A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Finite element handbook
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
Trends in curve and surface design
Computer-Aided Design
Modifying the shape of rational B-splines. part2: surfaces
Computer-Aided Design
Modifying the shape of rational B-splines. part 1: curves
Computer-Aided Design
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Good vibrations: modal dynamics for graphics and animation
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Layered construction for deformable animated characters
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Representing PDE surfaces in terms of B-splines
Computer-Aided Design
Physical modeling with B-spline surfaces for interactive design and animation
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Using partial differential equations to generate free-form surfaces: 91787
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
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
Surface modeling with oriented particle systems
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
Linear constraints for deformable non-uniform B-spline surfaces
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
2-D shape blending: an intrinsic solution to the vertex path problem
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A generalization of dynamic constraints
CVGIP: Graphical Models and Image Processing
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Constraints methods for flexible models
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Shape Averaging and it's Applications to Industrial Design
IEEE Computer Graphics and Applications
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From Conics to NURBS: A Tutorial and Survey
IEEE Computer Graphics and Applications
Computer-aided design applications of the rational b-spline approximation form.
Computer-aided design applications of the rational b-spline approximation form.
Dynamic manipulation of triangular B-splines
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Volume-preserving free-form solid
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Fast construction of accurate quaternion splines
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Dynamic smooth subdivision surfaces for data visualization
VIS '97 Proceedings of the 8th conference on Visualization '97
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
An anthropometric face model using variational techniques
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Proceedings of the SIGCHI conference on Human Factors in Computing Systems
Integrated mechanically based CAE system
Proceedings of the fifth ACM symposium on Solid modeling and applications
Fast volume-preserving free form deformation using multi-level optimization
Proceedings of the fifth ACM symposium on Solid modeling and applications
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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)
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ACM Transactions on Graphics (TOG)
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Proceedings of the 28th annual conference on Computer graphics and interactive techniques
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VRST '00 Proceedings of the ACM symposium on Virtual reality software and technology
FreeDrawer: a free-form sketching system on the responsive workbench
VRST '01 Proceedings of the ACM symposium on Virtual reality software and technology
A multiresolution framework for dynamic deformations
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
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IEEE Transactions on Visualization and Computer Graphics
D-NURBS: A Physics-Based Framework for Geometric Design
IEEE Transactions on Visualization and Computer Graphics
Dynamic Free-Form Deformations for Animation Synthesis
IEEE Transactions on Visualization and Computer Graphics
Dynamic Catmull-Clark Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
Dynamic Modeling of Butterfly Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
A Simple Technique for NURBS Shape Modification
IEEE Computer Graphics and Applications
Interactive Deformation of Irregular Surface Models
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Efficient Shape Description Using NURBS
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
An Automated Segmentation Method of Kidney Using Statistical Information
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
P3DMA: A Physical 3D Deformable Modelling and Animation System
AMDO '02 Proceedings of the Second International Workshop on Articulated Motion and Deformable Objects
Dynamic maintenance and visualization of molecular surfaces
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Efficient And Accurate Interference Detection For Polynomial Deformation
CA '96 Proceedings of the Computer Animation
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PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Interactive Global and Local Deformations for Virtual Clay
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Interactive global and local deformations for virtual clay
Graphical Models - Special issue on pacific graphics 2003
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Graphical Models - Special issue on pacific graphics 2003
NURBS-based Galerkin method and application to skeletal muscle modeling
Proceedings of the 2005 ACM symposium on Solid and physical modeling
An analytic pseudo-spectral method to generate a regular 4-sided PDE surface patch
Computer Aided Geometric Design
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Proceedings of the 2006 ACM symposium on Solid and physical modeling
Applied Numerical Mathematics - Applied scientific computing: Recent approaches to grid generation, approximation and numerical modelling
Cords: Geometric Curve Primitives for Modeling Contact
IEEE Computer Graphics and Applications
A discrete model of thin shells
ACM SIGGRAPH 2006 Courses
Modeling with multiresolution subdivision surfaces
ACM SIGGRAPH 2006 Courses
A discrete model of thin shells
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Image and Vision Computing
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Dynamic spherical volumetric simplex splins with application in biomedical simulation
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Dynamic Axial Curve ---Pair Based Deformation
Edutainment '08 Proceedings of the 3rd international conference on Technologies for E-Learning and Digital Entertainment
Deformation-Based Animation of Snake Locomotion
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
An evolutionary algorithm for surface modification
Acta Cybernetica
Applied Numerical Mathematics - Applied scientific computing: Recent approaches to grid generation, approximation and numerical modelling
An analytic pseudo-spectral method to generate a regular 4-sided PDE surface patch
Computer Aided Geometric Design
Approximate swept volumes of NURBS surfaces or solids
Computer Aided Geometric Design
New multiresolution modeling techniques in CAD
Computer-Aided Design
High-resolution object deformation reconstruction with active range camera
Proceedings of the 32nd DAGM conference on Pattern recognition
Proceedings of the 24th annual ACM symposium on User interface software and technology
Challenges in computer applications for ship and floating structure design and analysis
Computer-Aided Design
Deformation of dynamic surfaces
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Morphees: toward high "shape resolution" in self-actuated flexible mobile devices
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Efficient energy evaluations for active B-Spline/NURBS surfaces
Computer-Aided Design
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The Visual Computer: International Journal of Computer Graphics
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This article develops a dynamic generalization of the nonuniform rational B-spline (NURBS) model. NURBS have become a defacto standard in commercial modeling systems because of their power to represent free-form shapes as well as common analytic shapes. To date, however, they have been viewed as purely geometric primitives that require the user to manually adjust multiple control points and associated weights in order to design shapes. Dynamic NURBS, or D-NURBS, are physics-based models that incorporate mass distributions, internal deformation energies, and other physical quantities into the popular NURBS geometric substrate. Using D-NURBS, a modeler can interactively sculpt curves and surfaces and design complex shapes to required specifications not only in the traditional indirect fashion, by adjusting control points and weights, but also through direct physical manipulation, by applying simulated forces and local and global shape constraints. D-NURBS move and deform in a physically intuitive manner in response to the user's direct manipulations. Their dynamic behavior results from the numerical integration of a set of nonlinear differential equations that automatically evolve the control points and weights in response to the applied forces and constraints. To derive these equations, we employ Lagrangian mechanics and a finite-element-like discretization. Our approach supports the trimming of D-NURBS surfaces using D-NURBS curves. We demonstrate D-NURBS models and constraints in applications including the rounding of solids, optimal surface fitting to unstructured data, surface design from cross sections, and free-form deformation. We also introduce a new technique for 2D shape metamorphosis using constrained D-NURBS surfaces.