geometry-processing-js

Class: SimplicialComplexOperators

Projects. SimplicialComplexOperators

new SimplicialComplexOperators(mesh)

This class implements various operators (e.g. boundary, star, link) on a mesh.

Parameters:
Name Type Description
mesh module:Core.Mesh

The input mesh this class acts on.
Properties:
Name Type Description
mesh module:Core.Mesh

The input mesh this class acts on.
A0 module:LinearAlgebra.SparseMatrix

The vertex-edge adjacency matrix of mesh.
A1 module:LinearAlgebra.SparseMatrix

The edge-face adjacency matrix of mesh.

Methods

assignElementIndices(mesh)

Assigns indices to the input mesh's vertices, edges, and faces

Parameters:
Name Type Description
mesh module:Core.Mesh

The input mesh which we index.

buildVertexEdgeAdjacencyMatrix(mesh)

Returns the vertex-edge adjacency matrix of the given mesh.

Parameters:
Name Type Description
mesh module:Core.Mesh

The mesh whose adjacency matrix we compute.
Returns:

The vertex-edge adjacency matrix of the given mesh.

Type
module:LinearAlgebra.SparseMatrix

buildEdgeFaceAdjacencyMatrix(mesh)

Returns the edge-face adjacency matrix.

Parameters:
Name Type Description
mesh module:Core.Mesh

The mesh whose adjacency matrix we compute.
Returns:

The edge-face adjacency matrix of the given mesh.

Type
module:LinearAlgebra.SparseMatrix

buildVertexVector(subset)

Returns a column vector representing the vertices of the
given subset.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

A column vector with |V| entries. The ith entry is 1 if
vertex i is in the given subset and 0 otherwise

Type
module:LinearAlgebra.DenseMatrix

buildEdgeVector(subset)

Returns a column vector representing the edges of the
given subset.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

A column vector with |E| entries. The ith entry is 1 if
edge i is in the given subset and 0 otherwise

Type
module:LinearAlgebra.DenseMatrix

buildFaceVector(subset)

Returns a column vector representing the faces of the
given subset.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

A column vector with |F| entries. The ith entry is 1 if
face i is in the given subset and 0 otherwise

Type
module:LinearAlgebra.DenseMatrix

star(subset)

Returns the star of a subset.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

The star of the given subset.

Type
module:Core.MeshSubset

closure(subset)

Returns the closure of a subset.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

The closure of the given subset.

Type
module:Core.MeshSubset

Returns the link of a subset.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

The link of the given subset.

Type
module:Core.MeshSubset

isComplex(subset)

Returns true if the given subset is a subcomplex and false otherwise.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

True if the given subset is a subcomplex and false otherwise.

Type
boolean

isPureComplex(subset)

Returns the degree if the given subset is a pure subcomplex and -1 otherwise.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh.
Returns:

The degree of the given subset if it is a pure subcomplex and -1 otherwise.

Type
number

boundary(subset)

Returns the boundary of a subset.

Parameters:
Name Type Description
subset module:Core.MeshSubset

A subset of our mesh. We assume subset is a pure subcomplex.
Returns:

The boundary of the given pure subcomplex.

Type
module:Core.MeshSubset