You know I think the I•N is something called a dot product.
THAT'S IT! I've always read Cheetah3D's label as an abbreviation: I - N. It actually is I • N ( the Dot Product of the Incidence Vector and the Normal Vector )! Darned tiny type! Now the name makes sense to me!
The Incidence Vector is a unit vector indicating the path of the light being reflected to the Camera from the surface/polygon.
The Normal Vector is a unit vector that its perpendicular to the surface/polygon.
A Dot Product ( A • B ) tells you how far the first vector ( A ) reaches in the direction of the second vector ( B ).
So given that both I & N are 1 unit long: If N reflects directly back along the length of I, the value of the Dot Product is 1. If N is perpendicular to the length of I, the value of the Dot Product is 0!
Mathematically, the Dot Product produces another vector, so it could be a negative value, but here, the Incidence must strike the front of the polygon, so the angle between it and the Normal ( called the Angle of Incidence ) can never be greater than 90° - so the value can never be less than 0.
A fun side effect: since this value is literally determined by the interaction between the raytracing vector from the camera and the surface of the polygon, the value will always be determined the same way, even if you are viewing a reflection of the back of that same object. Its reflection will render as if your camera were viewing the object from the surface of the mirror - so if you use the I • N value to create a transparency map, you won't see the same geometry in the reflection.