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**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

### MSC:

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 |

### Keywords:

computer aided geometric design; projective geometry; B-splines; computer graphics; rational Béziers splines; torus patches; surfaces of revolution; modeling### References:

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