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
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
GradientFittedMesh — mesh from points by fitting gradients
ConcaveHullMesh — mesh from points built from alpha shapes
ReconstructionMesh — mesh from point clouds
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 Search
NearestMeshCells — find the nearest mesh cells to a point
AdjacentMeshCells — find the adjacent mesh cells to a cell
MeshConnectivityGraph — compute all different connectivity graphs for a mesh
Mesh Standard Annotations »
Annotation — associate a cell with a particular annotation
AnnotationValue — get and set annotation values for cells
MeshCellStyle ▪ MeshCellLabel ▪ MeshCellHighlight ▪ MeshCellShapeFunction ▪ MeshCellMarker ▪ MeshCellMeasure ▪ MeshCellCentroid ▪ MeshCellQuality
Solvers over Regions »
NDSolve — solve partial differential equations over regions
NIntegrate ▪ Plot3D ▪ ...