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On the computational geometry of ruled surfaces

✍ Scribed by Martin Peternell; Helmut Pottmann; Bahram Ravani

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 428 KB
Volume: 31
Category: Article
ISSN: 0010-4485
DOI: 10.1016/s0010-4485(98)00077-3

No coin nor oath required. For personal study only.

✦ Synopsis

This article presents a brief introduction to the classical geometry of ruled surfaces with emphasis on the Klein image and studies aspects which arise in connection with a computational treatment of these surfaces. As ruled surfaces are one parameter families of lines, one can apply curve theory and algorithms to the Klein image, when handling these surfaces. We study representations of rational ruled surfaces and get efficient algorithms for computation of planar intersections and contour outlines. Further, low degree boundary curves, useful for tensor product representations, are studied and illustrated at hand of several examples. Finally, we show how to compute efficiently low degree rational G 1 ruled surfaces.

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