Biquintic G 2 surfaces

This paper gives a construction to complete, at extraordinary points, an otherwise bi-cubic spline surface – so that the resulting surface is curvature continuous everywhere. To fill the n-sided gap in the bi-cubic surface, a cap is constructed from n spline patches, each consisting of 2× 2 pieces of polynomial degree bi-5. Particular care is taken to continue the curvature distribution from the bicubic boundary of the gap into the cap, and gently average out such propagated curvature in the neighborhood of the extraordinary point.

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