Charles Bloom algorithm for sphere-cone intersection

gistfile1.txt

V = sphere.center - cone.apex_location
a = V * cone.direction_normal
b = a * cone.tan
c = sqrt( V*V - a*a )
d = c - b
e = d * cone.cos

now  if ( e >= sphere.radius ) , cull the sphere
else if ( e <=-sphere.radius ) , totally include the sphere
else the sphere is partially included.

What's going on in this cone-sphere test? Basically, I'm trying to find 'e' which is the shortest distance from the center of the sphere to the surface of the cone. You can draw some pictures and see what's going on. 'a' is how far along the ray of the cone the sphere's center is. 'b' is the radius of the cone at 'a'. 'c' is the distance from the center of the sphere to the axis of the cone, and 'd' is the distance from the center of the sphere to the surface of the cone, along a line perpendicular to the axis of the cone (which is not the closest distance).

Note that once you compute 'a' you could tell that the sphere intersects the cone just by testing

	Square( a ) <= V*V * Square( cone.cos )

This is very fast and nice, but it can't tell us if the sphere was partially included or totally included, so it's no good for heirarchy.