Example Programs in the Simplicial Mesh Package.

The following programs in the example directory show how to use the data structures and algorithms to generate and optimize meshes.

Element Quality

• The quality program prints quality statistics for a mesh.
• simplexQuality assesses the quality of a single simplex.
• jacobianDecomposition calculates the decomposition of the Jacobian of mapping from the ideal simplex to the physical simplex.
• mapSimplexJac maps a simplex using a Jacobian matrix.
• mapSimplexOSA maps a simplex using the orientation, skew and aspect ratio matrices.

Geometric Optimization

• geometricOptimize uses geometric optimization to optimize the position of interior vertices in a mesh.
• geomOptBoundaryCondition uses geometric optimization subject to the constraint that the boundary vertices remain on a specified curve/surface.
• geomOptContentConstraint uses geometric optimization of vertex positions subject to a constant content constraint. That is, the area/volume of the mesh remains constant.
• laplacianSolve applies Laplacian smoothing to the interior vertices.
• laplacian applies sweeps of Laplacian smoothing to the interior vertices.
• laplacianBoundary applies sweeps of Laplacian smoothing to the boundary vertices.

Topological Optimization

• The flip program performs edges flips in a 2-D mesh to improve quality.
• topologicalOptimize does topological optimization of 3-D meshes. It performs edge removal and face removal operations to improve the mesh quality.
• incidenceOptimize optimizes the cell-node incidence relations.

Coarsening and Refinement

• The coarsen program coarsens a mesh by collapsing edges.
• The refine program refines a mesh by splitting edges.
• coarsenCells removes a specified set of cells by collapsing edges.
• refineCells refines a specified set of cells by splitting edges.
• refineBoundaryDistance refines a mesh according to the distance from the boundary.
• The refineBoundary program refines the boundary cells of a mesh so the boundary more closely matches a specified curve.

Subspace Methods

• The subspace program coarsens and refines a mesh by collapsing and splitting edges. During this process the node-cell incidence relationships are optimized and the node positions are updated with Laplacian smoothing.

Boundary Operations

• The moveBoundary program moves the boundary vertices of a 2-D/3-D mesh to lie on a curve/surface.
• fitBoundary fits the boundary of a mesh to a specified curve.
• fitMesh fits a mesh to a specified curve.

Mesh Generation

• tile meshes a curve/surface by tiling the interior with triangles/tetrahedra.
• centerPointMesh creates a mesh from the boundary and a center point.

Utilities

• The boundary program extracts the boundary of a simplicial mesh.
• iss2vtk converts a text file for a simplicial mesh to a VTK file. (VTK files can be viewed with Paraview.)
• The orientPositive orients the simplices of a mesh to have non-negative content.
• randomize randomly moves the interior vertices of a mesh to produce a distorted mesh.
• The removeLowAdjacencies progam removes the simplices that have low adjacencies.
• reverseOrientation reverses the orientation of a mesh.
• orient tries to orient the simplices in a mesh.