Gets the normal vector n=(n1,n2,n3) of the normal coordinate form of the plane n1*x + n2*y + n3*z = d, |n|=1, d>0.

Namespace:  ceometric.VectorGeometry
Assembly:  ceometric.VectorGeometry (in ceometric.VectorGeometry.dll) Version: (


public Vector3d NCF_normal { get; }
Visual Basic (Declaration)
Public ReadOnly Property NCF_normal As Vector3d
Visual C++
property Vector3d^ NCF_normal {
	Vector3d^ get ();

Field Value

A normalized normal vector of the plane.


The normal coordinate form (NCF) is a special form of the coordinate form a*x + b*y + c*z = d. In the normal coordinate form, the normal vector n = (a,b,c) of the coordinate form is normalized (|n|=1). In addition, the resulting equation n1*x + n2*y + n3*z = d is factored so that d >= 0 is guaranteed.

One advantage of the NCF over the coordinate form is that for a point p to test, the value

  • NCF_normal * p - NCF_d is zero if the point lies on the plane,
  • NCF_normal * p - NCF_d is positive if the point p and the origin are divided by the plane and
  • NCF_normal * p - NCF_d is negative if the point p and the origin lie on the same side of the plane.

Also, Math.Abs(NCF_d) directly gives the distance of the plane to the origin.

See Also