Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Generating blend surfaces using partial differential equations
Computer-Aided Design
Interactive techniques for implicit modeling
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Volumetric shape description of range data using “Blobby Model”
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Generalized implicit functions for computer graphics
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functionality in solids obtained from partial differential equations
Geometric modelling
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Realistic animation of liquids
GI '96 Proceedings of the conference on Graphics interface '96
Modeling the motion of a hot, turbulent gas
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Three dimensional freeform sculpting via zero sets of scalar trivariate functions
Proceedings of the fifth ACM symposium on Solid modeling and applications
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Shape transformation using variational implicit functions
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)
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Computer Vision and Image Understanding
Kizamu: a system for sculpting digital characters
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
A procedural approach to authoring solid models
Proceedings of the 29th 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
Modelling with implicit surfaces that interpolate
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
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)
Integrating Physics-Based Modeling with PDE Solids for Geometric Design
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Haptic Sculpting of Volumetric Implicit Functions
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Implicit Surfaces that Interpolate
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Surface Representation Using Second, Fourth and Mixed Order Partial Differential Equations
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Dynamic Implicit Solids with Constraints for Haptic Sculpting
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Volume Sculpting Using the Level-Set Method
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Bender: a virtual ribbon for deforming 3D shapes in biomedical and styling applications
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Medial axis extraction and shape manipulation of solid objects using parabolic PDEs
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Free-Form Geometric Modeling by Integrating Parametric and Implicit PDEs
IEEE Transactions on Visualization and Computer Graphics
Technical Section: Interactive free-form level-set surface-editing operators
Computers and Graphics
| Hi-index | 0.00 |
Solid modeling based on Partial Differential Equations (PDEs) can potentially unify both geometric constraints and functional requirements within a single design framework to model real-world objects via its explicit, direct integration with parametric geometry. In contrast, implicit functions indirectly define geometric objects as the level-set of underlying scalar fields. To maximize the modeling potential of PDE-based methodology, in this paper we tightly couple PDEs with volumetric implicit functions in order to achieve interactive, intuitive shape representation, manipulation, and deformation. In particular, the unified approach can reconstruct the PDE geometry of arbitrary topology from scattered data points or a set of sketch curves. We make use of a fourth-order elliptic PDE to define the volumetric implicit function. The proposed implicit PDE model has the capability to reconstruct a complete solid model from partial information and facilitates the direct manipulation of underlying volumetric datasets via sketch curves, iso-surface sculpting, deformation of arbitrary interior regions, as well as a set of CSG operations inside the working space.The prototype system that we have developed allows designers to interactively sketch the curve outlines of the object, define intensity values and gradient directions, and specify interpolatory points in the 3D working space. The governing implicit PDE treats these constraints as generalized boundary conditions to determine the unknown scalar intensity values over the entire working space. The implicit shape is reconstructed with specified intensity value accordingly and can be deformed using a set of sculpting toolkits. We use the finite-difference discretization and variational interpolating approach with the localized iterative solver for the numerical integration of our PDEs in order to accommodate the diversity of generalized boundary constraints.