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BoundaryMesh[mreg]

gives a BoundaryMeshRegion from a MeshRegion mreg.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
See Also
Related Guides
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BoundaryMesh

BoundaryMesh[mreg]

gives a BoundaryMeshRegion from a MeshRegion mreg.

Details and Options

  • BoundaryMesh effectively represents the regular closure of mreg, i.e. lower-dimensional components in the region will be dropped.
  • BoundaryMesh takes the same options as MeshRegion.

Examples

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Basic Examples  (3)

Find the BoundaryMeshRegion representation of a full-dimensional MeshRegion in 1D:

Wolfram Language code: ℛ = MeshRegion[{{0}, {1}, {2}}, {Line[{1, 2}], Line[{2, 3}]}]

The boundary representation only has the outer points:

Wolfram Language code: BoundaryMesh[ℛ]

Find the BoundaryMeshRegion representation of a full-dimensional MeshRegion in 2D:

Wolfram Language code: ℛ = MeshRegion[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, {Triangle[{1, 2, 3}], Triangle[{4, 3, 2}]}]

The boundary representation only has the outer curve:

Wolfram Language code: BoundaryMesh[ℛ]

Find the BoundaryMeshRegion representation of a full-dimensional MeshRegion in 3D:

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {0, 2, 0}, {1, 1, 2}}, {Tetrahedron[{1, 2, 3, 5}], Tetrahedron[{1, 3, 4, 5}]}, MeshCellStyle -> 2 -> Opacity[0.5]]

The boundary representation only has the outer surface:

Wolfram Language code: HighlightMesh[BoundaryMesh[ℛ], Style[2, Opacity[0.5]]]

Scope  (4)

Find the BoundaryMeshRegion representation of a full-dimensional MeshRegion in 1D:

Wolfram Language code: ℛ = MeshRegion[{{0}, {1}, {2}}, {Line[{1, 2}], Line[{2, 3}]}]

The boundary representation only has the outer points:

Wolfram Language code: BoundaryMesh[ℛ]

Find the BoundaryMeshRegion representation of a full-dimensional MeshRegion in 2D:

Wolfram Language code: ℛ = MeshRegion[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, {Triangle[{1, 2, 3}], Triangle[{4, 3, 2}]}]

The boundary representation only has the outer curve:

Wolfram Language code: BoundaryMesh[ℛ]

Find the BoundaryMeshRegion representation of a full-dimensional MeshRegion in 3D:

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {0, 2, 0}, {1, 1, 2}}, {Tetrahedron[{1, 2, 3, 5}], Tetrahedron[{1, 3, 4, 5}]}, MeshCellStyle -> 2 -> Opacity[0.5]]

The boundary representation only has the outer surface:

Wolfram Language code: HighlightMesh[BoundaryMesh[ℛ], Style[2, Opacity[0.5]]]

BoundaryMesh will remove lower-dimensional components from a MeshRegion:

Wolfram Language code: ℛ = MeshRegion[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, {Triangle[{1, 2, 3}], Line[{3, 4}]}]

The boundary representation can only represent full-dimensional components:

Wolfram Language code: BoundaryMesh[ℛ]

Properties & Relations  (4)

A BoundaryMesh is always full dimensional:

Wolfram Language code: ℛ = BoundaryMesh[MeshRegion[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, {Triangle[{1, 2, 3}], Triangle[{4, 3, 2}]}]]
Wolfram Language code: RegionDimension[ℛ] == RegionEmbeddingDimension[ℛ]

TriangulateMesh for MeshRegion effectively triangulates BoundaryMesh:

Wolfram Language code: ℛ = MeshRegion[{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, {Triangle[{1, 2, 3}], Triangle[{4, 3, 2}]}]
Wolfram Language code: {TriangulateMesh[ℛ], TriangulateMesh[BoundaryMesh[ℛ]]}

The BoundaryMesh of a DelaunayMesh is the ConvexHullMesh:

Wolfram Language code: pts = RandomReal[{-1, 1}, {50, 2}]; dm = DelaunayMesh[pts]
Wolfram Language code: {BoundaryMesh[dm], ConvexHullMesh[pts]}

In 3D:

Wolfram Language code: pts = RandomReal[1, {50, 3}];
Wolfram Language code: {BoundaryMesh[DelaunayMesh[pts]], ConvexHullMesh[pts]}

For complex meshes, a boundary representation may save significant memory:

Wolfram Language code: ℛ = DiscretizeRegion[Ball[], MaxCellMeasure -> 0.0001]; ℬ = BoundaryMesh[ℛ]; ByteCount /@ {ℛ, ℬ}
Wolfram Research (2014), BoundaryMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/BoundaryMesh.html (updated 2015).

Text

Wolfram Research (2014), BoundaryMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/BoundaryMesh.html (updated 2015).

CMS

Wolfram Language. 2014. "BoundaryMesh." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/BoundaryMesh.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_boundarymesh, author="Wolfram Research", title="{BoundaryMesh}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/BoundaryMesh.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_boundarymesh, organization={Wolfram Research}, title={BoundaryMesh}, year={2015}, url={https://reference.wolfram.com/language/ref/BoundaryMesh.html}, note=[Accessed: 12-June-2026]}