Reasonable thickness determination for implicit porous sheet structure using persistent homology

Abstract

Porous structures are widely used in various industries because of their excellent properties. Porous surfaces have no thickness and should be thickened to sheet structures for further fabrication. For porous surfaces with implicit representation, sheet structures can be generated by extracting the region between two iso-surfaces. However, too small sheet thickness leads to extra small holes emerging on the sheet structure, and too large sheet thickness makes the pores closed. In this study, we propose a novel method for determining the sheet thickness for porous surfaces represented by implicit functions. Specifically, after calculating the persistent diagram (PD) of the scalar field dictated by the implicit function, the points in the PD are clustering into three clusters. Using these clusters, a topology control method is developed, which allows users to determine how many pores can be closed. Moreover, a reasonable thickness can be determined, by which all of the pores keep open, and the extra small holes are eliminated. Experimental results show the effectiveness of the developed method.