/// <summary>
/// Compute the normal vector of the specified face
/// </summary>
/// <returns>The normal.</returns>
/// <param name="face">Face.</param>
public static Vector3d FaceNormal(HE_Face face)
{
if (face.isBoundaryLoop())
{
return(null);
}
Vector3d u = Vector(face.HalfEdge);
Vector3d v = -Vector(face.HalfEdge.Prev);
return(u.Cross(v).Unit());
}
/// <summary>
/// Computes the area of the specified face
/// </summary>
/// <returns>The face area</returns>
/// <param name="face">Face.</param>
public static double Area(HE_Face face)
{
if (face.isBoundaryLoop())
{
return(0.0);
}
Vector3d u = Vector(face.HalfEdge);
Vector3d v = -Vector(face.HalfEdge.Prev);
return(0.5 * u.Cross(v).Length);
}
/// <summary>
/// Compute the centroid of the specified face
/// </summary>
/// <returns>The centroid.</returns>
/// <param name="face">Face.</param>
public static Point3d Centroid(HE_Face face)
{
HE_HalfEdge hE = face.HalfEdge;
Point3d a = hE.Vertex;
Point3d b = hE.Next.Vertex;
Point3d c = hE.Prev.Vertex;
if (face.isBoundaryLoop())
{
return((a + b) / 2);
}
return((a + b + c) / 3);
}
/// <summary>
/// Compute the circumcenter the specified face.
/// </summary>
/// <returns>The circumcenter.</returns>
/// <param name="face">Face.</param>
public static Point3d Circumcenter(HE_Face face)
{
HE_HalfEdge hE = face.HalfEdge;
Point3d a = hE.Vertex;
Point3d b = hE.Next.Vertex;
Point3d c = hE.Prev.Vertex;
if (face.isBoundaryLoop())
{
return((a + b) / 2);
}
Vector3d ac = c - a;
Vector3d ab = b - a;
Vector3d w = ab.Cross(ac);
Vector3d u = (w.Cross(ab)) * ac.Length2;
Vector3d v = (ac.Cross(w)) * ab.Length2;
Point3d x = (u + v) / (2 * w.Length2);
return(x + a);
}