Geometry in Animation

Some time ago, I was referencing pictures of dung beetles for a Character Design class. In my Animation class, I was just learning the four-legged walk cycle, which was giving me some trouble. One of my instructors walked by and spotted the photo, which depicted a beetle walking backwards with two feet propped up on a ball of dung. He said "Six-legged walk cycle, eh? That's gonna be a hell of a foot slip!"

This comment broke my brain. I was having enough trouble tracking four feet on a flat surface. The prospect of dealing with six legs was a bit much for me, and I had no idea how I would begin to track two of those feet on the surface of a circular object!

I hadn't thought of that for months, and then I encountered this animated GIF (or one very similar to it):



Why of course! Everything became instantly clear to me. If the circumference of a circle is equal to the width of 3.14 of them standing side by side, then the unrolled circumference becomes the length of your footslip.  And then you only need to divide the circle into the same number of pieces as your foot slip in order to make them track correctly.

Since I'm sure the above is clear as mud, I've included my own version of the diagram, geared to animators.  The tick marks on the ground are color-coded to match the tick marks on the circle:



This may be painfully obvious to some of you.  But it was quite the epiphany for me, so I thought I'd share.  Happy animating!

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Simmon Keith Barney is an animator living in Fort Collins, Colorado.