I’m trying to do hyperbolic pong in a Poincaré disk.
I'm using C++ and SFML.
Here is my problem: when the ball rebounds on a paddle, I deduce two coordinates allowing me to recover the equation of the hyperbola in circular equation form:
x² + y² + ax + by + 1 = 0
So, I have my equation and I can only move my sprite from x and y coordinates or I don’t know how to do it differently.
How can I do to move my sprite following this circle equation? Moreover, I would like, in a second time also represent the Poincaré metric, so the ball velocity will also vary in function of the metric and it position…