import numpy as np
import Types as t

MAT_ISO = np.array([[0.5, 0.25], [-0.5, 0.25]])
MAT_CART = np.linalg.inv(MAT_ISO)


def from_iso(
    uv: t.IsoCoord, scale: float = 1, origin: t.CartCoors = np.array([0, 0])
) -> t.CartCoors:
    return (uv @ MAT_ISO) * scale + origin


def from_cart(
    xy: t.CartCoors, scale: float = 1, origin: t.CartCoors = np.array([0, 0])
) -> t.IsoCoord:
    return (((xy - origin) / scale) @ MAT_CART + np.array([0.5, 0.5])).astype(np.int32)