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Welcome to GPDMink's documentation!
=====================

A Python implementation for **GPDMink**: gradient-parameterized deformable Minkowski sums between convex bodies with smooth bounding surface.

About
-----

This package provides implementations for computing Minkowski sums using the gradient-parameterized deformable method described in:

*"Gradient-parameterized deformable Minkowski sum with applications on contact detection"*
by Sipu Ruan and Jundong Mei in the journal `Multibody System Dynamics`.

- Article link: https://doi.org/10.1007/s11044-025-10134-5
- Supplimentary Video: https://static-content.springer.com/esm/art%3A10.1007%2Fs11044-025-10134-5/MediaObjects/11044_2025_10134_MOESM1_ESM.mp4

Key Features
------------

- Compute Minkowski sums for convex bodies with smooth surfaces
- Support for linear transformations: rotation, shearing, scaling
- Support for nonlinear deformation capabilities: tapering, bending
- Answer collision detection queries between convex bodies
- Support for ellipsoids and superquadrics geometric models

Usage
-----

See the demonstration scripts in the ``test/`` directory:

- ``demo_minkowski_sum.py``: Minkowski sums with linear and nonlinear deformations
- ``demo_superquadrics.py``: Superquadrics with deformations
- ``demo_collision_detection.py``: Collision detection between convex bodies

.. toctree::
   :maxdepth: 2
   :caption: Contents:

   modules
   api


Indices and tables
==================

* :ref:`genindex`
* :ref:`search`