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arXiv · 1905.11853

Reconstruction of rational ruled surfaces from their silhouettes

Matteo Gallet·Niels Lubbes·Josef Schicho·Jan Vršek
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Abstract

We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We deal with the case of tangent developables and of general projections to $\mathbb{p}^3$ of rational normal scrolls. In the first case, we use the fact that every such surface is the projection of the tangent developable of a rational normal curve, while in the second we start by reconstructing the rational normal scroll. In both instances we then reconstruct the correct projection to $\mathbb{p}^3$ of these surfaces by exploiting the information contained in the singularities of the apparent contour.

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Matteo Gallet, Niels Lubbes, Josef Schicho, Jan Vršek. 2019-05-28. Reconstruction of rational ruled surfaces from their silhouettes. https://doi.org/10.1016/j.jsc.2020.08.002

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