Journal of Applied Mathematics
Volume 2010 (2010), Article ID 952420, 24 pages
Research Article

Smooth Local Interpolation of Surfaces Using Normal Vectors

VCAD System Research Program, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

Received 20 August 2009; Accepted 22 April 2010

Academic Editor: James Buchanan

Copyright © 2010 Takashi Nagata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a simple surface interpolation attaining tangent-plane continuity. It is a natural extension of the local quadratic C0 interpolator developed by the author (2005) in one of his works, which has already been applied successfully to diverse engineering problems. The methodology presented in this paper inherits most of the advantages possessed by the C0 scheme. That is, (i) The algorithm is efficient and completely local requiring only the position vectors and normals given at the nodes of a patch, and hence it is suitable for parallel processing. (ii) It converges rapidly to the given surface with the increase in the number of nodes. (iii) Singular points (apexes, sharp edges, etc.) and nonmanifolds can be treated quite easily. (iv) Because of the minimization criteria assigned to the surface coefficients, it is rather robust and amenable to computational analyses. Validity and effectiveness of the proposed technique are demonstrated through numerical examples.