Infinite cone-ray intersections

Infinite cone along y with apex

half-angle a has equation

x2 + z2 - y2 = 0.

The equation for a more general cone oriented along a line pa + vat,

with apex at pa:

cos2 a (q - pa - (va,q - pa)va)2 -

sin2 a (va,q - pa) 2 = 0

where q = (x,y,z) is a point on the

cone, and va is assumed to be of

unit length.