两条以不同速度旋转的线相交所描绘的曲线

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Twitter The curves traced out by the intersection of two lines rotating at different speeds

ratio = 1, circle
ratio = 3/2, limacon
ratio =13/12 bipolar cylindrical coord. curves
ratio = 2 Folium of Descartes
ratio = 3 branch of a conchoid, maybe

这个曲线族的参数化是

1. {2/(Tan[a*t] - Tan[b*(-c + t)]), Sin[a*t + b*(t-c)]/Sin[a*t +b*(c - t)]}

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$a,b$ 是速度，$c$ 是角度偏移。$t\in[-\pi,\pi]$.
WolframAlpha(a,b,c=2,3,0)