TriangulateMesh

TriangulateMesh[bmr]

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

Details and Options

Examples

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Basic Examples  (4)

Triangulate a BoundaryMeshRegion in 1D:

Control the cell quality and sizes by using options:

Triangulate a BoundaryMeshRegion in 2D:

Control the cell quality and sizes by using options:

Triangulate a BoundaryMeshRegion in 3D:

Control the cell quality and sizes by using options:

Triangulate a MeshRegion by triangulating its BoundaryMeshRegion representation:

Scope  (4)

Triangulate a BoundaryMeshRegion in 1D:

In 2D:

In 3D:

Triangulate a MeshRegion in 1D:

In 2D:

In 3D:

TriangulateMesh will remove lower-dimensional components:

MaxCellMeasure controls the maximum size a cell in the triangulation can be:

The measure used is arc length for 1D meshes, area for 2D, and volume for 3D:

Options  (28)

MaxCellMeasure  (6)

Set different length constraints for a 1D region:

Set different area constraints for a 2D region:

The areas for the different triangles:

Set an edge length constraint for a 2D region:

The lengths for different edges:

Set a volume constraint for a 3D region:

The volumes for different tetrahedra:

Set a face area constraint for a 3D region:

The areas for different faces:

Set an edge length constraint for a 3D region:

The lengths for different edges:

MeshCellHighlight  (3)

MeshCellHighlight allows you to specify highlighting for parts of a TriangulateMesh:

By making faces transparent, the internal structure of a 3D MeshRegion can be seen:

Individual cells can be highlighted using their cell index:

Or by the cell itself:

MeshCellLabel  (3)

MeshCellLabel can be used to label parts of a TriangulateMesh:

Label the vertices and edges of a polygon:

Individual cells can be labeled using their cell index:

Or by the cell itself:

MeshCellMarker  (1)

MeshCellMarker can be used to assign values to parts of a TriangulateMesh:

Use MeshCellLabel to show the markers:

MeshCellShapeFunction  (2)

MeshCellShapeFunction allows you to specify functions for parts of a TriangulateMesh:

Individual cells can be drawn using their cell index:

Or by the cell itself:

MeshCellStyle  (3)

MeshCellStyle allows you to specify styling for parts of a TriangulateMesh:

By making faces transparent, the internal structure of a 3D MeshRegion can be seen:

Individual cells can be highlighted using their cell index:

Or by the cell itself:

MeshQualityGoal  (4)

The default setting is Automatic:

Generate a "Minimal" quality triangulation:

Generate a "Maximal" quality triangulation:

Explicitly set a quantitative quality goal:

MeshRefinementFunction  (4)

Use MeshRefinementFunction to make the edges smaller left of the origin:

Use MeshRefinementFunction to make the triangles in the first quadrant smaller:

Set a continuously varying area constraint:

Discretize the region more finely in the first orthant:

PlotTheme  (2)

Use a theme with grid lines and a legend:

Use a theme to draw a wireframe:

Applications  (4)

Triangulate a polygon:

A minimal triangulation:

Triangulate the basic 3D primitives:

Minimal triangulations:

Triangulate inside the boundary of Monaco:

Triangulate using a minimal number of triangles:

Triangulate so that the maximum area is at most :

A nonlinear transformation of a region can be approximated by transforming vertices:

Because there are few vertices in the mesh, the transformation is poorly approximated:

By triangulating, a more accurate approximation may be made:

Properties & Relations  (4)

The output of TriangulateMesh is always a MeshRegion:

The cells in the output of TriangulateMesh are always simplices:

In 2D, simplices are triangles:

Internal cells in MeshRegion are removed before triangulation:

Note that the diagonal edge is not preserved in the triangulation:

Lower-dimensional components in MeshRegion are removed:

Introduced in 2014
 (10.0)
 |
Updated in 2015
 (10.2)