Explicit construction of C2 surfaces for meshes of arbitrary topology*

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1 Scopus citations


Presented in this paper is an approach to construct a C2-continuous surface for a mesh of arbitrary topology. The construction process is subdivision surface based, with modification performed on extra-ordinary patches to ensure C2-continuity of the resulting surface. Implementation is easy because modification is patch-based. The resulting surface has an explicit expression of the form WMG for each extra-ordinary patch where W is a parameter vector, M is a constant matrix and G is the patch-wise control point vector. Therefore, computing derivatives, normals and curvatures for points in the domain of the given mesh is very easy and, consequently, the resulting surface is suitable for operations such as shape analysis, shape optimization, surface energy minimization etc. The construction process includes constraints so that the shape of the resulting C2 surface is very similar to the surface generated by subdivision. More importantly, the resulting C2 surface satisfies the convex hull property.

Original languageEnglish
Pages (from-to)805-814
Number of pages10
JournalComputer-Aided Design and Applications
Issue number6
StatePublished - Sep 19 2017

Bibliographical note

Publisher Copyright:
©, This work was authored as part of the authors' official duties as Employees of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.


  • C
  • Parametrization
  • Smooth Surface Construction
  • Subdivision Surfaces

ASJC Scopus subject areas

  • Computational Mechanics
  • Computer Graphics and Computer-Aided Design
  • Computational Mathematics


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