Interactive Modeling of Cellular Structures on Surfaces with Application to Additive Manufacturing

Abstract

The rich and evocative patterns of natural tessellations endow them with an unmistakable artistic appeal and structural properties which are echoed across design, production, and manufacturing. Unfortunately, interactive control of such patterns‐as modeled by Voronoi diagrams, is limited to the simple two dimensional case and does not extend well tofreeform surfaces. We present an approach for direct modeling and editing of such cellular structures on surface meshes. The overall modeling experience is driven by a set of editing primitives which are efficiently implemented on graphics hardware. We feature a novel application for 3D printing on modern support‐free additive manufacturing platforms. Our method decomposes the input surface into a cellular skeletal structure which hosts a set of overlay shells. In this way, material saving can be channeled to the shells while structural stability is channeled to the skeleton. To accommodate the available printer build volume, the cellular structure can be further split into moderately sized parts. Together with shells, they can be conveniently packed to save on production time. The assembly of the printed parts is streamlined by a part numbering scheme which respects the geometric layout of the input model.

A Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfaces

“…Figure 4, leads to the creation of new separate regions and front collision requires colliding fronts to freeze thus blocking each other. These behavior patterns are similar to the natural tessellation model proposed in [ZMSS18; SMS*20] which describes the evolution of the interface of multiple cells growing simultaneously on a surface and yields Voronoi‐like surface tessellations.…”

“…The coefficients of the gradient energy a ij are set to 1/25, and those for the penalty term w i,j to when i ≠ j , and to 0 otherwise. We did not see any need for changing the parameter values proposed in [ZMSS18; SMS*20] despite the problem settings being completely different.…”

Geometrical Degrees of Freedom for Cellular Structures Generation: A New Classification Paradigm

“…In Savio et al [46]'s work, an FE model is first built based on loads and the surface is subdivided using computer graphic techniques. Researchers such as Stadlbauer et al [112] have worked on an approach to interactively generate cellular structures on existing meshes. With surface meshes as inputs, they can decompose their meshes into hollow cellular structures that act as a skeleton on the surface and a set of thin shells.…”