Singularity structure simplification for hex mesh via integer linear program

Topology optimization of hexahedral (hex) meshes has been a widely studied topic, with the primary goal of optimizing the singularity structure. Previous works have focused on simplifying complex singularity structures by collapsing sheets/chords. However, these works require a large number of checks during the process to prevent illegal operations. Moreover, the employed simplification strategies are not based on the topological characteristics of the structure, but rather on the rank of the components that can be simplified. To overcome these problems, we analyze how topology operations affect the degree of edges in hex meshes, and introduce a fast and automatic algorithm to simplify the singularity structure of hex meshes. The algorithm relies on sheet operations, using mesh volume as a metric to assess the degree of simplification. Moreover, it designs constraints to prevent illegal operations and employs integer linear program to plan the overall optimization strategy for a mesh. After that, we relax the singularity constraints to further simplify the structure, and handle unreasonable singularities via sheet inflation operation. Our algorithm can also improve singularity structure without merging singularities by adjusting the singularity constraint conditions. Numerous experiments demonstrate the effectiveness and efficiency of our algorithm.