TetGenTetrahedralize
TetGenTetrahedralize[expr,settings]
tetrahedralizes a TetGen expression using settings and returns the result in a new TetGen expression.
Details and Options
- To use TetGenTetrahedralize, you first need to load it using Needs["TetGenLink`"].
- The settings given to TetGenTetrahedralize are a string of different commands:
-
"p" tetrahedralize a piecewise linear complex (PLC) "q" quality mesh generation; a minimum radius-edge ratio may be specified (default 2.0) "a" apply a maximum tetrahedron volume constraint "A" assign attributes to identify tetrahedra in certain regions "r" reconstruct/refine a previously generated mesh "Y" suppress splitting of boundary facets/segments "YY" suppress splitting of exterior and interior boundary facets/segments "i" insert a list of additional points into mesh "M" do not merge coplanar facets "T" set a tolerance for coplanar test (default )
"d" detect intersections of PLC facets "o2" generate second-order subparametric elements "C" check the consistency of the final mesh "Q" quiet: no terminal output except error - An empty string " " given to TetGenTetrahedralize creates a Delaunay tetrahedralization.
- TetGenTetrahedralize has the following options:
-
"TetrahedronRefinement" None function to refine a tetrahedron
Examples
open allclose allBasic Examples (1)Summary of the most common use cases

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-cbf55e
This creates an instance of a TetGen expression:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-c6p5a4

This sets up points and facets to use:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-0kep9
This sets the points and facets in the TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-hk1sfz
This carries out the tetrahedralization, returning a new TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-bvezjn

This extracts the points and faces from the tetrahedralization:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-fw39wj

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-f42wyk

Set the "r" string in place of "p" to refine an existing TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-6ylwn4

This extracts the points and faces from the tetrahedralization:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-0ziik3

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-qsql9w

Options (1)Common values & functionality for each option
"TetrahedronRefinement" (1)

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-kq4lis
This creates an instance of a TetGen expression:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-hjin9y

This sets up points and facets to use:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-k4gtkb
This sets the points and facets in the TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-3tjs5w
This carries out the tetrahedralization, returning a new TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-iinjl

This extracts the points and faces from the tetrahedralization:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-2kfpdr

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-nnxzwa

This sets up a compiled function that returns True if a tetrahedron should be refined and False otherwise:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-rqjtps
This carries out the tetrahedralization with the refinement function, returning a new TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-v05hjl

In this case the "p" string is used as the refinement operates on the initial TetGen instance.
This extracts the points and faces from the tetrahedralization:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-d4ca6f

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-6dpb7k

Refine the already tetrahedralized TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-mu7zgu

In this case the "r" string is used as the refinement operates on an already tetrahedralized TetGen instance.
This extracts the points and faces from the tetrahedralization:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-sa75p9

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-84uxxb

Possible Issues (1)Common pitfalls and unexpected behavior
Refinement of an already tetrahedralized TetGen instance needs to be done with the "r" string.

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-7119a1
Set up and tetrahedralize an initial TetGen instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-h3mqcz

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-810k3t
Inspect the number of tetrahedra in the tetrahedralized instance:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-d4n9fq

Tetrahedralization of an already tetrahedralized TetGen instance as a piecewise linear complex (PLC) does not work. No new elements are generated:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-8cdqy3

Refinement of an already tetrahedralized TetGen instance needs to be done with the "r" string:

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-k4y114

https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-v3hgnr

Text
Wolfram Research (2010), TetGenTetrahedralize, Wolfram Language function, https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html (updated 2014).
CMS
Wolfram Language. 2010. "TetGenTetrahedralize." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html.
APA
Wolfram Language. (2010). TetGenTetrahedralize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html