Wolfram: Mesh Region

Mesh

Mesh is a efficient data structure that represent a 2D surface by triangles. e.g. 3D wireframe models.

Example of Use of Mesh

• Sphere represent a sphere of a given center and radius, but often you want to represent it as mesh of triangles, so that you can apply a function to points on the surface.
• A line is given by 2 end points. But you want to apply a transformation function to points on the line to deform it.

MeshRegion and BoundaryMeshRegion

Mesh in Wolfram language is MeshRegion and BoundaryMeshRegion. They represent generalized mesh, of arbitrary dimensions. In general, it represent manifold by simplexes.

About MeshRegion

• A 0D mesh element is point.
• A 1D mesh element is line, circle, or polygon made of lines.
• A 2D mesh element is disk (filled), polygon (filled), etc. They enclose an area.
• A 3D mesh element is sphere, torus, cylinder, etc. They enclose a volume.
• A mesh can be a combination 1 dimensional, 2 dimensional, 3 dimensional, objects.
• A mesh can have disjoint parts. (not just 1-single connected sheet) e.g. A set of points can be a mesh. A set of lines can be a mesh. a combination of set of points and lines can be a mesh too.
• 2D mesh elements have area.
• 3D mesh elements have volume.
• A mesh may have area, or volume, or none.

About BoundaryMeshRegion

BoundaryMeshRegion is a special case of MeshRegion, in that it represent a enclosed space. It always has an area or volume.

• MeshRegions

MeshRegion

a mesh as the disjoint union of cells

• MeshRegion

BoundaryMeshRegion

boundary mesh represents a enclosed region. e.g. area or volume.

• BoundaryMeshRegion

Convert Graphics to Mesh (Discretize Graphics)

BoundaryDiscretizeGraphics[Graphics3D[{Torus[]}]]

BoundaryDiscretizeGraphics[Graphics3D[{Sphere[]}]]

xx = DiscretizeGraphics[Rectangle[{0,0},{2,1}], MaxCellMeasure -> 0.01, Axes -> True]

• DiscretizeGraphics

• BoundaryDiscretizeGraphics

DiscretizeRegion

• DiscretizeRegion

DiscretizeRegion[Disk[], Axes -> True]
DiscretizeRegion[Disk[], MaxCellMeasure -> 0.1, Axes -> True]

BoundaryDiscretizeRegion

• BoundaryDiscretizeRegion

Convert Mesh Object to Graphics Primitives

• MeshPrimitives

use MeshPrimitives to turn a mesh to list of Graphics Primitive.