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Variable-Free Representation of Manifolds via Transfinite Blending with a Functional Language

  • Alberto Paoluzzi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2768)

Abstract

In this paper a variable-free parametric representation of manifolds is discussed, using transfinite interpolation or approximation, i.e. function blending in some functional space. This is a powerful approach to generation of curves, surfaces and solids (and even higher dimensional manifolds) by blending lower dimensional vector-valued functions. Transfinite blending, e.g. used in Gordon-Coons patches, is well known to mathematicians and CAD people. It is presented here in a very simple conceptual and computational framework, which leads such a powerful modeling to be easily handled even by the non mathematically sophisticated user of graphics techniques. In particular, transfinite blending is discussed in this paper by making use of a very powerful and simple functional language for geometric design.

Keywords

Coordinate Function Coordinate Representation Geometric Programming Actual Argument Parameter List 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Alberto Paoluzzi
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreRomaItaly

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