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MeshCellMeasure

is an annotation of MeshRegion and BoundaryMeshRegion objects that gives the measures of mesh cells.

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MeshCellMeasure

MeshCellMeasure

is an annotation of MeshRegion and BoundaryMeshRegion objects that gives the measures of mesh cells.

Details

Examples

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Basic Examples  (2)

Find the measures for the cells in a BoundaryMeshRegion object:

Wolfram Language code: ℛ = BoundaryDiscretizeRegion[Disk[], MaxCellMeasure -> {"Length" -> 0.5}]

Edge lengths:

Wolfram Language code: AnnotationValue[{ℛ, 1}, MeshCellMeasure]

Find the measures for the cells in a MeshRegion object:

Wolfram Language code: ℛ = DiscretizeRegion[Disk[], MaxCellMeasure -> .25]

Polygon areas:

Wolfram Language code: AnnotationValue[{ℛ, 2}, MeshCellMeasure]

Scope  (3)

Cell indices can be used to get MeshCellMeasure:

Wolfram Language code: ℛ = DelaunayMesh[RandomReal[1, {6, 2}]]
Wolfram Language code: AnnotationValue[{ℛ, {1, {2, 3, 4}}}, MeshCellMeasure]

Cells can be used to get MeshCellMeasure:

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

Label cells by their measure:

Wolfram Language code: ℛ = [image];
Wolfram Language code: AnnotationValue[{ℛ, {2, All}}, MeshCellLabel] = NumberForm[#, 3]& /@ AnnotationValue[{ℛ, {2, All}}, MeshCellMeasure];
Wolfram Language code: ℛ

Properties & Relations  (2)

The measure given is counting for 0D, arc length for 1D, area for 2D, and volume for 3D:

Wolfram Language code: ℛ = MeshRegion[{{0, 0, 0}, {1, 0, 0}, {2, 0, 0}, {3, 0, -1 / 2}, {3, 0, 1 / 2}, {4, -1 / 2, 0}, {4, 1 / 2, 0}}, {Point[1], Line[{2, 3}], Triangle[{3, 4, 5}], Tetrahedron[{4, 6, 5, 7}]}]

The measure of a cell in each dimension:

Wolfram Language code: AnnotationValue[{ℛ, {#, 1}}, MeshCellMeasure]& /@ {0, 1, 2, 3}

RegionMeasure is equal to the total of the measures of the highest-dimensional cells:

Wolfram Language code: ℛ = DelaunayMesh[RandomReal[1, {20, 2}]]
Wolfram Language code: Total[AnnotationValue[{ℛ, RegionDimension[ℛ]}, MeshCellMeasure]] == RegionMeasure[ℛ]

In 3D:

Wolfram Language code: ℛ = DelaunayMesh[RandomReal[1, {20, 3}]]
Wolfram Language code: Total[AnnotationValue[{ℛ, RegionDimension[ℛ]}, MeshCellMeasure]] == RegionMeasure[ℛ]

Possible Issues  (1)

MeshCellMeasure cannot be modified:

Wolfram Language code: mr = MeshRegion[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}, Polygon[{{1, 2, 3}, {3, 4, 1}}]]
Wolfram Language code: Annotate[{mr, 2}, MeshCellMeasure -> .5]
Wolfram Research (2014), MeshCellMeasure, Wolfram Language function, https://reference.wolfram.com/language/ref/MeshCellMeasure.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_meshcellmeasure, author="Wolfram Research", title="{MeshCellMeasure}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MeshCellMeasure.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_meshcellmeasure, organization={Wolfram Research}, title={MeshCellMeasure}, year={2014}, url={https://reference.wolfram.com/language/ref/MeshCellMeasure.html}, note=[Accessed: 12-June-2026]}