Abstract
This paper describes a stepwise synthesis process for surface generation which leads from a set of prefaired curves, which form a regular or irregular mesh topology, via a mesh fairing process to a free-form surface that interpolates the mesh curves with G 1 or G 2 continuity and is subsequently faired based on some choice of variational fairness criterion. After briefly reviewing earlier work on the construction of a fair curve mesh the paper concentrates on two main ideas:
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1.
The interpolation of the given mesh topologies for given continuity and compatibility conditions with minimal polynomial degrees by local interpolants in Bézier form. Irregular, n-sided mesh cells are decomposed into assemblies of quadrilaterals.
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2.
A fairing process is applied to each patch. The free interior Bézier control points and twist vectors are determined by minimizing a chosen fairness measure. The effects of different variational fairness criteria on the shape and quality of the surface are explored.
The methods for surface construction are illustrated by representative examples.
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© 1997 Springer-Verlag Berlin Heidelberg
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Nowacki, H., Jin, F., Ye, X. (1997). A Synthesis Process for Fair Free-Form Surfaces. In: Strasser, W., Klein, R., Rau, R. (eds) Geometric Modeling: Theory and Practice. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60607-6_3
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DOI: https://doi.org/10.1007/978-3-642-60607-6_3
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