If I have a Px(t) = At^3 + Bt^2 + Ct + 0 and Py(t) = 0 for my character's position while running and a constant radians/second that my character can turn, how can I transform that into an explicit formula for Px(t) and Py(t) after turning is applied? Is this related to fresnel and euler spirals or track transition curves? Much thanks to anyone who can give me a strong kick in the right direction.
Edit: I figured out a piece, that I ought to be figuring out P''x(t) and P''y(t) instead of thinking about curves at all.
Edited by pTymN, 10 March 2014 - 09:37 PM.