By carefully choosing Marios position \(p in P\) and velocity \(v in T_p P\), the SM64 community was able to reach a desired positions \(q\) in \(B\) up to collision detection (for reaching some door, collecting a star, etc.). They did this by checking which \(t_1, \dots, t_k\) SM64 actually uses for calculations and then making the right choices, so that \(\rho(\exp_v(t_i)) = q\) for some \(i\) and for all other \(j \neq i\) \(\rho(\exp_v(t_j))\) is not a position that would trigger a collision detection with negative consequences (like resetting \(v\)).
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