/// <summary>
/// Computes the angle defect at the given vertex.
/// </summary>
/// <param name="vertex">Vertex to compute angle defect.</param>
/// <returns>Number representing the deviation of the current vertex from $2\PI$.</returns>
public static double AngleDefect(MeshVertex vertex)
{
var angleSum = 0.0;
foreach (var c in vertex.AdjacentCorners())
{
angleSum += Angle(c);
}
// if (vertex.OnBoundary()) angleSum = Math.PI - angleSum;
return(vertex.OnBoundary() ? Math.PI - angleSum : 2 * Math.PI - angleSum);
}
/// <summary>
/// Computes the sphere inscribed normal around the specified vertex.
/// </summary>
/// <returns>The normal vector at that vertex.</returns>
/// <param name="vertex">Vertex.</param>
public static Vector3d VertexNormalSphereInscribed(MeshVertex vertex)
{
var n = new Vector3d();
foreach (var c in vertex.AdjacentCorners())
{
var u = Vector(c.HalfEdge.Prev);
var v = -Vector(c.HalfEdge.Next);
n += u.Cross(v) / (u.LengthSquared * v.LengthSquared);
}
return(n.Unit());
}
/// <summary>
/// Computes the angle weighted normal around the specified vertex.
/// </summary>
/// <returns>The normal vector at that vertex.</returns>
/// <param name="vertex">Vertex.</param>
public static Vector3d VertexNormalAngleWeighted(MeshVertex vertex)
{
var n = new Vector3d();
foreach (var c in vertex.AdjacentCorners())
{
var normal = FaceNormal(c.HalfEdge.Face);
var angle = Angle(c);
n += normal * angle;
}
return(n.Unit());
}
