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OK, let's do it step by step, don't refresh functions that aren't changed. Let start from one-dimensional moving. 1) Suppose that we are starting from zero and have a lot of distance (X - target position) to reach maximal acceleration (A) and speed (V). Let j - jerk, a - acceleration, v - speed, x - coordinate. Then on this phase a=j*t, v=j*t^2/2, x=j*t^3/6; the end of phase is a=A, t=t1=A/j, v=v1, x=x1. 2) Now we are moving with constant acceleration, a=A, so v=v1+A*(t-t1), x=x1+v1*(t-t1)+A*(t-t1)^2/s; at the end of this phase v=v2, x=x2, t=t2. 3) Decreasing acceleration until max speed reached: a=A-j*(t-t2), v=v2+A*(t-t2)-j*(t-t2)^2/2, x=x2+v2*(t-t2)+A*(t-t2)^2/2-j*(t-t2)^3/6; end of phase: a=0, v=V, x=x3, t-t3. 4) Moving with constant speed: a=0, v=V, x=x3+V*(t-t3) until need of decreasing speed; now v=V, x=x4, t=t4. 5) Decrease speed: a=-j*(t-t4), v=V-j*(t-t4)^2/2, x=x4+V*t-j*(t-t4)^3/6; end of phase: a=-A, v=v5, x=x5, t=t5. 6) Constant deceleration: a=-A, v=v5-A*(t-t5), x=x5+v5*(t-t5)-A*(t-t5)^2/2; end of phase v=v6, t=t6, x=x6. 7) Decrease deceleration: a=-A+j*(t-t6), v=v6-A*(t-t6)+j*(t-t6)^2/2, x=v6*(t-t6)-A*(t-t6)^2/2+j*(t-t6)^3/6; end of phase is when a=0 and minimal speed, v=vmin, x=x7, t=t7. 8) Shortest phase - reaching of target position (the better we calculate all previous phases, the shorter is this phase): a=0, v=vmin, x=x7+vmin*(t-t7) until x=X.

So, in common case we need first calculate all moments of time or coordinate to know, when each stage should be started (also some stages could be omitted if, say, we don't need to go with constant acceleration or constant speed). If maximal acceleration or maximal speed are unreachable, we should calculate another (reachable) values due to real ramp.

И он тупо описал все состояния, как в ТЗ. Хотя я ему уже неоднократно намекал, что может не хватить времени для достижения максимального ускорения или максимальной скорости!