Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Compute the parametrization of a curve projected onto the unit sphere
ResourceFunction["InverseStereographicProjection"][{u,v}] projects {u,v} from a plane onto the unit sphere. |
Compute the inverse stereographic projection of a generic point:
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Define an ellipse:
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Project an ellipse onto the sphere:
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Plot the projected ellipse:
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Define a logarithmic spiral curve:
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A plot of the logarithmic spiral:
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Project the spiral onto the sphere; it becomes a spherical loxodrome:
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Compute the norm of the logarithmic spiral:
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Plot the projected spiral with meridians:
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Plot the spherical loxodrome:
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Define the second butterfly curve:
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Project the curve onto the sphere:
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Plot the curve and the projection:
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The norm of the stereographic sphere:
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Project a grid of points in Cartesian coordinates:
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A Cartesian grid on the plane appears distorted on the sphere; show the points and their projections onto the sphere:
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Project a grid of lines instead:
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Show the lines and their projections:
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The same mesh can be generated by ParametricPlot3D. The grid lines are still perpendicular, but the sectors get smaller close to the north pole:
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