![]() ![]() In their paper, "Layered Fields for Natural Tessellations on Surfaces," the authors successfully demonstrate their new method on several large-scale test cases beyond the capabilities of state-of-the-art. The annual conference features the most respected technical and creative members in the field of computer graphics and interactive techniques, and showcases leading edge research in science, art, gaming and animation, among other sectors. Zayer, Steinberger and their collaborators, which include Hans-Peter Seidel at Max Planck Institute for Informatics, and Daniel Mlakar at Graz University of Technology, will present their novel method at SIGGRAPH Asia 2018 in Tokyo 4 December to 7 December. "Observing the progress made in parallelizing existing serial Voronoi diagram codes over the last two decades, the performance gains achieved by our proposed method are very considerable," adds Markus Steinberger, coauthor of the work and an assistant professor at Graz University of Technology in Austria. "In this way, we provide small, concise, humanly readable and most importantly, platform-independent parallel code," notes Zayer. multiplication and addition, readily available, as they are the cornerstone of modern numerical computing. Their method relies mainly on basic sparse linear algebra kernels, i.e. Instead, they have developed a method that takes into account region boundaries in the pattern as narrow bands, which are not necessarily straight, and model the partition as a set of smooth functions layered over the surface. In this new work, researchers simplify the creation of natural tessellations on surface meshes by dropping the assumption that regions need to be separated by lines. Efforts at extending the same idea to surfaces are hampered by the extensive costs of accurate distance measurements, bookkeeping and intersection computations. In mathematics, A Voronoi diagram partitions planes in a pattern based on the distances between points. Typically, researchers have turned to the Voronoi model to mimic such repeat surface patterns. "To capture this behavior, we need to adopt an intrinsic view of the problem and depart from the widely adopted extrinsic perspective which requires full knowledge of all individual cell interactions and locations." ![]() Cells represent the shape or tiles that comprise intricate tessellation patterns. Hence, these designs are promising topologies for future applications.ģD Voronoi tessellation additive manufacturing bio-inspired mechanical properties."When we look at how natural tessellation occurs in nature, the individual cells grow simultaneously, and each individual cell does not necessarily know who are its neighboring cells nor their location or coordinates," explains lead author of the work, Rhaleb Zayer, researcher at Max Planck Institute for Informatics in Saarbrücken, Germany. For the Homogeneous and gradient II cylinders, elongated Voronoi structures show superior mechanical properties and energy absorption compared to normal Voronoi designs. The gradient I cylinder show the highest Young's modulus. Finally, a compression test was carried out to study and compare the mechanical properties of the designed samples. Then, stereolithography (SLA) additive manufacturing was utilized to fabricate biopolymeric materials. Thus, the Rhinoceros 7/Grasshopper software was used to design three geometric models for both normal and elongated Voronoi structures: homogeneous, gradient I, and gradient II. The proposed designs are inspired by nature, which has undoubtedly proven to be the best designer. ![]() Therefore, in the current work, new designs are proposed for lightweight 3D scaffolds based on Voronoi tessellation with high porosity. Irregular 3D biological scaffolds have been widely observed in nature. ![]()
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