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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" Nonefunction to refine a tetrahedron

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

First, load the package:

In[1]:=1
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-cbf55e

This creates an instance of a TetGen expression:

In[2]:=2
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-c6p5a4
Out[2]=2

This sets up points and facets to use:

In[3]:=3
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-0kep9

This sets the points and facets in the TetGen instance:

In[4]:=4
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-hk1sfz

This carries out the tetrahedralization, returning a new TetGen instance:

In[5]:=5
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-bvezjn
Out[5]=5

This extracts the points and faces from the tetrahedralization:

In[6]:=6
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-fw39wj

This plots the faces:

In[7]:=7
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-f42wyk
Out[7]=7

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

In[8]:=8
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-6ylwn4
Out[8]=8

This extracts the points and faces from the tetrahedralization:

In[9]:=9
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-0ziik3

This plots the faces:

In[10]:=10
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-qsql9w
Out[10]=10

Options  (1)Common values & functionality for each option

"TetrahedronRefinement"  (1)

First, load the package:

In[1]:=1
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-kq4lis

This creates an instance of a TetGen expression:

In[2]:=2
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-hjin9y
Out[2]=2

This sets up points and facets to use:

In[3]:=3
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-k4gtkb

This sets the points and facets in the TetGen instance:

In[4]:=4
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-3tjs5w

This carries out the tetrahedralization, returning a new TetGen instance:

In[5]:=5
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-iinjl
Out[5]=5

This extracts the points and faces from the tetrahedralization:

In[6]:=6
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-2kfpdr

This plots the faces:

In[7]:=7
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-nnxzwa
Out[7]=7

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

In[8]:=8
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-rqjtps

This carries out the tetrahedralization with the refinement function, returning a new TetGen instance:

In[9]:=9
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-v05hjl
Out[9]=9

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:

In[10]:=10
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-d4ca6f

This plots the faces:

In[11]:=11
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-6dpb7k
Out[11]=11

Refine the already tetrahedralized TetGen instance:

In[12]:=12
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-mu7zgu
Out[12]=12

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:

In[13]:=13
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-sa75p9

This plots the faces:

In[14]:=14
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-84uxxb
Out[14]=14

Possible Issues  (1)Common pitfalls and unexpected behavior

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

First, load the package:

In[1]:=1
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-7119a1

Set up and tetrahedralize an initial TetGen instance:

In[2]:=2
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-h3mqcz
In[3]:=3
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-810k3t

Inspect the number of tetrahedra in the tetrahedralized instance:

In[4]:=4
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-d4n9fq
Out[4]=4

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

In[5]:=5
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-8cdqy3
Out[5]=5

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

In[6]:=6
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-k4y114
In[7]:=7
✖
https://wolfram.com/xid/0cdrsi0hlky4keefbfwxjmmvlsgsywa-v3hgnr
Out[7]=7
Wolfram Research (2010), TetGenTetrahedralize, Wolfram Language function, https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html (updated 2014).
✖
Wolfram Research (2010), TetGenTetrahedralize, Wolfram Language function, https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html (updated 2014).

Text

Wolfram Research (2010), TetGenTetrahedralize, Wolfram Language function, https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html (updated 2014).

✖
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.

✖
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

✖
Wolfram Language. (2010). TetGenTetrahedralize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html

BibTeX

@misc{reference.wolfram_2025_tetgentetrahedralize, author="Wolfram Research", title="{TetGenTetrahedralize}", year="2014", howpublished="\url{https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html}", note=[Accessed: 25-June-2025 ]}

✖
@misc{reference.wolfram_2025_tetgentetrahedralize, author="Wolfram Research", title="{TetGenTetrahedralize}", year="2014", howpublished="\url{https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html}", note=[Accessed: 25-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_tetgentetrahedralize, organization={Wolfram Research}, title={TetGenTetrahedralize}, year={2014}, url={https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html}, note=[Accessed: 25-June-2025 ]}

✖
@online{reference.wolfram_2025_tetgentetrahedralize, organization={Wolfram Research}, title={TetGenTetrahedralize}, year={2014}, url={https://reference.wolfram.com/language/TetGenLink/ref/TetGenTetrahedralize.html}, note=[Accessed: 25-June-2025 ]}