A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Curve and surface constructions using rational B-splines
Computer-Aided Design
Generating blend surfaces using partial differential equations
Computer-Aided Design
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Representing PDE surfaces in terms of B-splines
Computer-Aided Design
Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Blend design as a boundary-value problem
Theory and practice of geometric modeling
Computer-Aided Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Dressing animated synthetic actors with complex deformable clothes
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functionality in solids obtained from partial differential equations
Geometric modelling
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Simulating facial surgery using finite element models
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Wires: a geometric deformation technique
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Haptic sculpting of dynamic surfaces
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
A novel FEM-based dynamic framework for subdivision surfaces
Proceedings of the fifth ACM symposium on Solid modeling and applications
Techniques for interactive design using the PDE method
ACM Transactions on Graphics (TOG)
Displaced subdivision surfaces
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Computer Vision and Image Understanding
Virtual clay: a real-time sculpting system with haptic toolkits
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Modeling inelastic deformation: viscolelasticity, plasticity, fracture
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
D-NURBS: A Physics-Based Framework for Geometric Design
IEEE Transactions on Visualization and Computer Graphics
A Level-Set Approach for the Metamorphosis of Solid Models
IEEE Transactions on Visualization and Computer Graphics
IEEE Computer Graphics and Applications
Generating Fair Meshes with G1 Boundary Conditions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Dynamic PDE Surfaces with Flexible and General Geometric Constraints
PG '00 Proceedings of the 8th Pacific Conference on Computer Graphics and Applications
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Dynamic Implicit Solids with Constraints for Haptic Sculpting
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
G2 surface modeling using minimal mean-curvature-variation flow
Computer-Aided Design
Free-Form Geometric Modeling by Integrating Parametric and Implicit PDEs
IEEE Transactions on Visualization and Computer Graphics
A general framework for surface modeling using geometric partial differential equations
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Mixed finite element methods for geometric modeling using general fourth order geometric flows
Computer Aided Geometric Design
Editing level-set models with sketched curves
Proceedings of the 6th Eurographics Symposium on Sketch-Based Interfaces and Modeling
G1 surface modelling using fourth order geometric flows
Computer-Aided Design
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Technical Section: Interactive free-form level-set surface-editing operators
Computers and Graphics
Cyber surgery: parameterized mesh for multi-modal surgery simulation
PCM'05 Proceedings of the 6th Pacific-Rim conference on Advances in Multimedia Information Processing - Volume Part I
Minimal mean-curvature-variation surfaces and their applications in surface modeling
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Deformation of dynamic surfaces
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Automatic shape optimisation of pharmaceutical tablets using Partial Differential Equations
Computers and Structures
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PDE surfaces, which are defined as solutions of partial differential equations (PDEs), offer many modeling advantages in surface blending, free-form surface modeling, and specifying surface's aesthetic or functional requirements. Despite the earlier advances of PDE surfaces, previous PDE-based techniques exhibit certain difficulties such as lack of interactive sculpting capabilities and restrained topological structure of modeled objects. This paper presents an integrated approach that can incorporate PDE surfaces into the powerful physics-based modeling framework, to realize the full potential of PDE methodology. We have developed a prototype system that allows interactive design of flexible topological surfaces as PDE surfaces and displacements using generalized boundary conditions as well as a variety of geometric and physical constraints, hence supporting various interactive techniques beyond the conventional boundary control. The system offers a set of sculpting toolkits that allow users to interactively modify arbitrary points, curve spans, and/or regions of interest across the entire PDE surfaces and displacements in an intuitive and physically meaningful way. To achieve real-time performance, we employ several simple, yet efficient numerical techniques, including the finite-difference discretization, the multigrid-like subdivision, and the mass-spring approximation of elastic PDE surfaces and displacements. In addition, we present the standard bivariant B-spline finite element approximations of dynamic PDEs, which can subsequently be sculpted and deformed directly in real-time subject to the intrinsic PDE constraints. Our experiments demonstrate many attractive advantages of the physics-based PDE formulation such as intuitive control, real-time feedback, and usability to both professional and common users.