NCF_d Property
Gets the right side d 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: 1.8.0.0 (1.8.0.0)

Syntax

C#
public double NCF_d { get; }
Visual Basic (Declaration)
Public ReadOnly Property NCF_d As Double
Visual C++
public:
property double NCF_d {
	double get ();
}

Field Value

The value d in the normal coordinate form of the plane n1*x + n2*y + n3*z = d, |n|=1, d>0.

Remarks

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.

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

  • NCF_normal * p - NCF_d is less than AbsoluteEpsilon and greater than -AbsoluteEpsilon 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