * znear
    bottom = -top
    right = tanHalfFovX * znear
    left = -right

    P = torch.zeros(4, 4)

    z_sign = 1.0

    P[0, 0] = 2.0 * znear / (right - left)
    P[1, 1] = 2.0 * znear / (top - bottom)
    P[0, 2] = (right + left) / (right - left)
    P[1, 2] = (top + bottom) / (top - bottom)
    P[3, 2] = z_sign
    P[2, 2] = z_sign * zfar / (zfar - znear)
    P[2, 3] = -(zfar * znear) / (zfar - znear)
    return P

def fov2focal(fov, pixels):
    return pixels / (2 * math.tan(fov / 2))

def focal2fov(focal, pixels):
    return 2*math.atan(pixels/(2*focal))