Rotate a sphere with Quaternions (Wolfram Mathematica Software)
Rotate a sphere with Quaternions (Wolfram Mathematica Software)
The code below is used in Wolfram Mathematica software to build a cube like box and rotate it, using the set of the Quaternions:
<< Quaternions`
Q = Quaternion;
rotateq[theta_, v_] := Q @@ (Cos[theta/2], 0, 0, 0 + (Sin[theta/2] Prepend[v, 0])/Sqrt[ Plus @@ (v^2)]);
Rotaterho[vector_, angle_, axis_] := N[rotateq[angle,axis] ** (Q @@ (Prepend[vector, 0])) ** (rotateq[angle, axis])^-1] // Rest// Chop
faces = 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0,
0, 1, 0, 0, 1, 1, 1, 1, 1;
axis = 1, 1, 1;
dots = .5, 0, 1, .5, 1, 1, 1.5, .5, .5, -.5, .5, .5;
Manipulate[t = ANGLE Degree;
points = Table[List @@ Rotaterho[dots[[m]], t, axis], m, 1, 4];
rotatedfaces = Table[Table[List @@ Rotaterho[faces[[c, m]], t, axis], m, 1, 4], c, 1, 4];
box = Table[Polygon[rotatedfaces[[m]]], m, 1, 4];
Graphics3D[EdgeForm[Thick, Blue], FaceForm[Red, LightBlue], box,
Thickness[Medium], Line[-2, -2, -2, 2, 2, 2], PointSize[.03],Yellow, Point[points[[1]]], Green, Point[points[[2]]], Purple,
Point[points[[3]]], Point[points[[4]]],
Line[points[[3]], points[[4]]], Black, Point[0, 0, 0],
Point[1, 1, 1], Axes -> True,
Lighting -> Automatic, BaseStyle -> FontSize -> 13, Boxed -> True,
BoxStyle -> Directive[Dashed], AxesLabel -> x, y, z,
PlotRange -> -2, 2, -2, 2, -2, 2], ANGLE, 0., 360., 1.]
The result is shown in this picture
https://i.stack.imgur.com/75NAb.jpg
How to addapt that code and build a sphere like structure and obtain a similar result?
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