Some Maths For Animators

Here's a little real word maths problem that's just come my way...

A stop motion animator is moving something on set by 25mm for each frame taken to create movement at a steady speed. Over the next 20 frames he wishes the movement to decelerate smoothly until a rate of 10mm per increment is achieved.
Calculate the distance the object is to be moved for each of the 20 inbetween increment positions to achieve a smooth deceleration.

Well, it's taken me a few hours over this Bank Holiday weekend, but I think I've worked out the solution for this in time for tomorrow's shoot. I've drawn on some school maths and a few Excel spreadsheet tutorials, but I've knocked up a calculator that can figure this out. i.e. Calculate the in-beteweens and print out charts (to scale) for the animator to use as fairing rulers on set. The sine wave based equation I've developed, spits out these figures for the increments.


Maybe this graph looks pretty, but it wont help the animator too much...

I've then added another column to the spreadsheet to aggregate these figures and give the actual (cumulative) measurements in mm.

I eventually found that Excel's 'Scatter Graph' could be formatted to give something like a useful chart, which when printed to the correct scale can be used on-set as a useful ruler.



So this is very basic stuff for anyone involved in the science of Motion Control, but I offer it here in the hope this might come in handy for anyone (like me) needing to work this out for themselves.

Oh, and the answer to the question is...
25, 24.9, 24.6, 24.2, 23.6, 22.8,21.9, 20.9, 19.8, 18.7, 17.5, 16.3, 15.2, 14.1, 13.1, 12.2, 11.4, 10.8, 10.4, 10.1, 10.0 (mm)