# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# TriangulateMesh

TriangulateMesh[bmr]
generates a MeshRegion by triangulating inside the boundaries of a BoundaryMeshRegion bmr.

## Details and OptionsDetails and Options

• TriangulateMesh is also known as triangulation, tetrahedralization, simplicial decomposition, and mesh generation.
• TriangulateMesh generates a MeshRegion consisting of line cells in 1D, triangles in 2D, and tetrahedra in 3D.
• For high-quality triangulation, constrained Delaunay triangulation is typically used.
• TriangulateMesh[mr] with a MeshRegion mr effectively uses to re-triangulate the mesh region mr.
• TriangulateMesh has the same options as MeshRegion, with the following additions and changes:
•  MaxCellMeasure Automatic maximum cell measure MeshQualityGoal Automatic quality goal for mesh cells MeshRefinementFunction None function that returns True if a mesh cell needs refinement PerformanceGoal \$PerformanceGoal whether to consider speed or quality
• With , the function is applied to each simplex created, where vlist is a list of the vertices and m is the measure. If returns True, the simplex will be refined.

## ExamplesExamplesopen allclose all

### Basic Examples  (4)Basic Examples  (4)

Triangulate a BoundaryMeshRegion in 1D:

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Control the cell quality and sizes by using options:

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Triangulate a BoundaryMeshRegion in 2D:

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Control the cell quality and sizes by using options:

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Triangulate a BoundaryMeshRegion in 3D:

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Control the cell quality and sizes by using options:

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Triangulate a MeshRegion by triangulating its BoundaryMeshRegion representation:

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