> So how do I model the reel of 3? The general case of reels of 3 with > dancers going at varying speeds and crossing through the center at > varying intervals is just too complicated for me. So I will make some > simplifying assumptions that I think are pretty close to what dancers > actually do. First I assume that all three dancers dance at the same > constant speed around the entire reel and that all dancers dance on > the same figure of 8 track. Next I assume that the dancers cross > through the middle at equal intervals in time. What this means is > that each dancer is 1/3 of the total path length of the reel behind > the dancer s/he is following.
Er, sorry, these simplifying assumptions are, quite frankly, invalid.
You have one person in the middle, and two people trying to swap ends
in half the duration of the reel. The lead dancer has it easy. The
other two ARE TRYING TO BE IN THE SAME PLACE AT THE SAME TIME (in
theory). So what you get is all three people on a lissajou figure
(slower round the end 'cos you can dance as fast when turning), and
the two non-dancers have an extra sinusoidal permutation on their
speed across the centre - one person speeding up then slowing down,
the other doing the opposite - to avoid crashing into each other.
At least, that's how I modelled it for my dance animation program for
my final year degree project...which I must get round to putting up
on my web site as I have been promising various people for years...
Ian Brockbank, Indigo Active Vision Systems, The Edinburgh Technopole,
Bush Loan, Edinburgh EH26 0PJ Tel: 0131-475-7234 Fax: 0131-475-7201
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