# DimensionalMeshComponents

gives a list {r0,r1,} of regions such that rd has dimension d for a mesh region mr.

# Details and Options

• DimensionalMeshComponents is also known as stratification.
• The length of the returned list is given by n+1 where n is .
• When there is no component of dimension d, rd will be represented by EmptyRegion[n].

# Examples

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## Basic Examples(2)

Separate parts of a mesh that have different dimensional elements:

The geometric dimensions of each component with cells are different:

The embedding dimension is the same:

Separate dimensional components in 3D:

The geometric dimensions of each component with cells are different:

The embedding dimension is the same:

## Scope(3)

A MeshRegion in 1D can have components that are 0D or 1D:

The RegionDimension of each component:

A MeshRegion in 2D can have components that are 0D, 1D, or 2D:

The RegionDimension of each component:

A MeshRegion in 3D can have components that are 0D, 1D, 2D, or 3D:

The RegionDimension of each component:

## Properties & Relations(5)

Every element of DimensionalMeshComponents will be a MeshRegion or an EmptyRegion:

This mesh has components in dimensions 1 and 2 but not 0:

The 0D component is EmptyRegion, while the 1D and 2D components are MeshRegion:

A BoundaryMeshRegion has only a full-dimensional component:

The lower-dimensional components are EmptyRegion:

The output of DelaunayMesh has only a full-dimensional component:

The output of VoronoiMesh has only a full-dimensional component:

The output of TriangulateMesh has only a full-dimensional component:

The lower-dimensional components are ignored when triangulating:

So only a full-dimensional component remains:

Wolfram Research (2014), DimensionalMeshComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/DimensionalMeshComponents.html.

#### Text

Wolfram Research (2014), DimensionalMeshComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/DimensionalMeshComponents.html.

#### CMS

Wolfram Language. 2014. "DimensionalMeshComponents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DimensionalMeshComponents.html.

#### APA

Wolfram Language. (2014). DimensionalMeshComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DimensionalMeshComponents.html

#### BibTeX

@misc{reference.wolfram_2024_dimensionalmeshcomponents, author="Wolfram Research", title="{DimensionalMeshComponents}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/DimensionalMeshComponents.html}", note=[Accessed: 21-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_dimensionalmeshcomponents, organization={Wolfram Research}, title={DimensionalMeshComponents}, year={2014}, url={https://reference.wolfram.com/language/ref/DimensionalMeshComponents.html}, note=[Accessed: 21-June-2024 ]}