A cascadic geometric filtering approach to subdivision.
type: Item
instance of: scholarly article
title: A cascadic geometric filtering approach to subdivision.
zbMATH Open document ID: 1043.68103
DOI: 10.1016/S0167-8396(02)00150-4
author: U. Diewald
author: Serena Morigi
author: Martin Rumpf
published in: Computer Aided Geometric Design
publication date: 2003-01-21T00:00:00Z
review text: A new approach to subdivision based on the evolution of surfaces under curvature motion is presented. Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width. Thus, subdivision can be interpreted as the application of a geometric filter on an initial surface. The concrete scheme is a model of such a filtering based on a successively improved spatial approximation starting with some initial coarse mesh and leading to a smooth limit surface. In every subdivision step the underlying grid is refined by some regular refinement rule and a linear finite element problem is either solved exactly or, especially on fine grid levels, one confines to a small number of smoothing steps within the corresponding iterative linear solver. The approach closely connects subdivision to surface fairing concerning the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure. The derived method does not distinguish between different valences of nodes nor between different mesh refinement types. Furthermore, the method comes along with a new approach for the theoretical treatment of subdivision.
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 1856178
zbMATH Keywords: Variational subdivision
zbMATH Keywords: Surface fairing
zbMATH Keywords: Curves and surfaces
zbMATH Keywords: Geometric modeling
zbMATH Keywords: Image processing
MaRDI profile type: Publication
cites work: The cascadic multigrid method for elliptic problems
cites work: Q3344779
cites work: Techniques of scientific computing (Part 2)
cites work: Discrete anisotropic curvature flow of graphs
cites work: A finite element method for surface restoration with smooth boundary conditions
cites work: A 4-point interpolatory subdivision scheme for curve design
cites work: A butterfly subdivision scheme for surface interpolation with tension control
cites work: An algorithm for evolutionary surfaces
cites work: Q3139888
cites work: Q4040640
cites work: Q3709786
cites work: The volume preserving mean curvature flow.
cites work: A variational approach to subdivision
cites work: Q4525472
cites work: Computing Discrete Minimal Surfaces and Their Conjugates
cites work: A unified approach to subdivision algorithms near extraordinary vertices
cites work: Geometric fairing of irregular meshes for free-form surface design
cites work: Galerkin finite element methods for parabolic problems
cites work: 4--8 Subdivision
cites work: A Method for Analysis ofC1-Continuity of Subdivision Surfaces
description: scientific article; zbMATH DE number 1856178