Totally Twisted Dayglo Topology -- Experiment #1



This page represents an experiment in morphing 3-D models based on parameteric curves. By generating a large number of very small cylinders along the path of a parametrically defined curve in R3, I can then render (via Blue Moon Rendering Tools, in this case) some cool knots. While mathematical interpolation between these forms is simple, I wanted to test a more generic form of morphing -- from the modeled data itself.















So, I wrote a little program to take the finite element models, align the elements, and interpolate the element sizes and positions between frames. I deliberately modeled each knot with the same number of cylinders to ease this part. I think you'll find the results very pleasing!





The coloring of the surface was generated from the parameter beta, where linear interpolation between the colors was performed based on the following nodes: 
beta / 2 pi             color
-----------             -----
0                       Red 
1/6                     Yellow
1/3                     Green
1/2                     Cyan
2/3                     Blue
5/6                     Magenta
1                       Red


In addition to giving the shapes an eye-catching color scheme, it also provides information about the nature of the curves. The color gradient is inversely proportional to the speed along the path (i.e. areas of near-constant color are moving rapidly). I think I'll investigate this further in a future project.

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