Convert a plane from Point/Normal/D to plane equation

Question

I have a plane class that stores a plane as

Vector position;
Vector normal;
float d;

(Vector is just x,y,z in a helper class)

Been using it for years, serves almost all my purposes. However, I use it as a savant without really thinking much about how/why it works.

So... I need to convert it to to a float[4] format for a friend to use for some OpenGL rendering. What's the right way to convert point/normal/d to the plane equation in float[4]? Everything I try seems to be off a little bit.

[Edit] This is the plane's Create() function, which assigns a value to d...

void            Create(Vector thePoint, Vector theNormal)
    {
        theNormal.Normalize();
        pos=thePoint;
        normal=theNormal;
        d=-theNormal.Dot(thePoint);
    }

Answer 1

Using homogeneous coordinates points are

 Point = [x,y,z,1] 

To define the equation of a plane

you need the following 4 values for the coordinates of the plane

Plane = [n_x,n_y,n_z,-d]

Where (n_x,n_y,n_z) is the normal vector, and d the distance to the origin.

Now taking the dot product of the point and the plane yields the equation

[x,y,z,1] . [n_x,n_y,n_z,-d] = 0

x*n_x + y*n_y + z*n_z - d = 0

In C# code this is

public float[] GetCoord(Plane plane)
{
   return new float[] { plane.normal.X, plane.normal.Y, plane.normal.Z, -plane.d };
}