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TetGenDelaunay[points]

generates a Delaunay tetrahedralization for a 3D point set.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
See Also
Tech Notes
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TetGenLink`
TetGenLink`

TetGenDelaunay

TetGenDelaunay[points]

generates a Delaunay tetrahedralization for a 3D point set.

Details and Options

  • To use TetGenDelaunay, you first need to load it using Needs["TetGenLink`"].
  • TetGenDelaunay returns a list of points and tetrahedra.
  • TetGenDelaunay will find a tetrahedralization that connects all points.

Examples

Basic Examples  (2)

To use TetGenLink it must first be loaded:

Wolfram Language code: Needs["TetGenLink`"]

This creates some 3D data:

Wolfram Language code: data3D = RandomReal[{0, 1}, {100, 3}];

You can compute the Delaunay tetrahedralization of the data with TetGenDelaunay:

Wolfram Language code: {pts, tetrahedra} = TetGenDelaunay[data3D];

The result is a list of points and tetrahedra. The list of tetrahedra is a list of four integers that refer to the coordinate positions. To visualize the tetrahedra as a wireframe, you can use a supporting function:

Wolfram Language code: TetrahedraWireframe[i_] := Line[Union /@ Sort /@ Flatten[ i[[All, #]]& /@ {{1, 2}, {2, 3}, {3, 1}, {1, 4}, {2, 4}, {3, 4}}, 1]]
Wolfram Language code: Graphics3D[GraphicsComplex[pts, TetrahedraWireframe[tetrahedra]]]

To use TetGenLink it must first be loaded:

Wolfram Language code: Needs["TetGenLink`"]

Load geometry data:

Wolfram Language code: data3D = ExampleData[{"Geometry3D", "Cone"}, "VertexData"];

To compute the Delaunay tetrahedralization of the data, use TetGenDelaunay:

Wolfram Language code: {pts, tetrahedra} = TetGenDelaunay[data3D];
Wolfram Language code: TetrahedraWireframe[i_] := Line[Union /@ Sort /@ Flatten[ i[[All, #]]& /@ {{1, 2}, {2, 3}, {3, 1}, {1, 4}, {2, 4}, {3, 4}}, 1]]
Wolfram Language code: Graphics3D[GraphicsComplex[pts, TetrahedraWireframe[tetrahedra]]]

Note that the points returned need not be the same as the original input data:

Wolfram Language code: Length[data3D] === Length[pts]

Duplicate coordinates are deleted:

Wolfram Language code: Length[DeleteDuplicates[data3D]] === Length[pts]
Wolfram Research (2010), TetGenDelaunay, Wolfram Language function, https://reference.wolfram.com/language/TetGenLink/ref/TetGenDelaunay.html.

Text

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

CMS

Wolfram Language. 2010. "TetGenDelaunay." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/TetGenLink/ref/TetGenDelaunay.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_tetgendelaunay, author="Wolfram Research", title="{TetGenDelaunay}", year="2010", howpublished="\url{https://reference.wolfram.com/language/TetGenLink/ref/TetGenDelaunay.html}", note=[Accessed: 15-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_tetgendelaunay, organization={Wolfram Research}, title={TetGenDelaunay}, year={2010}, url={https://reference.wolfram.com/language/TetGenLink/ref/TetGenDelaunay.html}, note=[Accessed: 15-June-2026]}