Tuesday, May 01, 2018

[hevxgxxm] Circle blobs

Investigate the family of blobby shapes defined in polar coordinates:

r(theta) = a0 + a1*sin(theta+phi1) + a2*sin(2*theta+phi2) + a3*sin(3*theta+phi3) + ...

This is very related to Fourier series of course.  The a1 term merely translates the circle of radius a0 so could be skipped.  a0 is the DC offset.

The a2 term does not create an ellipse, though it would be cool if it did.

We probably want to avoid the sum going negative to keep things from becoming confusing.  Higher harmonics should have smaller coefficients.  Motivation is, in a shape the first thing you notice is the DC offset (the size), and on closer examination you notice it is not a perfect circle and notice the details of the higher harmonics.

They could also be animated: amplitude modulated as a function of time, or phase changes as a function of time.  The latter seems better.  Each term could have different frequency: probably higher terms have lower frequency to avoid it becoming frenetic.  We would like to explore all combinations of phase angles, so maybe throw in some factors of the golden ratio (a different phi than the phase angle phi).

In 3D, spherical harmonics.

Previously similar.

No comments :