# [GIF] Making Tracks (Deformations of a spherical curve)

Posted 3 years ago
2942 Views
|
|
5 Total Likes
| Making TracksThe underlying curve here is the intersection of the quartic surface $(1-x^2)^2+(1-y^2)^2=(1-z^2)^2$ with the unit sphere. This surface comes up in an interesting way in a project I'm currently working and which I'll describe in more detail at some point; for now, here are ten Gaussian translates.Code: DynamicModule[{cols, rands, y}, SeedRandom; cols = RGBColor /@ {"#B36458", "#353E55"}; rands = Table[RandomVariate[NormalDistribution[0, .05], 3], {10}]; Manipulate[ Graphics3D[{cols[], Thickness[.005], Opacity[.5], Table[y = Haversine[Clip[π s, {0, π}]]; {2 (-1)^m Norm[rands[[m]]] + # & /@ cols[], Line[Table[{Sqrt[(1 - y^2)/(1 + y^2)], y, y Sqrt[(1 - y^2)/(1 + y^2)]}*{i, j, k} + rands[[m]], {s, Max[0, t - 1], Min[t, 1], 1/50}]]}, {i, {-1, 1}}, {j, {-1, 1}}, {k, {-1, 1}}, {m, 1, 10}]}, Lighting -> "Neutral", PlotRange -> 1.2, Boxed -> False, Axes -> None, ViewAngle -> π/8, ImageSize -> 540, Background -> cols[]], {t, 0, 2}] ] Answer - another post of yours has been selected for the Staff Picks group, congratulations !We are happy to see you at the top of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming! Answer