Generating blend surfaces using partial differential equations
Computer-Aided Design
Computer-Aided Design
Minimal Surfaces Based Object Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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)
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
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
Polyhedral Surface Smoothing with Simultaneous Mesh Regularization
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Fair Triangle Mesh Generation with Discrete Elastica
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
Discrete Laplace-Beltrami operators and their convergence
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
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
Mixed finite element methods for geometric modeling using general fourth order geometric flows
Computer Aided Geometric Design
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Bicubic B-spline blending patches with optimized shape
Computer-Aided Design
Sparse representation of deformable 3D organs with spherical harmonics and structured dictionary
Journal of Biomedical Imaging - Special issue on Machine Learning in Medical Imaging
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Spline surfaces of arbitrary topology with continuous curvature and optimized shape
Computer-Aided Design
On the curvature effect of thin membranes
Journal of Computational Physics
Consistent approximations of several geometric differential operators and their convergence
Applied Numerical Mathematics
| Hi-index | 0.00 |
In this paper, a general framework for surface modeling using geometric partial differential equations (PDEs) is presented. Starting with a general integral functional, we derive an Euler-Lagrange equation and then a geometric evolution equation (also known as geometric flow). This evolution equation is universal, containing several well-known geometric partial differential equations as its special cases, and is discretized under a uniform framework over surface meshes. The discretization of the equation involves approximations of curvatures and several geometric differential operators which are consistently discretized based on a quadratic fitting scheme. The proposed algorithm can be used to construct surfaces for geometric design as well as simulate the behaviors of various geometric PDEs. Comparative experiments show that the proposed approach can handle a large number of geometric PDEs and the numerical algorithm is efficient.