transforms

Functions for coordinate transforms.

There are 6 relevant coordinate systems here, belonging to two sets of three. Each set is a global, a primary, and a secondary coordinate system; where primary and secondary are internal to those mirrors. The two sets of coordinates are the optical coordinates and the coordinates used by vertex. We denote these six coordinate systems as follows:

- opt_global
- opt_primary
- opt_secondary
- va_global
- va_primary
- va_secondary

affine_basis_transform(aff, sft, cfrom, cto, src_or_dst=True)

Take an affine transform defined in one coordinate system and move it to another. The valid coordinate systems are the same as in coord_transform.

Parameters:

Name	Type	Description	Default
aff	NDArray[float32]	Affine matrix to tranform. Should be a (3, 3) array.	required
sft	NDArray[float32]	Shift vector to tranform. Should be a (3,) array.	required
cfrom	str	The coordinate system that aff and sft is currently in.	required
cto	str	The coordinate system to put aff and sft into.	required
src_or_dst	bool	If True then the coordinate transform is done on the source points that we are affine transforming. This is equivalent to doing aff@(coord_transform(src)) + sft. If False then the coordinate transform is done on the destination points obtained by the affine transform. This is equivalent to doing coord_transform(aff@src + sft)	True

Returns:

Name	Type	Description
aff_transformed	NDArray[float32]	aff transformed into cto.
sft_transformed	NDArray[float32]	sft transformed into cto.

Source code in lat_alignment/transforms.py

def affine_basis_transform(
    aff: NDArray[np.float32],
    sft: NDArray[np.float32],
    cfrom: str,
    cto: str,
    src_or_dst: bool = True,
) -> tuple[NDArray[np.float32], NDArray[np.float32]]:
    """
    Take an affine transform defined in one coordinate system and move it to another.
    The valid coordinate systems are the same as in `coord_transform`.

    Parameters
    ----------
    aff : NDArray[np.float32]
        Affine matrix to tranform.
        Should be a `(3, 3)` array.
    sft : NDArray[np.float32]
        Shift vector to tranform.
        Should be a `(3,)` array.
    cfrom : str
        The coordinate system that `aff` and `sft` is currently in.
    cto : str
        The coordinate system to put `aff` and `sft` into.
    src_or_dst : bool, default: True
        If `True` then the coordinate transform is done on the source
        points that we are affine transforming.
        This is equivalent to doing `aff@(coord_transform(src)) + sft`.
        If `False` then the coordinate transform is done on the destination
        points obtained by the affine transform.
        This is equivalent to doing `coord_transform(aff@src + sft)`

    Returns
    -------
    aff_transformed : NDArray[np.float32]
        `aff` transformed into `cto`.
    sft_transformed : NDArray[np.float32]
        `sft` transformed into `cto`.
    """
    # Make a grid of reference points
    line = np.array((-1, 0, 1), np.float32)
    x, y, z = np.meshgrid(line, line, line)
    xyz = np.column_stack((x.ravel(), y.ravel(), z.ravel()))

    # Apply the affine transform
    xyz_transformed = apply_transform(xyz, aff, sft)

    # Move to the new coordinate system
    if src_or_dst:
        xyz = coord_transform(xyz, cfrom, cto)
    else:
        xyz_transformed = coord_transform(xyz_transformed, cfrom, cto)

    # Get the new affine transform
    aff, sft = get_affine(xyz, xyz_transformed)

    return aff, sft

coord_transform(coords, cfrom, cto)

Transform between the six defined mirror coordinates:

- opt_global
- opt_primary
- opt_secondary
- va_global
- va_primary
- va_secondary

Parameters:

Name	Type	Description	Default
coords	NDArray[float32]	Coordinates to transform. Should be a (npoint, 3) array.	required
cfrom	str	The coordinate system that coords is currently in.	required
cto	str	The coordinate system to put coords into.	required

Returns:

Name	Type	Description
coords_transformed	NDArray[float32]	coords transformed into cto.

Source code in lat_alignment/transforms.py

def coord_transform(
    coords: NDArray[np.float32], cfrom: str, cto: str
) -> NDArray[np.float32]:
    """
    Transform between the six defined mirror coordinates:

        - opt_global
        - opt_primary
        - opt_secondary
        - va_global
        - va_primary
        - va_secondary

    Parameters
    ----------
    coords : NDArray[np.float32]
        Coordinates to transform.
        Should be a `(npoint, 3)` array.
    cfrom : str
        The coordinate system that `coords` is currently in.
    cto : str
        The coordinate system to put `coords` into.

    Returns
    -------
    coords_transformed : NDArray[np.float32]
        `coords` transformed into `cto`.
    """
    if cfrom == cto:
        return coords
    match f"{cfrom}-{cto}":
        case "opt_global-opt_primary":
            return _opt_global_to_opt_primary(coords)
        case "opt_global-opt_secondary":
            return _opt_global_to_opt_secondary(coords)
        case "opt_primary-opt_global":
            return _opt_primary_to_opt_global(coords)
        case "opt_secondary-opt_global":
            return _opt_secondary_to_opt_global(coords)
        case "opt_primary-opt_secondary":
            return _opt_primary_to_opt_secondary(coords)
        case "opt_secondary-opt_primary":
            return _opt_secondary_to_opt_primary(coords)
        case "va_global-va_primary":
            return _va_global_to_va_primary(coords)
        case "va_global-va_secondary":
            return _va_global_to_va_secondary(coords)
        case "va_primary-va_global":
            return _va_primary_to_va_global(coords)
        case "va_secondary-va_global":
            return _va_secondary_to_va_global(coords)
        case "va_primary-va_secondary":
            return _va_primary_to_va_secondary(coords)
        case "va_secondary-va_primary":
            return _va_secondary_to_va_primary(coords)
        case "opt_global-va_global":
            return _opt_global_to_va_global(coords)
        case "opt_global-va_primary":
            return _opt_global_to_va_primary(coords)
        case "opt_global-va_secondary":
            return _opt_global_to_va_secondary(coords)
        case "opt_primary-va_global":
            return _opt_primary_to_va_global(coords)
        case "opt_primary-va_primary":
            return _opt_primary_to_va_primary(coords)
        case "opt_primary-va_secondary":
            return _opt_primary_to_va_secondary(coords)
        case "opt_secondary-va_global":
            return _opt_secondary_to_va_global(coords)
        case "opt_secondary-va_primary":
            return _opt_secondary_to_va_primary(coords)
        case "opt_secondary-va_secondary":
            return _opt_secondary_to_va_secondary(coords)
        case "va_global-opt_global":
            return _va_global_to_opt_global(coords)
        case "va_global-opt_primary":
            return _va_global_to_opt_primary(coords)
        case "va_global-opt_secondary":
            return _va_global_to_opt_secondary(coords)
        case "va_primary-opt_global":
            return _va_primary_to_opt_global(coords)
        case "va_primary-opt_primary":
            return _va_primary_to_opt_primary(coords)
        case "va_primary-opt_secondary":
            return _va_primary_to_opt_secondary(coords)
        case "va_secondary-opt_global":
            return _va_secondary_to_opt_global(coords)
        case "va_secondary-opt_primary":
            return _va_secondary_to_opt_primary(coords)
        case "va_secondary-opt_secondary":
            return _va_secondary_to_opt_secondary(coords)
        case _:
            raise ValueError("Invalid coordinate system provided!")