public static Double AngleBetween(IVector3D vector1, IVector3D vector2)
{
Double dot = IVector3D.Dot(vector1, vector2);
Double m1 = Math.Sqrt((vector1.X * vector1.X) + (vector1.Y * vector1.Y) + (vector1.Z * vector1.Z));
Double m2 = Math.Sqrt((vector2.X * vector2.X) + (vector2.Y * vector2.Y) + (vector2.Z * vector2.Z));
Double angle = Math.Acos(dot / (m1 * m2));
if (Double.IsNaN(angle))
{
angle = (double)0;
}
return(angle);
}
public static double AngleBetween(IPoint3D pt1, IPoint3D pt2, IPoint3D origin)
{
IVector3D v1 = IVector3D.CreateVector(pt1, origin);
IVector3D v2 = IVector3D.CreateVector(pt2, origin);
double dot = IVector3D.Dot(v1, v2);
double cos = dot / (v1.Mag() * v2.Mag());
double angle = Math.Acos(cos);
if (Double.IsNaN(angle))
{
angle = (double)0;
}
return(angle);
}
/// <summary>
/// Return the cosine dihedral angles among pairs of two-dimensional elements incident to the given edge.
/// More than one dihedral angle can be returned since the data structure supports non-manifold meshes.
/// </summary>
/// <param name="vKey1"></param>
/// <param name="vKey2"></param>
/// <returns></returns>
public double[] ComputeEdgeCosDihedralAngle(int vKey1, int vKey2)
{
int[] eKey = GetEdgeIncidentElements(vKey1, vKey2);
double[] dA = new double[0];
if (eKey.Length > 1)
{
IVector3D n1, n2, p1, p2;
double d;
int count = eKey.Length - 1;
int next_i;
if (eKey.Length > 2)
{
count = eKey.Length;
}
dA = new double[count];
for (int i = 0; i < count; i++)
{
next_i = i + 1;
if (i == eKey.Length - 1)
{
next_i = 0;
}
ComputeTwoDimensionalElementNormal(eKey[i], out n1, out p1);
ComputeTwoDimensionalElementNormal(eKey[next_i], out n2, out p2);
d = IVector3D.Dot(n1, n2);
if (d > 1)
{
d = 1;
}
else if (d < -1)
{
d = -1;
}
dA[i] = d;
}
}
return(dA);
}
/// <summary>
/// Computes the discrete Gaussian curvature as in the paper "Discrete Differential-Geometry Operators for Triangulated
/// 2-Manifolds" (http://www.cs.caltech.edu/~mmeyer/Publications/diffGeomOps.pdf)
/// </summary>
public double ComputesGaussianCurvature(int vKey)
{
IVector3D meanCurvatureVector = new IVector3D();
if (IsNakedVertex(vKey))
{
return(0.0);
}
IVector3D vect1 = new IVector3D();
IVector3D vect2 = new IVector3D();
IVector3D vect3 = new IVector3D();
double mixed = 0.0;
double gauss = 0.0;
int[] nKey = iM.Topology.GetVertexAdjacentVertices(vKey);
ITopologicVertex v = iM.GetVertexWithKey(vKey);
int next_i;
for (int i = 0; i < nKey.Length; i++)
{
next_i = i + 1;
if (i == nKey.Length - 1)
{
next_i = 0;
}
ITopologicVertex p1 = iM.GetVertexWithKey(nKey[i]);
ITopologicVertex p2 = iM.GetVertexWithKey(nKey[next_i]);
vect1 = IVector3D.CreateVector(v.Position, p1.Position);
vect2 = IVector3D.CreateVector(p1.Position, p2.Position);
vect3 = IVector3D.CreateVector(p2.Position, v.Position);
double c12 = IVector3D.Dot(vect1, vect2);
double c23 = IVector3D.Dot(vect2, vect3);
double c31 = IVector3D.Dot(vect3, vect1);
vect2 = IVector3D.Cross(vect1, vect3, false);
double area = 0.5 * vect2.Mag();
// This angle is obtuse
if (c31 > 0.0)
{
mixed += 0.5 * area;
}
else if (c12 > 0.0 || c23 > 0.0)
{
mixed += 0.25 * area;
}
else
{
if (area > 0.0 && area > -1e-9 * (c12 + c23))
{
mixed -= 0.125 * 0.5 * (c12 * IVector3D.Dot(vect3, vect3) + c23 * IVector3D.Dot(vect1, vect1)) / area;
}
}
gauss += Math.Abs(Math.Atan2(2.0 * area, -c31));
vect3 *= c12;
vect1 *= -c23;
vect3 += vect1;
meanCurvatureVector += vect3 * (0.5 / area);
}
meanCurvatureVector *= (0.5 / mixed);
// Discrete gaussian curvature
return((2.0 * Math.PI - gauss) / mixed);
}