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.
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Paoluzzi, A. (2003). Variable-Free Representation of Manifolds via Transfinite Blending with a Functional Language. In: Wilson, M.J., Martin, R.R. (eds) Mathematics of Surfaces. Lecture Notes in Computer Science, vol 2768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39422-8_22
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DOI: https://doi.org/10.1007/978-3-540-39422-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20053-6
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