generates a triangulation of the mesh region mr.
Details and Options
- TriangulateMesh is also known as triangulation, tetrahedralization, simplicial decomposition, mesh generation and mesh refinement.
- Typically used to generate a partition of a region into lines (1D), triangles (2D) or tetrahedra (3D) optimized to some criteria.
- 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 Method Automatic method to use PerformanceGoal $PerformanceGoal whether to consider speed or quality
- Possible settings for the Method option include:
"ConformingDelaunay" triangulation that satisfies the Delaunay condition "ConstrainedDelaunay" triangulation that preserves original 1D boundary cells and almost satisfies the Delaunay condition "ConstrainedQuality" triangulation that adds fewer 0D cells and almost satisfies the Delaunay condition
- A triangulation of a mesh mr satisfies the Delaunay condition if no original point on the boundary of mr is inside the circumsphere of any simplex in .
Examplesopen allclose all
Basic Examples (3)
Triangulate a BoundaryMeshRegion in 1D:
Triangulate a MeshRegion in 1D:
TriangulateMesh works individually on dimensional components:
MaxCellMeasure controls the maximum size a cell in the triangulation can be:
The default setting is Automatic:
Wolfram Research (2014), TriangulateMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/TriangulateMesh.html (updated 2020).
Wolfram Language. 2014. "TriangulateMesh." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/TriangulateMesh.html.
Wolfram Language. (2014). TriangulateMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TriangulateMesh.html