Class MeshGeometry

Represents the geometry of a HE_Mesh such as positions at vertices.

Inheritance

System.Object

MeshGeometry

Namespace: Paramdigma.Core.Geometry

Assembly: Paramdigma.Core.dll

Syntax

public static class MeshGeometry : object

Methods

Angle(MeshCorner)

Compute the angle (in radians) at the specified corner.

Declaration

public static double Angle(MeshCorner corner)

Parameters

Type	Name	Description
MeshCorner	corner	Corner.

Returns

Type	Description
System.Double	The angle (in radians).

AngleDefect(MeshVertex)

Computes the angle defect at the given vertex.

Declaration

public static double AngleDefect(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex to compute angle defect.

Returns

Type	Description
System.Double	Number representing the deviation of the current vertex from $2\PI$.

Area(MeshFace)

Computes the area of the specified face.

Declaration

public static double Area(MeshFace face)

Parameters

Type	Name	Description
MeshFace	face	Face.

Returns

Type	Description
System.Double	The face area.

BarycentricDualArea(MeshVertex)

Computes the barycentric dual area around a given mesh vertex.

Declaration

public static double BarycentricDualArea(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
System.Double	The dual area.

Centroid(MeshFace)

Compute the centroid of the specified face.

Declaration

public static Point3d Centroid(MeshFace face)

Parameters

Type	Name	Description
MeshFace	face	Face.

Returns

Type	Description
Point3d	The centroid.

Circumcenter(MeshFace)

Compute the circumcenter the specified face.

Declaration

public static Point3d Circumcenter(MeshFace face)

Parameters

Type	Name	Description
MeshFace	face	Face.

Returns

Type	Description
Point3d	The circumcenter.

CircumcentricDualArea(MeshVertex)

Computes the circumcentric dual area around a given mesh vertex.

Declaration

public static double CircumcentricDualArea(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
System.Double	The dual area.

Cotan(MeshHalfEdge)

Computes the cotangent of the angle opposite to a half-edge.

Declaration

public static double Cotan(MeshHalfEdge hE)

Parameters

Type	Name	Description
MeshHalfEdge	hE	The half-edge

Returns

Type	Description
System.Double	The cotangent value.

DihedralAngle(MeshHalfEdge)

Computes the signed angle (in radians) between the faces adjacent to the specified half-edge.

Declaration

public static double DihedralAngle(MeshHalfEdge hE)

Parameters

Type	Name	Description
MeshHalfEdge	hE	H e.

Returns

Type	Description
System.Double	The angle (in radians) between faces.

FaceNormal(MeshFace)

Compute the normal vector of the specified face.

Declaration

public static Vector3d FaceNormal(MeshFace face)

Parameters

Type	Name	Description
MeshFace	face	Face.

Returns

Type	Description
Vector3d	The normal.

Length(MeshEdge)

Calculates the length of the specified edge.

Declaration

public static double Length(MeshEdge edge)

Parameters

Type	Name	Description
MeshEdge	edge	Edge.

Returns

Type	Description
System.Double	The length.

MeanEdgeLength(Mesh)

Calculates the mean edge length of the mesh.

Declaration

public static double MeanEdgeLength(Mesh mesh)

Parameters

Type	Name	Description
Mesh	mesh	Mesh.

Returns

Type	Description
System.Double	The mean edge length of the mesh.

MidPoint(MeshEdge)

Calculates the midpoint of the specified edge.

Declaration

public static Point3d MidPoint(MeshEdge edge)

Parameters

Type	Name	Description
MeshEdge	edge	Edge.

Returns

Type	Description
Point3d	The point.

OrthonormalBases(MeshFace)

Compute the orthonormal bases of the specified face.

Declaration

public static Vector3d[] OrthonormalBases(MeshFace face)

Parameters

Type	Name	Description
MeshFace	face	Face.

Returns

Type	Description
Vector3d[]	Array containing the 2 Vector3d.

PrincipalCurvatures(MeshVertex)

Compute the principal curvature scalar values at a given vertex.

Declaration

public static double[] PrincipalCurvatures(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex to compute the curvature.

Returns

Type	Description
System.Double[]	Returns an array of 2 values {k1, k2}.

ScalarGaussCurvature(MeshVertex)

Compute the Gaussian curvature at the given vertex.

Declaration

public static double ScalarGaussCurvature(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex to compute Gaussian curvature.

Returns

Type	Description
System.Double	Number representing the gaussian curvature at that vertex.

ScalarMeanCurvature(MeshVertex)

Compute the Mean curvature at the given vertex.

Declaration

public static double ScalarMeanCurvature(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex to compute Mean curvature.

Returns

Type	Description
System.Double	Number representing the Mean curvature at that vertex.

TotalAngleDefect(Mesh)

Compute the total angle defect of the mesh.

Declaration

public static double TotalAngleDefect(Mesh mesh)

Parameters

Type	Name	Description
Mesh	mesh	Mesh to compute angle defect.

Returns

Type	Description
System.Double	Returns the total angle defect as a scalar value.

TotalArea(Mesh)

Computes the total area of the mesh.

Declaration

public static double TotalArea(Mesh mesh)

Parameters

Type	Name	Description
Mesh	mesh	Mesh.

Returns

Type	Description
System.Double	The mesh area.

Vector(MeshHalfEdge)

Calculate the vector of a specified half-edge.

Declaration

public static Vector3d Vector(MeshHalfEdge halfEdge)

Parameters

Type	Name	Description
MeshHalfEdge	halfEdge	Half edge.

Returns

Type	Description
Vector3d	The half-edge vector.

VertexNormalAngleWeighted(MeshVertex)

Computes the angle weighted normal around the specified vertex.

Declaration

public static Vector3d VertexNormalAngleWeighted(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
Vector3d	The normal vector at that vertex.

VertexNormalAreaWeighted(MeshVertex)

Computes the area weighted normal around the specified vertex.

Declaration

public static Vector3d VertexNormalAreaWeighted(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
Vector3d	The normal vector at that vertex.

VertexNormalEquallyWeighted(MeshVertex)

Computes the equally weighted normal around the specified vertex.

Declaration

public static Vector3d VertexNormalEquallyWeighted(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
Vector3d	The normal vector at that vertex.

VertexNormalGaussCurvature(MeshVertex)

Computes the gauss curvature weighted normal around the specified vertex.

Declaration

public static Vector3d VertexNormalGaussCurvature(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
Vector3d	The normal vector at that vertex.

VertexNormalMeanCurvature(MeshVertex)

Computes the mean curvature weighted normal around the specified vertex.

Declaration

public static Vector3d VertexNormalMeanCurvature(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
Vector3d	The normal vector at that vertex.

VertexNormalSphereInscribed(MeshVertex)

Computes the sphere inscribed normal around the specified vertex.

Declaration

public static Vector3d VertexNormalSphereInscribed(MeshVertex vertex)

Parameters

Type	Name	Description
MeshVertex	vertex	Vertex.

Returns

Type	Description
Vector3d	The normal vector at that vertex.