TetGenLink`
TetGenLink`

TetGenSetTetrahedraVolumes

TetGenSetTetrahedraVolumes[expr,volumes]

constrains tetrahedra volumes for refinement.

Details and Options

  • To use TetGenSetTetrahedraVolumes, you first need to load it using Needs["TetGenLink`"].
  • TetGenSetTetrahedraVolumes constrains the tetrahedra volume in a refinement of a TetGen instance.

Examples

Basic Examples  (1)

To use TetGenLink, it must first be loaded:

You start by specifying the coordinates and displaying them:

Then you create the input instance and set the points:

Next, the list of facets is created:

Set the facets in the input instance of TetGen:

Tetrahedralize the input with an area constraint:

To extract the faces and visualize them, you use TetGenGetFaces:

To compute the volume of each of the tetrahedra of the object, you write a support function first:

The volume of each tetrahedron can then be computed in the following manner:

The total volume can then be computed:

To refine some tetrahedra, choose a selection of coordinates. For example, all coordinates where the component is larger than 0.7:

The refinement elements are then found:

The tetrahedra that should keep their volume during refinement are the complement of all tetrahedra and the tetrahedra selected for refinement:

Each tetrahedron that is to be refined gets a new volume assigned. Those tetrahedra that should remain unchanged are assigned a :

Set a TetGen instance with the new tetrahedra volumes:

By specifying the string "r", the TetGen instance is refined. The string "a" implies that volume constraints are to be fulfilled:

To extract the refined faces and visualize them, you use TetGenGetFaces:

Wolfram Research (2012), TetGenSetTetrahedraVolumes, Wolfram Language function, https://reference.wolfram.com/language/TetGenLink/ref/TetGenSetTetrahedraVolumes.html.

Text

Wolfram Research (2012), TetGenSetTetrahedraVolumes, Wolfram Language function, https://reference.wolfram.com/language/TetGenLink/ref/TetGenSetTetrahedraVolumes.html.

CMS

Wolfram Language. 2012. "TetGenSetTetrahedraVolumes." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/TetGenLink/ref/TetGenSetTetrahedraVolumes.html.

APA

Wolfram Language. (2012). TetGenSetTetrahedraVolumes. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/TetGenLink/ref/TetGenSetTetrahedraVolumes.html

BibTeX

@misc{reference.wolfram_2023_tetgensettetrahedravolumes, author="Wolfram Research", title="{TetGenSetTetrahedraVolumes}", year="2012", howpublished="\url{https://reference.wolfram.com/language/TetGenLink/ref/TetGenSetTetrahedraVolumes.html}", note=[Accessed: 01-March-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_tetgensettetrahedravolumes, organization={Wolfram Research}, title={TetGenSetTetrahedraVolumes}, year={2012}, url={https://reference.wolfram.com/language/TetGenLink/ref/TetGenSetTetrahedraVolumes.html}, note=[Accessed: 01-March-2024 ]}