Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Optimal good-aspect-ratio coarsening for unstructured meshes
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Conforming Delaunay triangulations in 3D
Proceedings of the eighteenth annual symposium on Computational geometry
Dynamic maintenance and visualization of molecular surfaces
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Delaunay refinement mesh generation
Delaunay refinement mesh generation
Meshing skin surfaces with certified topology
Computational Geometry: Theory and Applications
Liquid simulation on lattice-based tetrahedral meshes
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Geometric modeling applications in rational drug design: a survey
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Quality meshing of implicit solvation models of biomolecular structures
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Quality tetrahedral mesh generation for macromolecules
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedra that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry.