Finite element handbook
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Conditions for tangent plane continuity over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
Good vibrations: modal dynamics for graphics and animation
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
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
An investigation of curvature variations over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovery of Nonrigid Motion and Structure
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Dynamic deformation of solid primitives with constraints
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Boundary Finding with Parametrically Deformable Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear constraints for deformable non-uniform B-spline surfaces
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Multiresolution stochastic hybrid shape models with fractal priors
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Hierarchical shape representation using locally adaptive finite elements
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
A variational approach to subdivision
Computer Aided Geometric Design
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Dynamic smooth subdivision surfaces for data visualization
VIS '97 Proceedings of the 8th conference on Visualization '97
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Subdivision surfaces in character animation
Proceedings of the 25th 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
Non-uniform recursive subdivision surfaces
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
Edge and vertex insertion for a class of C1 subdivision surfaces
Computer Aided Geometric Design
Stationary Subdivision
D-NURBS: A Physics-Based Framework for Geometric Design
IEEE Transactions on Visualization and Computer Graphics
Dynamic Catmull-Clark Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
Shape and Nonrigid Motion Estimation Through Physics-Based Synthesis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Superquadrics and Free-Form Deformations: A Global Model to Fit and Track 3D Medical Data
CVRMed '95 Proceedings of the First International Conference on Computer Vision, Virtual Reality and Robotics in Medicine
Smoothness of Stationary Subdivision on Irregular Meshes
Smoothness of Stationary Subdivision on Irregular Meshes
Analysis and application of subdivision surfaces
Analysis and application of subdivision surfaces
Shape Recovery Using Dynamic Subdivision Surfaces
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A geometric database for gene expression data
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Towards fast and smooth subdivision surface reconstruction
International Journal of Computers and Applications
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
Model creation by velocity controlled surface deformation
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
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In this paper, we develop integrated techniques that unify physics-based modeling with geometric subdivision methodology and present a scheme for dynamic manipulation of the smooth limit surface generated by the (modified) butterfly scheme using physics-based 驴force驴 tools. This procedure-based surface model obtained through butterfly subdivision does not have a closed-form analytic formulation (unlike other well-known spline-based models) and, hence, poses challenging problems to incorporate mass and damping distributions, internal deformation energy, forces, and other physical quantities required to develop a physics-based model. Our primary contributions to computer graphics and geometric modeling include: 1) a new hierarchical formulation for locally parameterizing the butterfly subdivision surface over its initial control polyhedron, 2) formulation of dynamic butterfly subdivision surface as a set of novel finite elements, and 3) approximation of this new type of finite elements by a collection of existing finite elements subject to implicit geometric constraints. Our new physics-based model can be sculpted directly by applying synthesized forces and its equilibrium is characterized by the minimum of a deformation energy subject to the imposed constraints. We demonstrate that this novel dynamic framework not only provides a direct and natural means of manipulating geometric shapes, but also facilitates hierarchical shape and nonrigid motion estimation from large range and volumetric data sets using very few degrees of freedom (control vertices that define the initial polyhedron).