Principles of traditional animation applied to 3D computer animation
SIGGRAPH '87 Proceedings of the 14th 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
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
I-COLLIDE: an interactive and exact collision detection system for large-scale environments
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
The NURBS book
Polyhedral perturbations that preserve topological form
Computer Aided Geometric Design
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Communications of the ACM
Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Computing the writhing number of a polygonal knot
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Preventing Self-Intersection under Free-Form Deformation
IEEE Transactions on Visualization and Computer Graphics
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Ambient isotopic approximations for surface reconstruction and interval solids
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Computational topology: ambient isotopic approximation of 2-manifolds
Theoretical Computer Science - Topology in computer science
Extreme elevation on a 2-manifold
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Interactive collision detection between deformable models using chromatic decomposition
ACM SIGGRAPH 2005 Papers
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Collision detection and proximity queries
ACM SIGGRAPH 2004 Course Notes
Building triangulations using ε-nets
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computational topology of spline curves for geometric and molecular approximations
Computational topology of spline curves for geometric and molecular approximations
Computational topology for isotopic surface reconstruction
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
Preserving computational topology by subdivision of quadratic and cubic Bézier curves
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Unknots with highly knotted control polygons
Computer Aided Geometric Design
| Hi-index | 5.23 |
The art of animation relies upon modeling objects that change over time. A sequence of static images is displayed to produce an illusion of motion. Even for simple cases, a careful analysis exposes that formal topological guarantees are often lacking. This absence of rigor can result in subtle, but significant, topological flaws. A new modeling approach is proposed to integrate topological rigor with a continuous model of time. Examples will be given for Bezier curves, while indicating extensions to a richer class of parametric curves and surfaces. Applications to scientific visualization for molecular modeling are discussed. Prototype animations are available for viewing over the web.