Smooth Local Interpolation of Surfaces Using Normal Vectors

Abstract

This paper proposes a simple surface interpolation attaining tangent-plane continuity. It is a natural extension of the local quadratic ${C}^{0}$ 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 ${C}^{0}$ 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.