Rational Linkages
=================

Backend Utilities
-----------------

.. automodule:: rational_linkages.backend
   :members: set_backend, get_backend, is_symbolic
   :undoc-members:
   :show-inheritance:

AffineMetric
------------

.. automodule:: rational_linkages.AffineMetric
   :members:
   :undoc-members:
   :show-inheritance:

CollisionFreeOptimization
-------------------------

.. automodule:: rational_linkages.CollisionFreeOptimization
   :members: CollisionFreeOptimization, CombinatorialSearch
   :undoc-members:
   :show-inheritance:

Dual Quaternion
---------------

.. automodule:: rational_linkages.DualQuaternion
   :members:
   :undoc-members:
   :show-inheritance:

Dual Quaternion Symbolic
------------------------

.. automodule:: rational_linkages.DualQuaternionSymbolic
   :members:
   :undoc-members:
   :show-inheritance:

Dual Quaternion Action
----------------------

.. automodule:: rational_linkages.dualQuaternionAction
   :members:
   :undoc-members:
   :show-inheritance:

Exudyn Analysis
---------------

.. automodule:: rational_linkages.ExudynAnalysis
   :members:
   :undoc-members:
   :show-inheritance:

Factorization Provider
----------------------

.. automodule:: rational_linkages.FactorizationProvider
   :members:
   :exclude-members: Rational, Symbol
   :undoc-members:
   :show-inheritance:

Linkage
-------

.. automodule:: rational_linkages.Linkage
   :members: Linkage, PointsConnection, LineSegment
   :undoc-members:
   :show-inheritance:

MiniBall
--------

.. automodule:: rational_linkages.MiniBall
   :members:
   :undoc-members:
   :show-inheritance:

Motion Approximation
--------------------

.. automodule:: rational_linkages.MotionApproximation
   :members:
   :undoc-members:
   :show-inheritance:

Motion Designer
---------------

.. automodule:: rational_linkages.MotionDesigner
   :members: MotionDesigner, MotionDesignerWidget
   :undoc-members:
   :show-inheritance:

Motion Factorization
--------------------

.. automodule:: rational_linkages.MotionFactorization
   :members:
   :exclude-members: Poly, Symbol
   :undoc-members:
   :show-inheritance:

Motion Interpolation
--------------------

.. automodule:: rational_linkages.MotionInterpolation
   :members:
   :undoc-members:
   :show-inheritance:

Normalized Line
---------------

.. automodule:: rational_linkages.NormalizedLine
   :members:
   :undoc-members:
   :show-inheritance:

Normalized Line Symbolic
------------------------

.. automodule:: rational_linkages.NormalizedLineSymbolic
   :members:
   :undoc-members:
   :show-inheritance:

Normalized Plane
----------------

.. automodule:: rational_linkages.NormalizedPlane
   :members:
   :undoc-members:
   :show-inheritance:

Normalized Plane Symbolic
-------------------------

.. automodule:: rational_linkages.NormalizedPlaneSymbolic
   :members:
   :undoc-members:
   :show-inheritance:

Plotter
-------

.. automodule:: rational_linkages.Plotter
   :members:
   :undoc-members:
   :show-inheritance:

PlotterMatplotlib
-----------------

.. automodule:: rational_linkages.PlotterMatplotlib
   :members:
   :undoc-members:
   :show-inheritance:

PlotterPyqtgraph
----------------

.. automodule:: rational_linkages.PlotterPyqtgraph
   :members: PlotterPyqtgraph, FramePlotHelper, InteractivePlotter, InteractivePlotterWidget
   :undoc-members:
   :show-inheritance:

Point Homogeneous
-----------------

.. automodule:: rational_linkages.PointHomogeneous
   :members:
   :undoc-members:
   :show-inheritance:

Point Homogeneous Symbolic
--------------------------

.. automodule:: rational_linkages.PointHomogeneousSymbolic
   :members:
   :undoc-members:
   :show-inheritance:

Quaternion
----------

.. automodule:: rational_linkages.Quaternion
   :members:
   :undoc-members:
   :show-inheritance:

Quaternion Symbolic
-------------------

.. automodule:: rational_linkages.QuaternionSymbolic
   :members:
   :undoc-members:
   :show-inheritance:

Rational Bezier
---------------

.. automodule:: rational_linkages.RationalBezier
   :members: RationalBezier, BezierSegment, RationalSoo
   :undoc-members:
   :show-inheritance: rational_linkages.RationalCurve

Rational Curve
--------------

.. automodule:: rational_linkages.RationalCurve
   :members:
   :undoc-members:
   :show-inheritance:

Rational Mechanism
------------------

.. automodule:: rational_linkages.RationalMechanism
   :members:
   :undoc-members:
   :show-inheritance: rational_linkages.RationalCurve

Static Mechanism
----------------

.. automodule:: rational_linkages.StaticMechanism
   :members: StaticMechanism, SnappingMechanism
   :undoc-members:
   :show-inheritance:

Transformation Matrix
---------------------

.. automodule:: rational_linkages.TransfMatrix
   :members:
   :undoc-members:
   :show-inheritance:

Transformation Matrix Symbolic
------------------------------

.. automodule:: rational_linkages.TransfMatrixSymbolic
   :members:
   :undoc-members:
   :show-inheritance:

Utilities (Python)
------------------

.. automodule:: rational_linkages.utils
   :members:
   :undoc-members:
   :show-inheritance:

Utilities (Rust)
----------------

.. py:module:: rational_linkages.utils_rust

   Rust-compiled extension module for performance-critical operations.

.. py:function:: motion_interp_x3(p1, p2, p3)

   :param numpy.ndarray p1: First point.
   :param numpy.ndarray p2: Second point.
   :param numpy.ndarray p3: Third point.
   :returns: Interpolated result.
   :rtype: list

.. py:function:: sum_as_string(x, y)

   :param int x: First integer.
   :param int y: Second integer.
   :rtype: str