A Symbolic-Numeric Approach for Parametrizing Ruled Surfaces

• Published in: Journal of systems science and complexity Vol. 33; no. 3; pp. 799 - 820
• Main Authors: Pérez-Díaz, Sonia, Shen, Li-Yong
• Format: Journal Article
• Language: English
• Published: Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.06.2020; Springer Nature B.V
• Subjects: Algorithms; Complex Systems; Control; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Parameterization; Statistics; Systems Theory; standard parametrization; ruled surface; Implicit representation; numeric algorithm
• ISSN: 1009-6124; 1559-7067; 1559-7067
• DOI: 10.1007/s11424-019-8188-y

This paper presents symbolic algorithms to determine whether a given surface (implicitly or parametrically defined) is a rational ruled surface and find a proper parametrization of the ruled surface. However, in practical applications, one has to deal with numerical objects that are given approximately, probably because they proceed from an exact data that has been perturbed under some previous measuring process or manipulation. For these numerical objects, the authors adapt the symbolic algorithms presented by means of the use of numerical techniques. The authors develop numeric algorithms that allow to determine ruled surfaces “close” to an input (not necessarily ruled) surface, and the distance between the input and the output surface is computed.