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A plane is defined by the equation N . (X - X₀) = 0 where N = (a, b, c) and passes through the point X₀ = (x₀, y₀, z₀). X defines another point on this plane (x, y, z).

N . (X - X₀) = 0 can be described as (N . X) + (N . -X₀) = 0

or

(ax + by + cz) + (-ax₀-by₀-cz₀) = 0

where (-ax₀-by₀-cz₀) = d

Where d is the negative value of a point in the plane times the unit vector describing the orientation of the plane.

This gives us the general equation: (ax + by + cz + d = 0)

jME defines the Plane as ax + by + cz = -d. Therefore, during creation of the plane, the normal of the plane (a,b,c) and the constant d is supplied.

The most common usage of Plane is Camera frustum planes. Therefore, the primary purpose of Plane is to determine if a point is on the positive side, negative side, or intersecting a plane.

Plane defines the constants:

• NEGATIVE_SIDE - represents a point on the opposite side to which the normal points.
• NO_SIDE - represents a point that lays on the plane itself.
• POSITIVE_SIDE - represents a point on the side to which the normal points.

These values are returned on a call to whichSide.

Vector3f normal = new Vector3f(0,1,0);
float constant = new Vector3f(1,1,1).dot(normal);
Plane testPlane = new Plane(normal, constant);
 
int side = testPlane.whichSide(new Vector3f(2,1,0);
 
if(side == Plane.NO_SIDE) {
   System.out.println("This point lies on the plane");
}

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