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I used 1/(1+EXP(-x)) to generate the curve in excel, although others are possible.
Those Trinamic ICs look very interesting, hadnt seen them, but you see each move "slot" between pauses has its own seperate accel/constant/decell speed/distance routine (easy to do), with the overall step speed/distance calcs generating each slot values, so a dedicated continous motion IC would not be suitable, or at least just as difficult to control as the picaxe code. It would need constant parameters fed to it which need pre calculating anyway. I dont think just constantly pauseing a step speed profile it self generates would work.
Yes, the start/end curve speeds depend on the previous/next steps elapsed time and distance. Thats done (each step has seperate inputs). They are calculated automaticaly on just time/distance input. Speeds are a non inputed result.
The single exception is ramp to zero where there are 3 inputs, time, distance and end speed, hence the need to distort the curve for a non linear speed profile. Its even possible to need to go faster than the start speed during the ramp to zero profile, to cover a long distance with a low start speed. I havent started to tackle that, might be too hard.
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