Consider a canonical eliptical cone C with its vertex at the origin, with height h, and with a base given by:
(x/a)2+(y/b)2 = 1; z = h
a, b not equal to 0. Given a point p = (px, py, pz) how would you determine if p is interior to C? I realize I can first check to see if p is outside of the elliptical right cylinder where one base the base of the elliptical cone and the other is on the XY plane, so for grins, assume that check has already been made, and p is in fact inside that cylinder.
The most obvious solution I see is to linearly scale a and b by pz/h and see if p is inside the ellipse:
(h/pz)2[(x/a)2+(y/b)2]=1; z = pz
Are there other approaches? Thanks.