Math for VSFX

Updated on Nov 25  2017

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copyright Deborah R. Fowler




Deborah R. Fowler



Circle Illusion

Posted Sept 27  2015



Recently on Facebook I saw a video showing this circle illusion (not a kitty video!). This looked like a fun thing to try in Houdini. It really is all about sin curves and offsetting the phase of the curve for each individual sphere.

The spheres are moving on a straight line, but it gives the illusion they are moving in a circle. The key is that the motion is not constant.
There is an excellent explanation given here. The diagram below is from this site.

The velocity of each circle speeds up and slows down according to a cycloid (rim of the circle rolling along a line). (Galileo 1599)

In Houdini, this is simple to implement. Move a sphere along a line according to the sin of the frame number ($F) and then copy that line/sphere while offsetting the sin phase (you can easily do that with copy stamping.

Circle Illusion I created in Houdini. The key is to offset the phase of the sin (so you can use $CY * 90/4 in the copy stamp function and then add this to the sin curve as an offset ie. 5 * sin($F*4 + stamp("../copy1","offset",0)))


Network is below and if you get stuck, the hip file exists here (H14).


Our eyes have difficulty not seeing it as a circle, however below with the "saturn" rings around you can follow the linear path of the individual components more easily.