# Visual Curve Completion and Rotational Surfaces of Constant Negative Curvature

@article{Pmpano2019VisualCC, title={Visual Curve Completion and Rotational Surfaces of Constant Negative Curvature}, author={{\'A}lvaro P{\'a}mpano}, journal={arXiv: Differential Geometry}, year={2019} }

If a piece of the contour of a picture is missing to the eye vision, then the brain tends to complete it using some kind of sub-Riemannian geodesics of the unit tangent bundle of the plane, R2xS1. These geodesics can be obtained by lifting extremal curves of a total curvature type energy in the plane. We completely solve this variational problem, geometrically. Moreover, we also show a way of constructing rotational surfaces of constant negative curvature in R3 by evolving these extremal curves…

## One Citation

Rotational surfaces of constant astigmatism in space forms

- MathematicsJournal of Mathematical Analysis and Applications
- 2020

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