/// <summary>
/// Computes the circumcentric dual area around a given mesh vertex.
/// </summary>
/// <returns>The dual area.</returns>
/// <param name="vertex">Vertex.</param>
public static double CircumcentricDualArea(MeshVertex vertex)
{
return((from hE in vertex.AdjacentHalfEdges()
let u2 = Vector(hE.Prev).LengthSquared
let v2 = Vector(hE).LengthSquared
let cotAlpha = Cotan(hE.Prev)
let cotBeta = Cotan(hE)
select(u2 * cotAlpha + v2 * cotBeta) / 8).Sum());
}
/// <summary>
/// Compute the Mean curvature at the given vertex.
/// </summary>
/// <param name="vertex">Vertex to compute Mean curvature.</param>
/// <returns>Number representing the Mean curvature at that vertex.</returns>
public static double ScalarMeanCurvature(MeshVertex vertex)
{
var sum = 0.0;
foreach (var hE in vertex.AdjacentHalfEdges())
{
sum += 0.5 * Length(hE.Edge) * DihedralAngle(hE);
}
return(sum);
}
/// <summary>
/// Computes the mean curvature weighted normal around the specified vertex.
/// </summary>
/// <returns>The normal vector at that vertex.</returns>
/// <param name="vertex">Vertex.</param>
public static Vector3d VertexNormalMeanCurvature(MeshVertex vertex)
{
var n = new Vector3d();
foreach (var hE in vertex.AdjacentHalfEdges())
{
var weight = 0.5 * Cotan(hE) + Cotan(hE.Twin);
n -= Vector(hE) * weight;
}
return(n.Unit());
}
/// <summary>
/// Computes the gauss curvature weighted normal around the specified vertex.
/// </summary>
/// <returns>The normal vector at that vertex.</returns>
/// <param name="vertex">Vertex.</param>
public static Vector3d VertexNormalGaussCurvature(MeshVertex vertex)
{
var n = new Vector3d();
foreach (var hE in vertex.AdjacentHalfEdges())
{
var weight = 0.5 * DihedralAngle(hE) / Length(hE.Edge);
n -= Vector(hE) * weight;
}
return(n.Unit());
}
/// <summary>
/// Computes the circumcentric dual area around a given mesh vertex.
/// </summary>
/// <returns>The dualarea.</returns>
/// <param name="vertex">Vertex.</param>
public static double CircumcentricDualarea(MeshVertex vertex)
{
double area = 0.0;
foreach (MeshHalfEdge hE in vertex.AdjacentHalfEdges())
{
double u2 = Vector(hE.Prev).LengthSquared;
double v2 = Vector(hE).LengthSquared;
double cotAlpha = Cotan(hE.Prev);
double cotBeta = Cotan(hE);
area += ((u2 * cotAlpha) + (v2 * cotBeta)) / 8;
}
return(area);
}
