Abstract
The tensor product Bézier patch is one of the most widely used models for the representation of surfaces in CAGD. The shape of the objects to be designed is often complex so a piecewise representation is needed in most cases. If the resulting piecewise surface is to present a smooth aspect of its shape, then the geometric continuity between adjacent surface patches is essential.
Much research has been devoted to this problem, and diverse solutions have already been published. Nevertheless, various problems remain, especially the smooth connection between a non-four-number of patches meeting at a common corner. In this paper, we first study the general behaviour of the G 1 continuity constraints around an N-patch corner, which leads to useful results concerning the propagation of these constraints according to the parity of N. Then we present the conditions which allow a local determination of the surface patches, and analyze the remaining degrees of freedom which can be used to modify locally the surface shapes. These results are very useful for the design of a piecewise representation of smooth complex surfaces using Bézier patches where various configurations must be used for the connection at a corner of a different number of patches.
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© 1988 Springer-Verlag Berlin Heidelberg
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Du, WH., Schmitt, F.J.M. (1988). New Results for the Smooth Connection Between Tensor Product Bézier Patches. In: Magnenat-Thalmann, N., Thalmann, D. (eds) New Trends in Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83492-9_31
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DOI: https://doi.org/10.1007/978-3-642-83492-9_31
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