Generating blend surfaces using partial differential equations
Computer-Aided Design
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The surface diffusion flow for immersed hypersurfaces
SIAM Journal on Mathematical Analysis
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computer Vision and Image Understanding
A level-set method for flow visualization
Proceedings of the conference on Visualization '00
Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
C modeling with A-patches from rational trivariate functions
Computer Aided Geometric Design
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Level set surface editing operators
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
A Level-Set Approach for the Metamorphosis of Solid Models
IEEE Transactions on Visualization and Computer Graphics
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
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Convergence of discrete Laplace-Beltrami operators over surfaces
Computers & Mathematics with Applications
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Quality meshing of implicit solvation models of biomolecular structures
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Geometric surface evolution with tangential contribution
Journal of Computational and Applied Mathematics
Polynomial blending in a mesh hole-filling application
Computer-Aided Design
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
A multistep approach to restoration of locally undersampled meshes
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Surfaces filling polygonal holes with G1 quasi G2 continuity
Machine Graphics & Vision International Journal
Regularization of B-spline objects
Computer Aided Geometric Design
Bicubic B-spline blending patches with optimized shape
Computer-Aided Design
Construction of minimal subdivision surface with a given boundary
Computer-Aided Design
Mean Laplace-Beltrami operator for quadrilateral meshes
Transactions on edutainment V
Minimal mean-curvature-variation surfaces and their applications in surface modeling
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Surface-based imaging methods for high-resolution functional magnetic resonance imaging
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
Construction of subdivision surfaces by fourth-order geometric flows with G1 boundary conditions
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Explicit Mesh Surfaces for Particle Based Fluids
Computer Graphics Forum
Spline surfaces of arbitrary topology with continuous curvature and optimized shape
Computer-Aided Design
Consistent approximations of several geometric differential operators and their convergence
Applied Numerical Mathematics
Multiscale geometric modeling of macromolecules I: Cartesian representation
Journal of Computational Physics
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We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.