.. _s_exp:

S-Exp circle pattern
--------------------

.. image:: s_exp_transparent.jpg
   :width: 100%

In this example, we will construct an S-Exp orthogonal circle pattern
with the combinatorics of a square grid, see e.g. [BP99: Discretization of surfaces
and integrable systems]. For its construction we use the explicit formulas given in
[BHS06: Minimal surfaces from combinatorics].
The S-Exp circle pattern can
be used as Weierstrass data for constructing discrete S-isothermic
minimal and maximal catenoids in Euclidean and Lorentz-Minkowski space,
as we will do in :ref:`this example <minimal_catenoid>`.

You can download the full script
:download:`s_exp.py <../../../../examples/blender/docs/examples/s_exp.py>` and
an obj file with an example
:download:`s_exp.obj <../../../../examples/blender/docs/examples/s_exp.obj>`.

.. contents::
    :local:
    :backlinks: none

Setup
=====
We begin by importing required modules, clearing the Blender scene,
and defining a function to create the s_exp circle pattern.

.. literalinclude:: ../../../../examples/blender/docs/examples/s_exp.py
   :language: python
   :start-after: [setup]
   :end-before: [setup]

Construction
============
Using the previously defined function, we construct a halfedge object
storing the circle center and touching point coordinates.

.. literalinclude:: ../../../../examples/blender/docs/examples/s_exp.py
   :language: python
   :start-after: [construct]
   :end-before: [construct]

Visualization
=============
In the visualization step, we compute and display the circles of the orthogonal
circle pattern.

.. literalinclude:: ../../../../examples/blender/docs/examples/s_exp.py
   :language: python
   :start-after: [vis]
   :end-before: [vis]

Export OBJ
==========
We can also export an OBJ file for later use. You can download it here:
:download:`s_exp.obj <../../../../examples/blender/docs/examples/s_exp.obj>`.
We convert the coordinates to 3d coordinates with `z=0`.

.. literalinclude:: ../../../../examples/blender/docs/examples/s_exp.py
   :language: python
   :start-after: [obj]
   :end-before: [obj]