.. PyTorch-BSF documentation master file, created by
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Welcome to PyTorch-BSF!
=======================

**Fit smooth manifolds with explicit geometry and numerical evidence.**

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

Practical guides include reproducible comparisons, parameter tuning and
interpretation of numerical evidence for the unified API.

Start with installation and the quickstart to run your first fit, then read
the geometric introduction for the underlying concepts. Continue with the
practical guides for your workflow, and consult the reference when you need
exact arguments or migration details.

.. toctree::
   :maxdepth: 2
   :caption: Getting started

   installation
   quickstart
   whatis

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

   cli
   advanced
   applications
   faq

.. toctree::
   :maxdepth: 2
   :caption: Reference

   api
   migration
   references


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

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

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