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ASkeleton-Based Approach to Automated Hexahedral Mesh Generation for Solid Models

Turkiyyah, George, M., Duane W. Storti, Mark Ganter, Hao Chen

Proceeding, 4th International Meshing Roundtable, Sandia National Laboratories, pp.late addition, October 1995


We describe a systematic and conceptually simple method for generating hexahedral meshes for solid models of 3D objects and present results obtained by applying this method to three sample objects. The method is rational and systematic due to a consistent, recursive utilization of skeletons to associate points on object boundaries with lower dimensional skeleton entities. Essentially, the 3D meshing problem is reduced to a discretization of the object's 2D surface skeleton which is in turn reduced to a discretization of the 1D geodesic line skeleton of the surface skeleton. The reduced dimensions are recovered by consecutive retraction from the skeleton's to their associated boundary points. Retraction of the geodesic line skeleton to the boundary of the surface skeleton produces a 2D quadrilateral surface discretization. In turn, retraction of the surface discretization to the solid's boundary results in the desired hexahedral mesh. Skeleton surface patches which are not bounded by seams require a slightly different discretization procedure, which is also described. The geodesic skeleton is a generalization of the Euclidean skeleton of a planar shape to shapes on 2D manifolds. The meshes produced for the sample objects, illustrate that the method is capable of producing relatively coarse all-hexahedral meshes which resolve the geometry of the solid model and are sutable for further refinement to capture solution features.
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