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| 1 | loxodrome[\[Lambda]_, m_, \[Lambda]0_] := {Cos[\[Lambda]]/
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| 2 | Cosh[m (\[Lambda] - \[Lambda]0)], Sin[\[Lambda]]/ | |
| 3 | Cosh[m (\[Lambda] - \[Lambda]0)], Tanh[m (\[Lambda] - \[Lambda]0)]}; | |
| 4 | proj[{x_, y_, z_}] := {x/(1 - z), y/(1 - z)};
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| 5 | frame[\[Theta]_] := Rasterize@Module[{m, pp, umax, pr},
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| 6 | m = 0.45; | |
| 7 | pp = 30; | |
| 8 | umax = 0.8; | |
| 9 | range = 2.8; | |
| 10 | pr = {{-range, range}, {-range, range}, {-1.1, 1.1}};
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| 11 | texture = ParametricPlot[ | |
| 12 | proj[ | |
| 13 | RotationMatrix[\[Theta] + 0.5, {1, 0, 0}].RotationMatrix[
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| 14 | u, {0, 0, 1}].loxodrome[\[Lambda], m, 0]]
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| 15 | , {u, 0, umax}, {\[Lambda], -10, 10}, PlotRange -> 3,
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| 16 | Mesh -> False, | |
| 17 | PlotStyle -> Directive[RGBColor[0.15, 0.18, 0.5], Opacity[0.5]], | |
| 18 | BoundaryStyle -> None, Frame -> None, Axes -> None, | |
| 19 | PlotPoints -> pp, Background -> RGBColor[0.8, 0.8, 0.9]]; | |
| 20 | Show[ | |
| 21 | Graphics3D[{RGBColor[0.1, 0.6, 0.7], Opacity[0.2], Sphere[],
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| 22 | {Opacity[1.0], Texture[texture],
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| 23 | Polygon[{{-3, -3, -1}, {3, -3, -1}, {3, 3, -1}, {-3, 3, -1}},
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| 24 | VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]}
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| 25 | }, Lighting -> "Neutral", PlotRange -> pr, Boxed -> False], | |
| 26 | ParametricPlot3D[ | |
| 27 | {
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| 28 | RotationMatrix[\[Theta] + 0.5, {1, 0, 0}].RotationMatrix[
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| 29 | u, {0, 0, 1}].loxodrome[\[Lambda], m, 0]
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| 30 | } | |
| 31 | , {\[Lambda], -10, 10}, {u, 0, umax}, PlotRange -> pr,
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| 32 | PlotPoints -> pp, Mesh -> False, PlotStyle -> Darker@Red, | |
| 33 | BoundaryStyle -> None], ImageSize -> 300] | |
| 34 | ]; | |
| 35 | frame[1.07] |
