Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Robust Computational Algorithms for Dynamic Interface Tracking in Three Dimensions
SIAM Journal on Scientific Computing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A 2D kinetic triangulation with near-quadratic topological changes
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Untangling triangulations through local explorations
Proceedings of the twenty-fourth annual symposium on Computational geometry
Edge flips and deforming surface meshes
Proceedings of the twenty-seventh annual symposium on Computational geometry
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We present a method to maintain a mesh approximating a deforming surface, which is specified by a dense set of sample points. We identify a reasonable motion model for which a provably good surface mesh can be maintained. Our algorithm determines the appropriate times at which the mesh is updated to maintain a good approximation. The updates use simple primitives, and no costly computation such as line-surface intersection is necessary. Point insertions and deletions are allowed at the updates. Each update takes time linear in the size of the current sample set plus the new sample points inserted. We also construct examples for which, under the same model, no other algorithm makes asymptotically fewer changes to the mesh than our algorithm.