Generating blend surfaces using partial differential equations
Computer-Aided Design
Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Computer-Aided Design
Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st 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
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
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
Techniques for interactive design using the PDE method
ACM Transactions on Graphics (TOG)
Computer Vision and Image Understanding
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Fairing of non-manifolds for visualization
Proceedings of the conference on Visualization '00
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
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)
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
Discrete Laplace-Beltrami operators and their convergence
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
A general framework for surface modeling using geometric partial differential equations
Computer Aided Geometric Design
Mixed finite element methods for geometric modeling using general fourth order geometric flows
Computer Aided Geometric Design
Two Step Time Discretization of Willmore Flow
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Construction of minimal subdivision surface with a given boundary
Computer-Aided Design
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We use three fourth order geometric partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting with the G^1 boundary continuity. The non-linear equations we use include the surface diffusion flow, the quasi surface diffusion flow and the Willmore flow. These non-linear equations are discretized using a mixed finite element method based on a combination of the Loop's basis and the linear basis. The proposed approach is simple, efficient and gives very desirable results.