Zometool Rationalization of Freeform Surfaces

Abstract

Abstract-An ever broader availability of freeform designs together with an increasing demand for product customization has lead to a rising interest in efficient physical realization of such designs, the trend toward personal fabrication. Not only large-scale architectural applications are (becoming increasingly) popular but also different consumer-level rapid-prototyping applications, including toy and 3D puzzle creation. In this work we present a method for do-it-yourself reproduction of freeform designs without the typical limitation of state-of-the-art approaches requiring manufacturing custom parts using semi-professional laser cutters or 3d printers. Our idea is based on a popular mathematical modeling system (Zometool) commonly used for modeling higher dimensional polyhedra and symmetric structures such as molecules and crystal lattices. The proposed method extends the scope of Zometool modeling to freeform, disktopology surfaces. While being an efficient construction system on the one hand (consisting only of a single node type and 9 different edge types), this inherent discreteness of the Zometool system, on the other hand gives rise to a hard approximation problem. We base our method on a marching front approach, where elements are not added in a greedy sense, but rather whole regions on the front are filled optimally, using a set of problem specific heuristics to keep complexity under control.

Dr. KID: Direct Remeshing and K-set Isometric Decomposition for Scalable Physicalization of Organic Shapes

“…One of its main uses is generating isometric segments of the input surface. This complex geometric problem enhances reusability, reducing both complexity and costs [19,22,26,50]. Isometric decomposition has applications in tiling [16], modeling, and fabrication [26].…”

“…Zometool 1 is a mathematical and molecular modeling kit, which is a popular visualization and physicalization tool with a specific focus on repetitive patterns such as molecular structures, crystal lattices, and mathematical constructs. Further research [50,51] extended the scope of Zometool toward free-form, disk-topology surfaces. The studies [50,51] provide an insight into utilizing Zometool for architectural applications.…”

“…Further research [50,51] extended the scope of Zometool toward free-form, disk-topology surfaces. The studies [50,51] provide an insight into utilizing Zometool for architectural applications. Adopting the advancing front strategy, they start from a single vertex and grow forward for the physicalization of the model.…”

State of the art on stylized fabrication

“…The approach proposed in [ZLAK14] finds an initial zometool approximation using a voxelization of the input mesh, and then a sequence of local operations is used to optimize the final result. A different approach based on an advancing front technique is proposed in [ZK14].…”