Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Optimal coarsening of unstructured meshes
Journal of Algorithms
Curves and surfaces in geometric modeling: theory and algorithms
Curves and surfaces in geometric modeling: theory and algorithms
A parallel dynamic-mesh Lagrangian method for simulation of flows with dynamic interfaces
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
SIAM Journal on Optimization
Dynamic local remeshing for elastoplastic simulation
ACM SIGGRAPH 2010 papers
On Bézier surfaces in three-dimensional Minkowski space
Computers & Mathematics with Applications
Representing topological structures using cell-chains
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Simulating liquids and solid-liquid interactions with lagrangian meshes
ACM Transactions on Graphics (TOG)
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We present a new framework for maintaining the quality of two dimensional triangular moving meshes. The use of curved elements is the key idea that allows us to avoid excessive refinement and still obtain good quality meshes consisting of a low number of well shaped elements. We use B-splines curves to model object boundaries, and objects are meshed with second order Bézier triangles. As the mesh evolves according to a non-uniform flow velocity field, we keep track of object boundaries and, if needed, carefully modify the mesh to keep it well shaped by applying a combination of vertex insertion and deletion, edge flipping, and edge smoothing operations at each time step. Our algorithms for these tasks are extensions of known algorithms for meshes built of straight--sided elements and are designed for any fixed-order Bézier elements and B-splines. Although in this work we have concentrated on quadratic elements, most of the operations are valid for elements of any order and they generalize well to higher dimensions. We present results of our scheme for a set of objects mimicking red blood cells subject to a precomputed flow velocity field.