Voronoi Diagram: How to implement parabloas?

Question

I've been trying to implement a Voronoi Diagram using Fortunes Algorithm. I understand how it works but I'm stuck at how to store the parabolic arcs.

I understand all this is needed for the parabola is the sweeplines' Y position and the sites position but I'm I don't understand what to do with it.

I found this equation online (via this site ):

What is X in this equation?

Answer 1

I'd say that y = ax ² + bx + c is the equation of a parabola with vertical axis. In this case, a,b,c are given in more detail. l _y is a parameter which describes the current position of the sweep line and therefore influences the shape of the parabola. So your equation describes a whole family of parabolas, with p _j,x and p _j,y being the coordinates of the point you actually store in your data structure.