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Data and Mesh Regions

Data and Mesh Regions in Mathematica 10

Mathematica Version 10 adds full support for mesh-based geometric regions. Mesh-based regions can be explicitly specified or automatically generated from lists of points, from graphics, or from other regions. Mesh-based regions are flexible enough to approximate any other region and support fast algorithms for essentially any operation. The mesh-based regions fully support the geometric region framework, including computing properties (area, nearest point, etc.) and being used as inputs to solvers (integration, solving PDEs, etc.).

  • Full support for meshes in 1D, 2D, and 3D. »
  • Ability to represent low-dimensional regions, e.g. curves in 2D, surfaces in 3D.
  • Ability to represent non-manifold regions.
  • Full support for boundary representation meshes in 1D, 2D, and 3D. »
  • Ability to represent holes in 2D, as well as voids and tunnels in 3D.
  • High-level support for styling and labeling of mesh cells. »
  • Mesh generation from point sets, including Delaunay, Voronoi, and convex hull.
  • Support for mesh triangulation with high-level controls. »
  • Automatic discretization of 2D and 3D graphics. »
  • Automatic discretization of any region. »
  • Full support for computing key region properties such as membership test, distance computation, nearest points, measure (length, area, volume), centroids, etc. »
  • Integrate over mesh-based regions. »
  • Solve partial differential equations over mesh-based regions. »
  • Support for low-level programming operations involving cells and coordinates.
  • Support for cell-level properties, for instance, to store material or other properties.

Meshes in 1D »
Meshes in 2D »
Meshes in 3D »
Mixed-Dimension Meshes »

Convex Hulls »
Delaunay Meshes »
Triangulating Meshes »
Discretizing Regions »

Discretizing Graphics »
Create a Mesh Region from Image Data »
Create a Mesh Region from Geographic Data »
Create a Mesh Region from Lattice Points »

Highlight Mesh Components »
Label Mesh Components »
Styling Mesh Components »
Visualize Mesh Properties »

Measures »
Computing Distances and Nearest Points »
Testing Membership »
Computing Bounds »

Integrating over a Mesh »
Computing a Region's Moment of Inertia »
Solving Differential Equations on a Mesh »
Visualize PDE Solutions on a 3D Mesh »