/// <summary>
/// Compute the principal curvature scalar values at a given vertex.
/// </summary>
/// <param name="vertex">Vertex to compute the curvature.</param>
/// <returns>Returns an array of 2 values {k1, k2}.</returns>
public static double[] PrincipalCurvatures(MeshVertex vertex)
{
var a = CircumcentricDualArea(vertex);
var h = ScalarMeanCurvature(vertex) / a;
var k = AngleDefect(vertex) / a;
var discriminant = h * h - k;
if (discriminant > 0)
{
discriminant = Math.Sqrt(discriminant);
}
else
{
discriminant = 0;
}
var k1 = h - discriminant;
var k2 = h + discriminant;
return(new[] { k1, k2 });
}
/// <summary>
/// Compute the principal curvature scalar values at a given vertes.
/// </summary>
/// <param name="vertex">Vertex to compute the curvature.</param>
/// <returns>Returns an array of 2 values {k1, k2}.</returns>
public static double[] PrincipalCurvatures(MeshVertex vertex)
{
double a = CircumcentricDualarea(vertex);
double h = ScalarMeanCurvature(vertex) / a;
double k = AngleDefect(vertex) / a;
double discriminant = (h * h) - k;
if (discriminant > 0)
{
discriminant = Math.Sqrt(discriminant);
}
else
{
discriminant = 0;
}
double k1 = h - discriminant;
double k2 = h + discriminant;
return(new double[] { k1, k2 });
}
/// <summary> /// Compute the Gaussian curvature at the given vertex. /// </summary> /// <param name="vertex">Vertex to compute Gaussian curvature.</param> /// <returns>Number representing the gaussian curvature at that vertex.</returns> public static double ScalarGaussCurvature(MeshVertex vertex) => AngleDefect(vertex) / CircumcentricDualArea(vertex);
/// <summary>
/// Compute the Gaussian curvature at the given vertex.
/// </summary>
/// <param name="vertex">Vertex to compute Gaussian curvature.</param>
/// <returns>Number representing the gaussian curvature at that vertex.</returns>
public static double ScalarGaussCurvature(MeshVertex vertex)
{
return(AngleDefect(vertex) / MeshGeometry.CircumcentricDualarea(vertex));
}