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PN surfaces and their convolutions with rational surfaces. (English) Zbl 1172.14344

Summary: Rationally 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.

MSC:

14Q05 Computational aspects of algebraic curves
65D17 Computer-aided design (modeling of curves and surfaces)
14Q10 Computational aspects of algebraic surfaces
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
68U07 Computer science aspects of computer-aided design
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