TriangleGetNeighbors

TriangleGetNeighbors[expr]

gets the neighbors in a Triangle expression.

Details and Options

To use TriangleGetNeigbors, you first need to load it using Needs["TriangleLink`"].
TriangleGetNeigbors returns a list of a list of integers that specify which tetrahedra are next to each other. An entry of indicates that the respective triangle is on the boundary.
TriangleGetNeigbors needs the "n" switch to be set during the call to TriangleTriangulate.

First, load the package:

Wolfram Language code: Needs["TriangleLink`"]

This creates an instance of a Triangle expression:

Wolfram Language code: inst = TriangleCreate[]

This sets up points and segments to use:

Wolfram Language code:

pts = {{0., 0.}, {2., 0.}, {2., 2.}, {0., 2.}};
segments = {{1, 2}, {2, 3}, {3, 4}, {4, 1}};

This sets the points and facets in the Triangle instance:

Wolfram Language code:

TriangleSetPoints[inst, pts];
TriangleSetSegments[inst, segments];

This carries out the triangulation, returning a new Triangle instance. The switch "n" requests Triangle to compute the neighbors:

Wolfram Language code: outInst = TriangleTriangulate[ inst, "pqa0.5n"]

This extracts the points and elements from the triangulation:

Wolfram Language code:

coords = TriangleGetPoints[outInst];
meshElements = TriangleGetElements[outInst];

This is a list of the neighboring elements, with indicating a boundary:

Wolfram Language code: TriangleGetNeighbors[outInst]

You can visualize the triangles:

Wolfram Language code: Graphics[ {EdgeForm[LightDarkSwitched[Black, White]], FaceForm[], GraphicsComplex[coords, Polygon[meshElements]]}]

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