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A sphere with Jacobi's ellipsoidal parameterization. A single parameter controls the location of the umbilics and stands in for the eccentricity of the general triaxial ellipsoid. At both extremes this becomes a conventional spherical parameterization.pic.twitter.com/V7DQafxk4A
For a general ellipsoid, this parameterization follows the lines of curvature. Below the sphere is a stereographic projection of these lines. They correspond in shape (but not in spacing) to the mapping of a square grid under the Jacobi elliptic sn() function.
The visualization was created on
@math3dapp's awesome http://math3d.org .
Live version at https://www.math3d.org/yEzcZ6sV
More at http://mathworld.wolfram.com/Ellipsoid.html and https://en.wikipedia.org/wiki/Ellipsoid#Parameterization …
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