Smooth local interpolation of surfaces using normal vectors
type: Item
instance of: scholarly article
title: Smooth local interpolation of surfaces using normal vectors
zbMATH Open document ID: 1205.65042
DOI: 10.1155/2010/952420
author: Takashi Nagata
published in: Journal of Applied Mathematics
publication date: 2010-10-07T00:00:00Z
full work available at URL: https://eudml.org/doc/226290
review text: 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.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 5796701
Wikidata QID: Q58652437
MaRDI profile type: Publication
OpenAlex ID: W1966165146
cites work: Simple local interpolation of surfaces using normal vectors
cites work: Finite element simulation of springback in sheet metal forming using local interpolation for tool surfaces
description: scientific article; zbMATH DE number 5796701