Free-form multi-level porous model design based on truncated hierarchical B-spline functions

Abstract

Porous structures have been widely applied in aerospace, paramedical, transportation, and other fields owing to their high interconnectivity, low weight, and extensive internal surface areas. Multi-level porous structures with different hole shapes and distributions at varying scales have shown excellent biological and mechanical performances compared with single-level porous structures. However, designing multi-level porous models with complex topological and geometric structures is a challenge. In this work, we propose a multi-level porous model design framework. Given a model represented by a trivariate B-spline solid and porous structures represented by implicit functions, we design the porous model in the parametric domain. We use threshold distribution fields represented by truncated hierarchical B-spline (THB-spline) functions to control the pore shapes, locations, and number of levels. Furthermore, the proposed THB-spline least squares progressive-iterative approximation algorithm can flexibly adjust the porous model. The model meets the expected porosity through the proposed optimization algorithm. The porous structure in the parametric domain is finally mapped to the trivariate B-spline solid to generate the final model. Moreover, we define a new storage space-saving file format to store multi-level porous models. The experimental results demonstrate the effectiveness and efficiency of the method and the superior performance of the new storage format.