geometry-processing-js Class: Geometry

new Geometry(mesh, positions, normalizePositions)

This class represents the geometry of a Mesh. This includes information such
as the position of vertices as well as methods to compute edge lengths, corner
angles, face area, normals, discrete curvatures etc.

Parameters:

Name	Type	Description
`mesh`	module:Core.Mesh	The mesh this class describes the geometry of.
`positions`	Array.<module:LinearAlgebra.Vector>	An array containing the position of each vertex in a mesh.
`normalizePositions`	boolean	flag to indicate whether positions should be normalized. Default value is true.

Properties:

Name	Type	Description
`mesh`	module:Core.Mesh	The mesh this class describes the geometry of.
`positions`	Object	A dictionary mapping each vertex to a normalized position.

Methods

vector(h)

Computes the vector along a halfedge.

Parameters:

Name	Type	Description
`h`	module:Core.Halfedge	The halfedge along which the vector needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

length(e)

Computes the length of an edge.

Parameters:

Name	Type	Description
`e`	module:Core.Edge	The edge whose length needs to be computed.

Returns:

Type: number

midpoint(e)

Computes the midpoint of an edge.

Parameters:

Name	Type	Description
`e`	module:Core.Edge	The edge whose midpoint needs to be computed.

Returns:

Type: number

meanEdgeLength()

Computes the mean edge length of all the edges in a mesh.

Returns:

Type: number

area(f)

Computes the area of a face.

Parameters:

Name	Type	Description
`f`	module:Core.Face	The face whose area needs to be computed.

Returns:

Type: number

totalArea()

Computes the total surface area of a mesh.

Returns:

Type: number

faceNormal(f)

Computes the normal of a face.

Parameters:

Name	Type	Description
`f`	module:Core.Face	The face whose normal needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

centroid(f)

Computes the centroid of a face.

Parameters:

Name	Type	Description
`f`	module:Core.Face	The face whose centroid needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

circumcenter(f)

Computes the circumcenter of a face.

Parameters:

Name	Type	Description
`f`	module:Core.Face	The face whose circumcenter needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

orthonormalBases(f)

Computes an orthonormal bases for a face.

Parameters:

Name	Type	Description
`f`	module:Core.Face	The face on which the orthonormal bases needs to be computed.

Returns:

An array containing two orthonormal vectors tangent to the face.

Type: Array.<module:LinearAlgebra.Vector>

angle(c)

Computes the angle (in radians) at a corner.

Parameters:

Name	Type	Description
`c`	module:Core.Corner	The corner at which the angle needs to be computed.

Returns:

The angle clamped between 0 and π.

Type: number

cotan(h)

Computes the cotangent of the angle opposite to a halfedge.

Parameters:

Name	Type	Description
`h`	module:Core.Halfedge	The halfedge opposite to the angle whose cotangent needs to be computed.

Returns:

Type: number

dihedralAngle(h)

Computes the signed angle (in radians) between two adjacent faces.

Parameters:

Name	Type	Description
`h`	module:Core.Halfedge	The halfedge (shared by the two adjacent faces) on which the dihedral angle is computed.

Returns:

The dihedral angle.

Type: number

barycentricDualArea(v)

Computes the barycentric dual area of a vertex.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex whose barycentric dual area needs to be computed.

Returns:

Type: number

circumcentricDualArea(v)

Computes the circumcentric dual area of a vertex.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex whose circumcentric dual area needs to be computed.

See:

http://cs.cmu.edu/~kmcrane/Projects/Other/TriangleAreasCheatSheet.pdf

Returns:

Type: number

vertexNormalEquallyWeighted(v)

Computes the normal at a vertex using the "equally weighted" method.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex on which the normal needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

vertexNormalAreaWeighted(v)

Computes the normal at a vertex using the "face area weights" method.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex on which the normal needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

vertexNormalAngleWeighted(v)

Computes the normal at a vertex using the "tip angle weights" method.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex on which the normal needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

vertexNormalGaussCurvature(v)

Computes the normal at a vertex using the "gauss curvature" method.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex on which the normal needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

vertexNormalMeanCurvature(v)

Computes the normal at a vertex using the "mean curvature" method (same as the "area gradient" method).

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex on which the normal needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

vertexNormalSphereInscribed(v)

Computes the normal at a vertex using the "inscribed sphere" method.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex on which the normal needs to be computed.

Returns:

Type: module:LinearAlgebra.Vector

angleDefect(v)

Computes the angle defect at a vertex (= 2π minus the sum of incident angles
at an interior vertex or π minus the sum of incident angles at a boundary vertex).

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex whose angle defect needs to be computed.

Returns:

Type: number

scalarGaussCurvature(v)

Computes the (integrated) scalar gauss curvature at a vertex.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex whose gauss curvature needs to be computed.

Returns:

Type: number

scalarMeanCurvature(v)

Computes the (integrated) scalar mean curvature at a vertex.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex whose mean curvature needs to be computed.

Returns:

Type: number

totalAngleDefect()

Computes the total angle defect (= 2π times the euler characteristic of the mesh).

Returns:

Type: number

principalCurvatures(v)

Computes the (pointwise) minimum and maximum principal curvature values at a vertex.

Parameters:

Name	Type	Description
`v`	module:Core.Vertex	The vertex on which the principal curvatures need to be computed.

Returns:

An array containing the minimum and maximum principal curvature values at a vertex.

Type: Array.<number>

laplaceMatrix(vertexIndex)

Builds a sparse laplace matrix. The laplace operator is negative semidefinite;
instead we build a positive definite matrix by multiplying the entries of the
laplace matrix by -1 and shifting the diagonal elements by a small constant (e.g. 1e-8).

Parameters:

Name	Type	Description
`vertexIndex`	Object	A dictionary mapping each vertex of a mesh to a unique index.

Returns:

Type: module:LinearAlgebra.SparseMatrix

massMatrix(vertexIndex)

Builds a sparse diagonal mass matrix containing the barycentric dual area of each vertex
of a mesh.

Parameters:

Name	Type	Description
`vertexIndex`	Object	A dictionary mapping each vertex of a mesh to a unique index.

Returns:

Type: module:LinearAlgebra.SparseMatrix

complexLaplaceMatrix(vertexIndex)

Builds a sparse complex laplace matrix. The laplace operator is negative semidefinite;
instead we build a positive definite matrix by multiplying the entries of the
laplace matrix by -1 and shifting the diagonal elements by a small constant (e.g. 1e-8).

Parameters:

Name	Type	Description
`vertexIndex`	Object	A dictionary mapping each vertex of a mesh to a unique index.

Returns:

Type: module:LinearAlgebra.ComplexSparseMatrix