期刊
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
卷 28, 期 10, 页码 3391-3404出版社
IEEE COMPUTER SOC
DOI: 10.1109/TVCG.2021.3065457
关键词
Fabrics; Weaving; Shape; Yarn; Three-dimensional displays; Fabrication; Visualization; Space-filling shapes; 3D tile design; geometric interlocking; fabric weave; 3D printing; computational fabrication
资金
- Texas A&M Engineering Experiment Station
This article introduces a framework for the geometric design and fabrication of geometrically interlocking space-filling shapes called woven tiles. The framework is based on Voronoi partitioning of space and design of curve segments closed under symmetry operations. The mechanical behavior of the woven tiles is evaluated and compared through finite element analysis.
In this article, we introduce a framework for the geometric design and fabrication of a family of geometrically interlocking space-filling shapes, which we call woven tiles. Our framework is based on a unique combination of (1) Voronoi partitioning of space using curve segments as the Voronoi sites and (2) the design of these curve segments based on weave patterns closed under symmetry operations. The underlying weave geometry provides an interlocking property to the tiles and the closure property under symmetry operations ensure single tile can fill space. In order to demonstrate this general framework, we focus on specific symmetry operations induced by fabric weaving patterns. We specifically showcase the design and fabrication of woven tiles on flat and curved domains by using the most common 2-fold fabrics, namely, plain, twill, and satin weaves. We further evaluate and compare the mechanical behavior of the so created woven tiles through finite element analysis.
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