from jaxtyping import Float
from torch import Tensor


def homogenize_points(
    points: Float[Tensor, "*batch dim"],
) -> Float[Tensor, "*batch dim+1"]:
    """Turn n-dimensional points into (n+1)-dimensional homogeneous points."""

    raise NotImplementedError("This is your homework.")


def homogenize_vectors(
    points: Float[Tensor, "*batch dim"],
) -> Float[Tensor, "*batch dim+1"]:
    """Turn n-dimensional vectors into (n+1)-dimensional homogeneous vectors."""

    raise NotImplementedError("This is your homework.")


def transform_rigid(
    xyz: Float[Tensor, "*#batch 4"],
    transform: Float[Tensor, "*#batch 4 4"],
) -> Float[Tensor, "*batch 4"]:
    """Apply a rigid-body transform to homogeneous points or vectors."""

    raise NotImplementedError("This is your homework.")


def transform_world2cam(
    xyz: Float[Tensor, "*#batch 4"],
    cam2world: Float[Tensor, "*#batch 4 4"],
) -> Float[Tensor, "*batch 4"]:
    """Transform points or vectors from homogeneous 3D world coordinates to homogeneous
    3D camera coordinates.
    """

    raise NotImplementedError("This is your homework.")


def transform_cam2world(
    xyz: Float[Tensor, "*#batch 4"],
    cam2world: Float[Tensor, "*#batch 4 4"],
) -> Float[Tensor, "*batch 4"]:
    """Transform points or vectors from homogeneous 3D camera coordinates to homogeneous
    3D world coordinates.
    """

    raise NotImplementedError("This is your homework.")


def project(
    xyz: Float[Tensor, "*#batch 4"],
    intrinsics: Float[Tensor, "*#batch 3 3"],
) -> Float[Tensor, "*batch 2"]:
    """Project homogenized 3D points in camera coordinates to pixel coordinates."""

    raise NotImplementedError("This is your homework.")