# Parametric icon

## by kitwallace, published Feb 29, 2016

Parametric icon Feb 29, 2016
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# Summary

Uses the two parametric equations

``````x = cos(a*t) - pow(cos(b*t),j)
y = sin(c*t) - pow(sin(d*t),k)``````

to construct 6-parameter icons extruded to 3D

This uses the code for graphing general functions from http://www.thingiverse.com/thing:1376715

The functions are included in https://en.wikipedia.org/wiki/Parametric_equation under 'Sophisticated equations' which shows some explorations of this parametric space for low j and k.

For the printed icons, the values are

a=5;b=3;c=2;d=3;j=3;k=2;
and
a=1;b=3;c=3;d=2;j=5;k=6;

Fractional values of a-d will require additional cycles to complete the graph.

The number of possible combinations is in the order of millions, so this could be a bit of a timepit.

I would love to know the proper name for this set of equations.

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