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arXiv · 2105.10320

Note on Surfaces of Revolution with an Affine-Linear Relation between their Curvature Radii

Michael Robert Jimenez
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Abstract

This note derives parametrizations for surfaces of revolution that satisfy an affine-linear relation between their respective curvature radii. Alongside, parametrizations for the uniform normal offsets of those surfaces are obtained. Those parametrizations are found explicitly for a countably-infinite many of them, and of those, it is shown which are algebraic. Lastly, for those surfaces which have a constant ratio of principal curvatures, parametrizations with a constant angle between the parameter curves are found.

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Michael Robert Jimenez. 2021-05-21. Note on Surfaces of Revolution with an Affine-Linear Relation between their Curvature Radii. https://arxiv.org/abs/2105.10320

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