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A rational extension of Piegl's method for filling n-sided holes

Abstract : N-sided hole filling plays an important role in vertex blending. To deal with the case that the corner is surrounded by rational surfaces (i.e. NURBS surfaces), an algorithm to fill n-sided holes with ɛ-G1 continuous NURBS patches that interpolate the given boundary curves and approximate the given cross-boundary derivatives is presented based on Piegl's method. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance ɛ. The boundaries as well as cross-boundary derivatives can all be NURBS curves. No restrictions are imposed on the number of boundary curves, and the cross-boundary derivatives can be specified independently.
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https://hal.inria.fr/inria-00518326
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Yi-Jun Yang, Jun-Hai Yong, Hui Zhang, Jean-Claude Paul, Jia-Guang Sun. A rational extension of Piegl's method for filling n-sided holes. Computer-Aided Design, Elsevier, 2006, 38 (11), pp.1166-1178. ⟨10.1016/j.cad.2006.07.001⟩. ⟨inria-00518326⟩

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