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Journal of Scientific Computing
Published in: Journal of Scientific Computing 3/2015

01-03-2015

Design of Loop’s Subdivision Surfaces by Fourth-Order Geometric PDEs with \(G^1\) Boundary Conditions

Authors: Guoliang Xu, Qing Pan

Published in: Journal of Scientific Computing | Issue 3/2015

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Abstract

In this paper, we present a method for constructing Loop’s subdivision surface patches with given \(G^1\) boundary conditions and a given topology of control polygon, using several fourth-order geometric partial differential equations. These equations are solved by a mixed finite element method in a function space defined by the extended Loop’s subdivision scheme. The method is flexible to the shape of the boundaries, and there is no limitation on the number of boundary curves and on the topology of the control polygon. Several properties for the basis functions of the finite element space are developed.
previous article Convergence Analysis of a Minimax Method for Finding Multiple Solutions of Semilinear Elliptic Equation: Part I—On Polyhedral Domain
next article KdV Equation and Computations of Solitons: Nonlinear Error Dynamics

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Metadata
Title
Design of Loop’s Subdivision Surfaces by Fourth-Order Geometric PDEs with Boundary Conditions
Authors
Guoliang Xu
Qing Pan
Publication date
01-03-2015
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 3/2015
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-014-9872-7

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