Layered modeling of porous structures with voronoi diagrams

Abstract

Existing computer-aided geometric design methods are inadequate to model and design 3D porous structures. A layer-based approach with 2D Voronoi tessellation is proposed to reduce the 3D challenge to a 2D problem. We define each Voronoi generating point to be either solid or void point and organize the points into concentric clusters for designing small 2D shape regions. Dynamic 2D shape regions are achieved by specifying the motion of each generating point in the 2D plane. When expanding the time-dimension of these regions in the third dimension of the 2D plane, small pieces of 3D structures are defined. Moreover, when these regions undergo topological variations, small pieces of 3D branching structures are obtained. A technique on symmetry in 2D plane is utilized as a simple method to expand these structures to variations of large 3D branching and porous structures. The proposed method is a layer-based model as each horizontal cross-section of a final structure is a layer of region pattern specified by the dynamic generating points. The aim and novelty of the method presented are to provide a concise and flexible means of solid modeling for creating new porous structures.