High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Simulating facial surgery using finite element models
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Robust Computational Algorithms for Dynamic Interface Tracking in Three Dimensions
SIAM Journal on Scientific Computing
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Comparing Efficiency of Integration Methods for Cloth Simulation
CGI '01 Proceedings of the International Conference on Computer Graphics
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Maintaining deforming surface meshes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Gabriel meshes and Delaunay edge flips
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
A fast and simple surface reconstruction algorithm
Proceedings of the twenty-eighth annual symposium on Computational geometry
Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh
Computer Graphics Forum
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We study edge flips in a surface mesh and the maintenance of a deforming surface mesh. If the vertices are dense with respect to the local feature size and the triangles have angles at least a constant, we can flip edges in linear time such that all triangles have almost empty diametric balls. For a planar triangulation with a constant angle lower bound, we can flip it to the Delaunay triangulation in linear time. We combine edge flips and vertex nsertions and deletions in an algorithm to maintain a deforming surface mesh, specified only by a dense sample of n points that move with the surface. Under a reasonable motion model, we can enforce bounded aspect ratios and a small approximation error throughout the deformation. The update takes O(n) time at each time step. Our surface mesh maintenance algorithm also gives a good performance in experiments.