Reconstruction of rational ruled surfaces from their silhouettes. (May 2021)

• Record Type: Journal Article
• Authors: Gallet, Matteo; Lubbes, Niels; Schicho, Josef; Vršek, Jan
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 366
• Page End: 380
• Publication Date: 2021-05
• Subjects: Rational surface -- Projection -- Contour -- Discriminant -- Tangent developable; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.08.002
• Languages: English
• ISSNs: 0747-7171

Abstract

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.