# Line intersection algorithms for lines on 2D conic surfaces.

We are trying to write a small library of functions for performing 2D segment intersection. However the 2D surface is not an infinite Cartesian plane. It is a cone or cylinder. A point on the cone can be located by $Z$,$\theta$ and a segment is defined as $( Z_0,\theta_0 )$ to $(Z_1,\theta_1)$. I am aware that a line on a cone is helix like so that two lines can have multiple intersections.

I'm looking for some resources on the mathematics of 2D line intersection on conic surfaces but have been unable to find any.

• for the cylinder it is $e^{2 i \pi a t} = e^{2 i \pi (b t + \phi)}$ or $a t = b t + \phi + n$ i.e. $t = \frac{\phi + n}{a-b}$ where $a,b,\phi$ must be found from $(Z_i,\theta_i)$ – reuns Jan 18 '16 at 8:12
• Obvious when you think about it!! Thanks. If you write this as an answer I'll pick it as the correct one. In reality we have finite helices but this is a trivial extension. – bradgonesurfing Jan 18 '16 at 9:22