.. PyTorch-BSF documentation master file, created by
   sphinx-quickstart on Sun Jun 27 02:31:17 2021.
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Welcome to PyTorch-BSF!
=======================

**Fit smooth, high-dimensional manifolds to your data — from a single GPU to a multi-node cluster.**

PyTorch-BSF brings **B**\ ézier **S**\ imploid **F**\ itting (BSF) to PyTorch.
A Bézier simplex is a high-dimensional generalization of the Bézier curve: it can model an arbitrarily complex point cloud as a smooth parametric hyper-surface in any number of dimensions (see `Bézier simplex fitting`_).
`Bézier simploids`_ go further: they are tensor products of Bézier simplices defined on products of simplices such as prisms and cubes, and simploidal sets glue such cells along common faces.
This makes them a natural tool for representing **Pareto fronts** in multi-objective optimization, interpolating scattered observations, and fitting geometric structures in high-dimensional spaces.

The project is on `GitHub`_.

.. note::

   BSF formerly stood for *Bézier Simplex Fitting*, which remains the special case where the parameter domain is a single simplex.

.. _Bézier simplex fitting: whatis.html
.. _Bézier simploids: advanced/simploidal.html

.. image:: _static/bezier-simplex.png
   :width: 49%
   :alt: A Bézier simplex and its control points

.. image:: _static/bezier-simplex-fitting.png
   :width: 49%
   :alt: A Bézier simplex that fits to a dataset

.. toctree::
   :maxdepth: 2
   :caption: User guide

   whatis
   quickstart
   advanced
   applications
   faq
   references

.. toctree::
   :maxdepth: 2
   :caption: API reference

   modules


Indices and tables
------------------

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

.. _GitHub: https://github.com/opthub-org/pytorch-bsf