Parametric icon

thingiverse

Human beings use the two parametric equations x = cos(a*t) - pow(cos(b*t),j) and y = sin(c*t) - pow(sin(d*t),k) to construct 6-parameter icons extruded to three-dimensional space. This technique utilizes 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 showcases some explorations of this parametric space for low j and k values. For printed icons, specific parameter values are utilized: a=5, b=3, c=2, d=3, j=3, and k=2. Additionally, alternative parameters are used as well: a=1, b=3, c=3, d=2, j=5, and k=6. When using fractional values for a through d, additional cycles may be required to complete the graph accurately. The vast number of possible combinations amounts to millions, which can make this process quite time-consuming. I would greatly appreciate knowing the correct term for this set of equations.