Connectivity-guaranteed porous synthesis in free form model by persistent homology

Porous structure, that is, a three-dimensional structure with a complex topology, has been widely applied in aerospace, paramedical, transportation, and other fields. In the porous structure design, porous structures derived from nature usually have better properties than artificial porous structures. In this study, we propose a reverse design method for synthesizing a connectivity-guaranteed porous model from a porous sample. Using a small porous sample and a trivariate B-spline solid as input, the proposed method generates through a large-scale porous model whose pattern is similar to that of the porous sample. To ensure the connectivity of the model and its pores, we use distance-to-measure-based topology optimization to process the topologically complex porous structure. Finally, a porous structure represented by an implicit B-spline function is generated through progressive-iterative approximation. Moreover, a connected and smooth porous model is generated by mapping the implicit B-spline function to the trivariate B-spline solid. Experimental results show that the proposed method effectively produces connected porous models with a pore pattern similar to that of the input porous sample.