Implicit complex topology modeling design method based on Voronoi

Abstract

Porous structures with complex topologies have long been at the forefront of research in the field of additive manufacturing. However, existing methods exhibit limited capability in representing the morphology of pores in random porous structures, lack precision in gradient design, and struggle to accurately simulate the stochastic porous features found in nature. This paper proposes a novel modeling approach for random porous structures. Firstly, the method utilizes Voronoi tessellation to obtain the topological data of three-dimensional Voronoi diagrams. Based on this topology, a signed distance field is constructed to implicitly represent the porous model, providing exceptional flexibility in the expression of pore morphologies. Secondly, growth functions that describe natural growth processes are employed to achieve smooth transitions in pore morphology within the porous model, enabling precise control over transitions and facilitating the design of hierarchical and gradient porous structures. Finally, by introducing a radial basis function (RBF) weighted interpolation method, the transition region is generalized to the entire domain, allowing for complex gradient designs and biomimetic simulations. This study offers a new solution for the modeling of complex topologies.