BoundaryMeshRegion

BoundaryMeshRegion[{p1,p2,…},{bcell1[{i1,…}],bcell2[{j1,…}],…}]

yields a mesh with boundary cells bcellj, where coordinates given as integer i are taken to be pi, where the cells together represent a closed curve, surface, etc.

BoundaryMeshRegion[…,{…,wi[bcelli[…]],…}]

yields a mesh with cell properties defined by the symbolic wrapper wi.

BoundaryMeshRegion[…,boundary1,boundary2,…]

yields a mesh from multiple boundaries boundaryi.

Details 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.
  • BoundaryMeshRegion[…] 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 bi should not 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 bi if any infinite ray starting at p crosses the set of boundaries bi an odd number of times.
  • The following special wrappers wi can be used for boundary faces:
  • Labeled[cell,…]display the cell with labeling
    Style[cell,…]show the cell with the specified style
    Property[cell,name->value]associate the property name->value with cell
  • Each cell in a BoundaryMeshRegion is given a unique MeshCellIndex of the form {d,i}, 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 i1, …
    {c1,c2,…}list of explicit cells ci
  • The index specification ispec can have the following form:
  • icell index i
    {i1,i2,…}cells with indices ik
    Allall cells
    pattcells with indices matching the pattern patt
  • The dimension specification dspec can have the following form:
  • dexplicit dimension d
    Allall dimensions from 0 to geometric dimension of region
    pattdimensions 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 two, and the same options as Graphics3D for embedding dimension three, with the following additions and changes:
  • MeshCellLabelAutomaticlabels and placement for cells
    MeshCellShapeFunctionAutomaticshape functions for cells
    MeshCellStyleAutomaticstyles for cells
    MeshCellHighlight{}list of highlighted cells
    MeshCellMarker0integer markers for cells
    PlotTheme$PlotThemeoverall theme for the mesh
  • Possible settings for PlotTheme include common base themes, font features themes, and size features themes.
  • Mesh features themes affect the plot of mesh cells. Themes include:
  • "Points"0D cells
    "Lines"1D cells, wireframe
    "Polygons"2D cells
  • Rendering features themes affect the rendering of meshes. Themes include:
  • "SampledPoints"sampled points from mesh cells
    "SphereAndTube"points as spheres and lines as tubes
    "SmoothShading"smooth shading
    "FaceNormals"normal for each 2D cell
    "LargeMesh"optimized for large number of 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.

Examples

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Basic Examples  (5)

Specify an interval from its boundary points:

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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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Scope  (18)

Options  (127)

Applications  (6)

Properties & Relations  (8)

See Also

MeshRegion  BoundaryDiscretizeRegion  BoundaryDiscretizeGraphics  ConvexHullMesh  BoundaryMesh  FindMeshDefects  BoundaryMeshRegionQ  MeshCellCount  MeshCoordinates  MeshCells  MeshCellIndex  MeshPrimitives  Printout3D

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