Inversion of trefoil knot

[list][*]Trefoil knot - Black curve[/*][*]Inversion - Red curve[/*][/list]
GeoGebra script
[code]translateY = Slider(-3, 3, 0.01, 1, 200)[br][br]# Trefoil knot[br]fx(x) = sin(x) + 2sin(2x)[br]fy(x) = cos(x) - 2cos(2x) + translateY[br]fz(x) = -sin(3x)[br][br]trefoilKnot = Curve(fx(t), fy(t), fz(t), t, 0, 2pi)[br][br]# 2-sphere[br]sx(x, y) = cos(x) sin(y)[br]sy(x, y) = sin(x) sin(y)[br]sz(x, y) = cos(y)[br][br]twoSphere = Surface(sx(u, v), sy(u, v), sz(u, v), u, 0, 2pi, v, 0, pi)[br][br]# Inversion[br]norm2(x) = (fx(x))^2 + (fy(x))^2 + (fz(x))^2[br][br]trefoilKnotInverted = Curve(fx(t) / norm2(t), fy(t) / norm2(t) , fz(t) / norm2(t), t, 0, 2pi)[/code]

Information: Inversion of trefoil knot