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TitlePN surfaces and their convolutions with rational surfaces
Author(s) Bohumir Bastl, Miroslav Lávička
TypeArticle in Journal
AbstractRationally parameterized hypersurfaces can be classified with respect to their RC properties (Rational Convolutions) with the help of the Gröbner bases theory. This classification focuses on special classes of rational parameterizations which provide a rational description of convolution hypersurfaces generally (GRC parameterizations), or just in some special cases (SRC parameterizations). The main aim of this paper is to bring the theory of the so-called PN surfaces (surfaces with Pythagorean Normal vectors) and their PN parameterizations (parameterizations fulfilling the PN condition) in relation to the theory of SRC parameterizations and to show that this type of parameterizations can be further classified with respect to the degree of the construction of convolution surfaces. The connection of SRC PN parameterizations to the well-known concepts of proper and square-root parameterizations is also investigated.
KeywordsPN surfaces, Convolution surfaces, Offsets, Rational parameterizations, Proper parameterizations, Square-root parameterizations
URL http://www.sciencedirect.com/science/article/pii/S0167839608000769
JournalComputer Aided Geometric Design
Pages763 - 774
NoteClassical Techniques for Applied Geometry
Translation No
Refereed No