Finite element methods for geometric modeling and processing using general fourth order geometric flows

Authors:
Guoliang Xu
Affiliations:
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China
Venue:
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Year:
2008

Citing 16
Cited 1

Generating blend surfaces using partial differential equations

Computer-Aided Design
Using partial differential equations to generate free-form surfaces: 91787

Computer-Aided Design
Functionality in blend design

Computer-Aided Design
Implicit fairing of irregular meshes using diffusion and curvature flow

Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Techniques for interactive design using the PDE method

ACM Transactions on Graphics (TOG)
Anisotropic geometric diffusion in surface processing

Proceedings of the conference on Visualization '00
Anisotropic diffusion of surfaces and functions on surfaces

ACM Transactions on Graphics (TOG)
Generating Fair Meshes with G1 Boundary Conditions

GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Acoustics Scattering on Arbitrary Manifold Surfaces

GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
A finite element method for surface restoration with smooth boundary conditions

Computer Aided Geometric Design
Dynamic PDE-based surface design using geometric and physical constraints

Graphical Models
A general framework for surface modeling using geometric partial differential equations

Computer Aided Geometric Design
Discrete surface modelling using partial differential equations

Computer Aided Geometric Design
G1 surface modelling using fourth order geometric flows

Computer-Aided Design
Geometric fairing of irregular meshes for free-form surface design

Computer Aided Geometric Design

Generalized Koebe's method for conformal mapping multiply connected domains

2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling

Quantified Score

Hi-index	0.00

Visualization

Abstract

A variational formulation of a general form fourth order geometric partial differential equation is derived, and based on which a mixed finite element method is developed. Several surface modeling problems, including surface blending, hole filling and surface mesh refinement with the G1 continuity, are taken into account. The used geometric partial differential equation is universal, containing several well-known geometric partial differential equations as its special cases. The proposed method is general which can be used to construct surfaces for geometric design as well as simulate the behaviors of various geometric PDEs. Experimental results show that it is simple, efficient and gives very desirable results.