Mesh-Based Geometric Regions

The Wolfram Language provides rich support for mesh-based regions, including a boundary representation where the region is represented by its boundary (curves, surfaces, etc.) or where the region is represented as the disjoint union of simple cells. Mesh-based regions can be constructed in a variety of ways, including from points (Delaunay, convex hull, etc.), as a discretization of graphics (2D and 3D), as a discretization of any other region, or directly. Mesh-based regions work just like any other region in the Wolfram Language and can be analyzed, used as input to solvers, or used as a building block to construct more complex regions.

Mesh Regions from Cells

MeshRegion a mesh as the disjoint union of cells

BoundaryMeshRegion a boundary mesh representing an enclosed region

Mesh Regions from Parameters

SierpinskiMesh generate a Sierpiński triangle and sponge

MengerMesh  ▪  CantorMesh

Mesh Regions from Points and Arrays

DelaunayMesh Delaunay mesh from a collection of points

VoronoiMesh Voronoi mesh from a collection of points

ConvexHullMesh convex hull from a collection of points

ArrayMesh mesh from an array of cell values

ImageMesh mesh from 2D and 3D raster images

Mesh Regions from Other Objects

DiscretizeGraphics, BoundaryDiscretizeGraphics discretize 2D or 3D graphics

DiscretizeRegion, BoundaryDiscretizeRegion discretize a region

MaxCellMeasure  ▪  MeshQualityGoal  ▪  MeshRefinementFunction

Mesh Regions from Mesh Regions

HighlightMesh highlight cells of a mesh region

TriangulateMesh convert a BoundaryMeshRegion to MeshRegion

BoundaryMesh convert a MeshRegion to a BoundaryMeshRegion

Mesh Defects and Repair

FindMeshDefects find holes and other defects in a mesh region

RepairMesh automatically repair mesh defects

Import and Export

"STL" import and export mesh-based geometric regions as STL

"PLY"  ▪  "OBJ"  ▪  "OFF"  ▪  "DXF"  ▪  "DAE"  ▪  ...

Mesh Components

DimensionalMeshComponents split MeshRegion into different dimension components

ConnectedMeshComponents split MeshRegion into connected components

Mesh Parts

MeshCellCount the number of cells of different dimensions

MeshCoordinates the mesh vertex coordinates

MeshCells mesh cells from cell index and general cell specification

MeshCellIndex mesh cell indices from mesh cells and general cell specification

MeshPrimitives graphics primitives from mesh cell specification

Mesh Standard Properties »

Property associate a cell with a particular property

PropertyValue get and set property values for cells

MeshCellStyle  ▪  MeshCellLabel  ▪  MeshCellHighlight  ▪  MeshCellShapeFunction  ▪  MeshCellMarker  ▪  MeshCellMeasure  ▪  MeshCellCentroid  ▪  MeshCellQuality

Solvers over Regions »

NDSolve solve partial differential equations over regions

NIntegrate  ▪  Plot3D  ▪  ...

Region Properties and Measures »

RegionDimension  ▪  RegionMeasure  ▪  RegionNearest  ▪  ...