POV-ray cone: cap centers (base point and cap point) at p1 and p2, cap radii r1 and r2.
Then, assuming r1 not equal to r2 (otherwise it is a cylinder) in the equation of the infinite cone
apex: pa = p1 + r1(p2 - p1)/(r1 - r2);
axis direction: va = (p2- p1)/| p2- p1|;
tg a = (r1 - r2)/ |p2 - p1|