Abstract
A local construction of aGC 1 interpolating surface to given scattered data in ℝ3 can give rise to degenerate Bernstein-Bézier patches. This means that the parametrization at vertices is not regular in the sense that the length of the tangent vector to any curve passing through a vertex is zero at that vertex. This implies that the curvature of these curves tends to infinity whenever one approaches a vertex. This fact seems not to have a negative influence on the shape of the surface.
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Pfluger, P.R., Neamtu, M. On degenerate surface patches. Numer Algor 5, 569–575 (1993). https://doi.org/10.1007/BF02113892
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DOI: https://doi.org/10.1007/BF02113892