Smooth local interpolation of surfaces using normal vectors. (English) Zbl 1205.65042

Nagata, Takashi

J. Appl. Math. 2010, Article ID 952420, 24 p. (2010).

Summary: 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 [Comput. Aided Geom. Des. 22, No. 4, 327–347 (2005; Zbl 1205.65041)], 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.

MSC:

65D05	Numerical interpolation
65D17	Computer-aided design (modeling of curves and surfaces)

Citations:

Zbl 1205.65041

References:

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