• Analyzing a generalized Loop s...

Result: Analyzing a generalized Loop subdivision scheme

Title:
Analyzing a generalized Loop subdivision scheme
Authors:
GINKEL, I, UMLAUF, G
Source:
Special issue on geometric modeling (Dagstuhl 2005)Computing (Wien. Print). 79(2-4):353-363
Publisher Information:
Wien: Springer, 2007.
Publication Year:
2007
Physical Description:
print, 24 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Approximations et développements, Approximations and expansions, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Approximation numérique, Numerical approximation, Méthodes de calcul scientifique (y compris calcul symbolique, calcul algébrique), Methods of scientific computing (including symbolic computation, algebraic computation), Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Algorithme, Algorithm, Algoritmo, Analyse numérique, Numerical analysis, Análisis numérico, Approximation numérique, Numerical approximation, Aproximación numérica, Approximation spline, Spline approximation, Aproximación esplín, Calcul scientifique, Scientific computation, Computación científica, Polynôme, Polynomial, Polinomio, Surface, Superficie, 41A15, 65D07, 65D17, 65D18.; Subdivision, characteristic map, loop
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Sciences University of Kaiserslautern, 67653 Kaiserslautern, Germany
ISSN:
0010-485X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18791843
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems

Mathematics
Accession Number:
edscal.18791843
Database:
PASCAL Archive

Further Information

In this paper a class of subdivision schemes generalizing the algorithm of Loop is presented. The stencils have the same support as those from the algorithm of Loop, but allow a variety of weights. By varying the weights a class of C1 regular subdivision schemes is obtained. This class includes the algorithm of Loop and the midpoint schemes of order one and two for triangular nets. The proof of Cl regularity of the limit surface for arbitrary triangular nets is provided for any choice of feasible weights. The purpose of this generalization of the subdivision algorithm of Loop is to demonstrate the capabilities of the applied analysis technique. Since this class includes schemes that do not generalize box spline subdivision, the analysis of the characteristic map is done with a technique that does not need an explicit piecewise polynomial representation. This technique is computationally simple and can be used to analyze classes of subdivision schemes. It extends previously presented techniques based on geometric criteria.