Reconstruction of rational ruled surfaces from their silhouettes

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 $p^3$ 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 $p^3$ of these surfaces by exploiting the information contained in the singularities of the apparent contour.

17 pages

References in corpus (3)

• Characterization of Rational Ruled Surfaces
• Reconstruction of surfaces with ordinary singularities from their silhouettes
• Counting projections of rational curves