Reasonable thickness determination for implicit porous sheet structure using persistent homology

TL;DR

This paper introduces a novel method to generate and control the thickness of porous sheet structures from point clouds using implicit B-spline functions and persistent homology, enabling efficient 3D printing.

Contribution

It presents a new approach combining implicit B-splines and persistent homology for efficient porous sheet structure generation with controllable thickness.

Findings

Method is more efficient than traditional approaches.

Ensures manufacturability and pore preservation.

Supports direct slicing for 3D printing.

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. However, conventional methods for generating sheet structures are inefficient for porous surfaces because of the complexity of the internal structures. In this study, we propose a novel method for generating porous sheet structures directly from point clouds sampled on a porous surface. The generated sheet structure is represented by an implicit B-spline function, which ensures smoothness and closure. Moreover, based on the persistent homology theory, the topology structure of the generated porous sheet structure can be controlled, and a reasonable range of the uniform thickness of the sheet structure can be calculated to ensure manufacturability and pore existence. Finally, the implicitly B-spline represented sheet structures are sliced directly with the marching squares algorithm, and the contours can be used for 3D printing. Experimental results show the superiority of the developed method in efficiency over the traditional methods.