Research On Robust And Efficient Sheet Inflation Method

Among the common types of volumetric meshes,hexahedral mesh has the advantages of high analysis precision,fast convergence and memory saving.Therefore,hexahedral mesh has always been valued by academia and industry.However,the automatic generation of high-quality hexahedral mesh is still a challenging problem.In the process of hexahedral mesh generation,editing and optimization,it is often necessary to modify the topology structure of the hexahedral mesh in order to improve the mesh quality.In practice,researchers mainly use the dual operations to modify the topology structure of the hexahedral mesh.Sheet inflation is the most critical and the most useful dual operation.In this thesis,we propose a robust and efficient sheet inflation method to overcome the shortcomings of current sheet inflation methods in terms of reliability,quality and efficiency.The main research work includes the following aspects:(1)A single-sheet inflation algorithm which could guarantee the quality of mesh after sheet insertion is conducted.Firstly,the feasibility of the sheet inflation is predetermined to ensure that the mesh quality after sheet inflation is acceptable.Then,we generate the simple or complex shrink set based on the mesh context structure and the prediction of mesh quality.Finally,the topology structure of the inserted sheet is generated based on the shrink set and the geometric classification of the inserted sheet is determined.This algorithm can conduct the insertion of sheet with complex structure and guarantee the quality of the mesh after sheet inflation as well as the rational geometric classification of the new points in the inserted sheet.(2)An efficient and reliable multi-sheets inflation algorithm is proposed.This algorithm could deal with the intersected quad sets reliably and improves the efficiency of multi-sheet inflation by inserting as many sheets as possible as a whole.For cases where not all sheets can be inserted as a whole,the method divides them into groups and inserts group at a time to improve efficiency as much as possible.After the insertion of some sheet groups,complementation of the rest invalid quad sets is necessary to guarantee the validity of sheet inflation.