"""
Manage n-dimensional coordinate transformations via directed graphs.

``skbot.transform`` allows you to change the representation of a vector from one
coordinate system to another, i.e., it transforms the basis of the vector.
Contrary to similar libraries, this is not limited to 3D or affine
transformations, but can transform in N dimensions and between different
dimensions, too. Additionally, you can create chains - more precisely directed
graphs - of transformations between different frames, which allows you to
express quite complicated transformations.

If you come from a robotics background, this module is analogous to ROS tf2,
but works in (and between) n-dimensions. This means it naturally includes
projections, e.g. world space to pixel space, and it allows you to use more
esoteric transformations like spherical coordinates, too.


Examples
--------

>>> import skbot.transform as tf
>>> import numpy as np

Forward kinematics on a 1 DoF robot arm in 2D

>>> # setup of the arm
>>> link = tf.Translation((1, 0))
>>> joint = tf.Rotation((1, 0), (0, 1))
>>> tool_frame = tf.Frame(2)
>>> joint_frame = link(tool_frame)
>>> world = joint(joint_frame)
>>> joint.angle = 0
>>> # FK of initial position
>>> tool_pos = tool_frame.transform((0, 0), to_frame=world)
>>> assert np.allclose(tool_pos, (1, 0))
>>> # Set new joint angle and compute new FK
>>> joint.angle = np.pi / 2
>>> tool_pos = tool_frame.transform((0, 0), to_frame=world)
>>> assert np.allclose(tool_pos, (0, 1))

Base Elements
-------------

.. autosummary::
    :template: transform_class.rst
    :toctree:

    Frame
    Link

Available Transformations
-------------------------

.. rubric:: nD Links

.. autosummary::
    :template: transform_class.rst
    :toctree:

    AffineSpace
    Translation
    Rotation
    PerspectiveProjection

.. rubric:: 3D Links

.. autosummary::
    :template: transform_class.rst
    :toctree:

    EulerRotation
    QuaternionRotation
    RotvecRotation
    FrustumProjection
    RotationalJoint
    PrismaticJoint

.. rubric:: 2D Links

.. autosummary::
    :template: transform_class.rst
    :toctree:

    AngleJoint

.. rubric:: Other Links

.. autosummary::
    :template: transform_class.rst
    :toctree:

    CustomLink
    CompundLink
    InvertLink

Functions
---------

.. autosummary::
    :toctree:

    simplify_links


"""

from .base import (
    Frame,
    Link,
    CustomLink,
    InvertLink,
    CompundLink,
)

from .functions import (
    # basic transformations
    translate,
    rotate,
    reflect,
    shear,
    scale,
)

from .affine import Translation, Rotation, Inverse, AffineSpace
from .projections import PerspectiveProjection
from .utils3d import (
    FrustumProjection,
    EulerRotation,
    QuaternionRotation,
    RotvecRotation,
)
from .joints import RotationalJoint, PrismaticJoint, AngleJoint

from . import metrics
from .simplfy import simplify_links

__all__ = [
    # Core Classes for Frame Management
    "Frame",
    "metrics",  # transform chain metrics
    "Link",
    # nD Links
    "AffineSpace",
    "Rotation",
    "Translation",
    "PerspectiveProjection",
    # 2D Links
    "AngleJoint",
    # 3D Links
    "EulerRotation",
    "QuaternionRotation",
    "RotationalJoint",
    "PrismaticJoint",
    "RotvecRotation",
    "FrustumProjection",
    # Other Links
    "CustomLink",
    "InvertLink",
    "CompundLink",
    "Inverse",
    # basic transformation functions
    "translate",
    "rotate",
    "reflect",
    "shear",
    "scale",
    "simplify_links",
]
