Thursday, January 28, 2016

[mxinxccm] Minimizing maximum distortion

Given a portion of a sphere strictly less than a hemisphere, project it onto a plane minimizing the maximum distortion anywhere, for some appropriate measure of distortion.  Probably an underspecified problem.

Reverse: given a flat image, project it onto (at most) a hemisphere, minimizing distortion.

Do both in sequence (reverse, then forward).  Original motivation: slightly distorted QR codes.

Ellipsoid, hyperboloid, hyperbolic paraboloid, tractricoid (pseudosphere).  Hyperbolic plane (do we need to specify an embedding (immersion?) in 3-space to define distortion?).

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