/// <summary>
/// Compute the normal vector of the specified face.
/// </summary>
/// <returns>The normal.</returns>
/// <param name="face">Face.</param>
public static Vector3d FaceNormal(MeshFace face)
{
if (face.IsBoundaryLoop())
{
return(null);
}
var u = Vector(face.HalfEdge);
var 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(MeshFace face)
{
if (face.IsBoundaryLoop())
{
return(0.0);
}
var u = Vector(face.HalfEdge);
var 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(MeshFace face)
{
var 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(MeshFace face)
{
var hE = face.HalfEdge;
Point3d a = hE.Vertex;
Point3d b = hE.Next.Vertex;
Point3d c = hE.Prev.Vertex;
if (face.IsBoundaryLoop())
{
return((a + b) / 2);
}
var ac = c - a;
var ab = b - a;
var w = ab.Cross(ac);
var u = w.Cross(ab) * ac.LengthSquared;
var v = ac.Cross(w) * ab.LengthSquared;
var x = ( Point3d )(u + v) / (2 * w.LengthSquared);
return(x + a);
}
