tetgen 0.8.2
Python interface to tetgen
Requires Python: <3.15,>=3.10

########
 tetgen
########

.. image:: https://img.shields.io/pypi/v/tetgen.svg?logo=python&logoColor=white
   :target: https://pypi.org/project/tetgen/

This Python library is an interface to Hang Si's `TetGen
<https://github.com/ufz/tetgen>`__ C++ software. This module combines
speed of C++ with the portability and ease of installation of Python
along with integration to `PyVista <https://docs.pyvista.org>`_ for 3D
visualization and analysis. See the `TetGen
<https://github.com/ufz/tetgen>`__ GitHub page for more details on the
original creator.

This Python library uses the C++ source from TetGen (version 1.6.0,
released on August 31, 2020) hosted at `libigl/tetgen
<https://github.com/libigl/tetgen>`__.

Brief description from `Weierstrass Institute Software
<http://wias-berlin.de/software/index.jsp?id=TetGen&lang=1>`__:

   TetGen is a program to generate tetrahedral meshes of any 3D
   polyhedral domains. TetGen generates exact constrained Delaunay
   tetrahedralization, boundary conforming Delaunay meshes, and Voronoi
   partitions.

   TetGen provides various features to generate good quality and
   adaptive tetrahedral meshes suitable for numerical methods, such as
   finite element or finite volume methods. For more information of
   TetGen, please take a look at a list of `features
   <http://wias-berlin.de/software/tetgen/features.html>`__.

****************
 License (AGPL)
****************

The original `TetGen <https://github.com/ufz/tetgen>`__ software is
under AGPL (see `LICENSE
<https://github.com/pyvista/tetgen/blob/main/LICENSE>`_) and thus this
Python wrapper package must adopt that license as well.

Please look into the terms of this license before creating a dynamic
link to this software in your downstream package and understand
commercial use limitations. We are not lawyers and cannot provide any
guidance on the terms of this license.

Please see https://www.gnu.org/licenses/agpl-3.0.en.html

**************
 Installation
**************

From `PyPI <https://pypi.python.org/pypi/tetgen>`__

.. code:: bash

   pip install tetgen

From source at `GitHub <https://github.com/pyvista/tetgen>`__

.. code:: bash

   git clone https://github.com/pyvista/tetgen
   cd tetgen
   pip install .

***************
 Basic Example
***************

The features of the C++ TetGen software implemented in this module are
primarily focused on the tetrahedralization a manifold triangular
surface. This basic example demonstrates how to tetrahedralize a
manifold surface and plot part of the mesh.

.. code:: python

   import pyvista as pv
   import tetgen
   import numpy as np
   pv.set_plot_theme('document')

   sphere = pv.Sphere()
   tet = tetgen.TetGen(sphere)
   tet.tetrahedralize(order=1, mindihedral=20, minratio=1.5)
   grid = tet.grid
   grid.plot(show_edges=True)

.. figure:: https://github.com/pyvista/tetgen/raw/main/doc/images/sphere.png
   :width: 300pt

   Tetrahedralized Sphere

Extract a portion of the sphere's tetrahedral mesh below the xy plane
and plot the mesh quality.

.. code:: python

   # get cell centroids
   cells = grid.cells.reshape(-1, 5)[:, 1:]
   cell_center = grid.points[cells].mean(1)

   # extract cells below the 0 xy plane
   mask = cell_center[:, 2] < 0
   cell_ind = mask.nonzero()[0]
   subgrid = grid.extract_cells(cell_ind)

   # advanced plotting
   plotter = pv.Plotter()
   plotter.add_mesh(subgrid, 'lightgrey', lighting=True, show_edges=True)
   plotter.add_mesh(sphere, 'r', 'wireframe')
   plotter.add_legend([[' Input Mesh ', 'r'],
                       [' Tessellated Mesh ', 'black']])
   plotter.show()

.. image:: https://github.com/pyvista/tetgen/raw/main/doc/images/sphere_subgrid.png

Here is the cell quality as computed according to the minimum scaled
jacobian.

.. code::

   Compute cell quality

   >>> cell_qual = subgrid.cell_quality()['scaled_jacobian']

   Plot quality

   >>> subgrid.plot(scalars=cell_qual, stitle='Quality', cmap='bwr', clim=[0, 1],
   ...              flip_scalars=True, show_edges=True)

.. image:: https://github.com/pyvista/tetgen/raw/main/doc/images/sphere_qual.png

*************************
 Using a Background Mesh
*************************

A background mesh in TetGen is used to define a mesh sizing function for
adaptive mesh refinement. This function informs TetGen of the desired
element size throughout the domain, allowing for detailed refinement in
specific areas without unnecessary densification of the entire mesh.
Here's how to utilize a background mesh in your TetGen workflow:

#. **Generate the Background Mesh**: Create a tetrahedral mesh that
   spans the entirety of your input piecewise linear complex (PLC)
   domain. This mesh will serve as the basis for your sizing function.

#. **Define the Sizing Function**: At the nodes of your background mesh,
   define the desired mesh sizes. This can be based on geometric
   features, proximity to areas of interest, or any criterion relevant
   to your simulation needs.

#. **Optional: Export the Background Mesh and Sizing Function**: Save
   your background mesh in the TetGen-readable `.node` and `.ele`
   formats, and the sizing function values in a `.mtr` file. These files
   will be used by TetGen to guide the mesh generation process.

#. **Run TetGen with the Background Mesh**: Invoke TetGen, specifying
   the background mesh. TetGen will adjust the mesh according to the
   provided sizing function, refining the mesh where smaller elements
   are desired.

**Full Example**

To illustrate, consider a scenario where you want to refine a mesh
around a specific region with increased detail. The following steps and
code snippets demonstrate how to accomplish this with TetGen and
PyVista:

#. **Prepare Your PLC and Background Mesh**:

   .. code:: python

      import pyvista as pv
      import tetgen
      import numpy as np

      # Load or create your PLC
      sphere = pv.Sphere(theta_resolution=10, phi_resolution=10)


      # Generate a background mesh with desired resolution
      def generate_background_mesh(bounds, resolution=20, eps=1e-6):
          x_min, x_max, y_min, y_max, z_min, z_max = bounds
          grid_x, grid_y, grid_z = np.meshgrid(
              np.linspace(xmin - eps, xmax + eps, resolution),
              np.linspace(ymin - eps, ymax + eps, resolution),
              np.linspace(zmin - eps, zmax + eps, resolution),
              indexing="ij",
          )
          return pv.StructuredGrid(grid_x, grid_y, grid_z).triangulate()


      bg_mesh = generate_background_mesh(sphere.bounds)

#. **Define the Sizing Function and Write to Disk**:

   .. code:: python

      # Define sizing function based on proximity to a point of interest
      def sizing_function(
          points, focus_point=np.array([0, 0, 0]), max_size=1.0, min_size=0.1
      ):
          distances = np.linalg.norm(points - focus_point, axis=1)
          return np.clip(max_size - distances, min_size, max_size)


      bg_mesh.point_data["target_size"] = sizing_function(bg_mesh.points)


      # Optionally write out the background mesh
      def write_background_mesh(background_mesh, out_stem):
          """Write a background mesh to a file.

          This writes the mesh in tetgen format (X.b.node, X.b.ele) and a X.b.mtr file
          containing the target size for each node in the background mesh.
          """
          mtr_content = [f"{background_mesh.n_points} 1"]
          target_size = background_mesh.point_data["target_size"]
          for i in range(background_mesh.n_points):
              mtr_content.append(f"{target_size[i]:.8f}")

          pv.save_meshio(f"{out_stem}.node", background_mesh)
          mtr_file = f"{out_stem}.mtr"

          with open(mtr_file, "w") as f:
              f.write("\n".join(mtr_content))


      write_background_mesh(bg_mesh, "bgmesh.b")

#. **Use TetGen with the Background Mesh**:

   Directly pass the background mesh from PyVista to ``tetgen``:

   .. code:: python

      tet_kwargs = dict(order=1, mindihedral=20, minratio=1.5)
      tet = tetgen.TetGen(mesh)
      tet.tetrahedralize(bgmesh=bgmesh, **tet_kwargs)
      refined_mesh = tet.grid

   Alternatively, use the background mesh files.

   .. code:: python

      tet = tetgen.TetGen(sphere)
      tet.tetrahedralize(bgmeshfilename="bgmesh.b", **tet_kwargs)
      refined_mesh = tet.grid

This example demonstrates generating a background mesh, defining a
spatially varying sizing function, and using this background mesh to
guide TetGen in refining a PLC. By following these steps, you can
achieve adaptive mesh refinement tailored to your specific simulation
requirements.

*****************
 Acknowledgments
*****************

Software was originally created by Hang Si based on work published in
`TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator
<https://dl.acm.org/citation.cfm?doid=2629697>`__.