Volume Decomposition Based On Geometry Shape And Topology Structure

Hexahedral finite element mesh have offered some mathematical benefit over tetrahedral finite element meshes in terms of reduced error and smaller element counts.However,the automatic meshing of arbitrary objects with high quality,or well shaped hexahedra remains an open problem.One of the common method is dividing the mesh into small part and processing small one to make the problem easy.As CAD products become more complex,the integration of CAD and CAE is an urgent problems.The emergence of isogeometric analysis provides a new way to solve this problem and the modeling of spline solids became an important topic.It is also a feasible method to regenerate the spline solid after the decomposition.In order to get high quality hexhedral volumes which can fully reflect surface geometry shape and internal topological structure,we present a volume decomposition method based on heat diffusion.First,we select some points on surface of the input mesh as surface heat source.By solving the heat diffusion on surface of the mesh,we get the heat kernel which reflects the heat distribution.According to the heat distribution,the surface can be divided into sub-regions which can reflect the geometric information of the surface.Then we move the heat source point along the normal vector to inner,as part of the internal heat source,thus we can ensure that the results of internal heat diffusion would retain the feature on surface.Because the skeleton of a model can reflect the topological structure of the model,we extract the skeleton of the model and select some of the sample points on skeleton as the inner heat sources.From the above,by solving the inner heat diffusion equation via finite element method,we get the heat distribution and divide it into initial sub-volume.Finally we use the Laplace-smoothing algorithm and split these volumes into the hexhedral volumes.