I need to deal with some curves. Nothing too fancy and nothing precise. I really need a line, something that looks like a parabola. A circle and something similar to Bézier curves would be very nice. I'm working in two dimensions, real numbers only. What I have right now is a vector of two polynomials (P1(t), P2(t)). Note that some of my curves need to be functions of time (trajectories), while others can have any form (surfaces). I'm happy with curves available to me, but I have a problem. I need approximate t of intersections of the curves. To solve a system of polynomials seems rather challenging if I restrict myself to lines and parabolas. I won't be able to do even that for higher polynomials. I assume I should be able to approximate the t of intersection somehow, but I'm not much familiar with how that is done. I was hoping there was another way to write simple curves that would make finding intersections more simple. Although I can't think of anything myself. Thanks for your time.