On the use of infinite control points in CAGD. (English) Zbl 0622.65142

The author points out that it is a waste of computer resources to use polynomial Béziers and B-splines in computer graphics and CAD. Just as rational functions give numerical approximations superior to those by polynomials, so rational Béziers splines turn out to be very versatile even for low degrees. In addition, rational splines allow one to work in a projective setting and therefore use points at infinity (i.e., directions) as Beźiers. Explicit formulas are given for torus patches and surfaces of revolution and it is shown by impressive examples that these satisfy for a great many modeling problems.
Reviewer: H.Guggenheimer


65S05 Graphical methods in numerical analysis
41A20 Approximation by rational functions
65D07 Numerical computation using splines
53A04 Curves in Euclidean and related spaces
51N05 Descriptive geometry
51N15 Projective analytic geometry
53A05 Surfaces in Euclidean and related spaces
Full Text: DOI


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