# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# BoundaryMeshRegion

BoundaryMeshRegion[{p1,p2,},{bcell1[{i1,}],bcell2[{j1,}],}]
yields a mesh with boundary cells , where coordinates given as integer i are taken to be , where the cells together represent a closed curve, surface, etc.

BoundaryMeshRegion[,{,wi[bcelli[]],}]
yields a mesh with cell properties defined by the symbolic wrapper .

BoundaryMeshRegion[,boundary1,boundary2,]
yields a mesh from multiple boundaries .

## Details and OptionsDetails and Options

• BoundaryMeshRegion is also known as a boundary representation.
• BoundaryMeshRegion can represent a piecewise linear and full-dimensional region embedded in dimension 1, 2, or 3.
• displays in a notebook as a plot of a boundary mesh region.
• BoundaryMeshRegion is typically constructed using functions such as ConvexHullMesh, BoundaryMesh, BoundaryDiscretizeRegion, and BoundaryDiscretizeGraphics.
• The boundary cells need to represent a closed curve or surface without self intersections.
• In BoundaryMeshRegion[{p1,p2,},b1,b2,] the boundary curves or surfaces should cross themselves or each other.
• In BoundaryMeshRegion[{p1,p2,},b1,b2,] a point p is considered to be in the region enclosed by the boundary curves or surfaces if any infinite ray starting at p crosses the set of boundaries an odd number of times.
• The following special wrappers can be used for boundary faces:
•  Labeled[cell,…] dislplay the cell with labeling Style[cell,…] show the cell with the specified style Property[cell,name->value] associate the property with cell
• Each cell in a BoundaryMeshRegion is given a unique MeshCellIndex of the form , where d is the geometric dimension and i is the index.
• For purposes of selecting cells of a BoundaryMeshRegion, the following cell specifications may be used:
•  {d,i} cell with index i of dimension d {d,ispec} cells with index specification ispec of dimension d {dspec,…} cells of dimensions given by dspec h[{i1,…}] explicit cell with head h and vertex indices , … {c1,c2,…} list of explicit cells
• The index specification ispec can have the following form:
•  i cell index i {i1,i2,…} cells with indices All all cells patt cells with indices matching the pattern patt
• The dimension specification dspec can have the following form:
•  d explicit dimension d All all dimensions from 0 to geometric dimension of region patt dimensions matching the pattern patt
• BoundaryMeshRegion contains cells of maximal dimension n-1 where n is the embedding dimension.
• BoundaryMeshRegion is always converted to an optimized representation and treated as raw by functions like AtomQ for purposes of pattern matching.
• BoundaryMeshRegion has the same options as Graphics for embedding dimension 2 and the same options as Graphics3D for embedding dimension 3, with the following additions and changes:
•  MeshCellLabel Automatic labels and placement for cells MeshCellStyle Automatic styles for cells MeshCellMarker 0 integer markers for cells
• Style and other specifications for cells are effectively applied in the order MeshCellStyle, Style, and other wrappers, with later specifications overriding earlier ones.
• Label style and other specifications for cell labels are effectively applied in the order MeshCellLabel and Labeled, with later specifications overriding earlier ones.
• BoundaryMeshRegion can be used with functions such as RegionMember, RegionDistance, RegionMeasure, and NDSolve.

## ExamplesExamplesopen allclose all

### Basic Examples  (5)Basic Examples  (5)

Specify an interval from its boundary points:

 Out[1]=

It is full dimensional:

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The region is bounded:

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The length and centroid:

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Check point membership:

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Specify a triangle from its closed boundary curve:

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It is full dimensional:

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The region is bounded:

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The area and centroid:

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Check point membership:

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Specify a tetrahedron from its closed boundary surface:

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It is full dimensional:

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The region is bounded:

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The volume and centroid:

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Check point membership:

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Specify a 2D region from multiple closed boundary curves:

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Find its area:

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Specify a 3D region from multiple closed boundary surfaces:

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Find its volume:

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