Surface compression using a space of \(C^1\) cubic splines with a hierarchical basis
type: Item
instance of: scholarly article
title: Surface compression using a space of \(C^1\) cubic splines with a hierarchical basis
zbMATH Open document ID: 1067.41005
author: Yanyan Li
published in: Computing
publication date: 2004-10-28T00:00:00Z
review text: The authors consider surfaces which are defined as the graphs of real-valued functions defined on a domain \(\Omega\subset\mathbb{R}^2\) and deal, in particular, with \(C^1\) cubic splines defined on triangulations obtained from convex quadrangulations by drawing both diagonals in each quadrilateral. For such spline surfaces a compression scheme is developed, which does not require the construction of wavelets. The key to the presented method is to work with \(C^1\) cubic spline spaces which can be parametrized locally using the well-known FVS-macro-elements. The algorithms are based on constructing hierarchical bases for certain nested sequences of such spline spaces.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 68U10
zbMATH DE Number: 2111428
zbMATH Keywords: surface compression
zbMATH Keywords: splines
zbMATH Keywords: hierarchical bases
reviewed by: Daniela Kacsó
MaRDI profile type: Publication
full work available at URL: s00607-003-0048-0
OpenAlex ID: W2099957671
DOI: 10.1007/S00607-003-0048-0
description: scientific article; zbMATH DE number 2111428