Interpolating scattered data with \(C^ 2\) surfaces
type: Item
instance of: scholarly article
title: Interpolating scattered data with \(C^ 2\) surfaces
zbMATH Open document ID: 0826.65009
DOI: 10.1016/0010-4485(95)91137-A
author: Andreas Kolb
author: Hans-Peter Seidel
published in: CAD. Computer-Aided Design
publication date: 1995-07-24T00:00:00Z
review text: The authors present a method for interpolating scattered data over a region in \(\mathbb{R}^2\), such that the resulting surface of interpolation is guaranteed to be \(C^2\)-continuous. The two main steps of the method are: Find a network of curves (over a given triangulation of the region), which minimizes a certain functional, explicitly given in the paper. The main result of the paper says that there is a unique solution of this minimization problem, and that this solution is given by a certain spline under tension network. In a second step, one extends this network into the interior of the triangles by means of side-vertex interpolants on triangles, which transfer the geometric properties from the network to the resulting surface. A number of colour plates illustrates the method.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 777937
zbMATH Keywords: scattered data
zbMATH Keywords: interpolation
zbMATH Keywords: \(C^ 2\)-continuity
zbMATH Keywords: variational principle
zbMATH Keywords: surface of interpolation
zbMATH Keywords: spline under tension network
reviewed by: Guido Walz
MaRDI profile type: Publication
full work available at URL: 0010-4485(95)91137-a
OpenAlex ID: W2008607226
description: scientific article; zbMATH DE number 777937