Bi-Axial Woven Tiles: Interlocking Space-Filling Shapes Based on Symmetries of Bi-Axial Weaving Patterns (original) (raw)
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Computers & Graphics, 2020
In this paper, we present a simple and intuitive approach for designing a new class of space-filling shapes that we call Generalized Abeille Tiles (GATs). GATs are generalizations of Abeille vaults, introduced by the French engineer and architect Joseph Abeille in late 1600s. Our approach is based on two principles. The first principle is the correspondence between structures proposed by Abeille and the symmetries exhibited by woven fabrics. We leverage this correspondence to develop a theoretical framework for GATs beginning with the theory of bi-axial 2-fold woven fabrics. The second principle is the use of Voronoi decomposition with higher dimensional Voronoi sites (curves and surfaces). By configuring these new Voronoi sites based on weave symmetries, we provide a method for constructing GATs. Subsequently, we conduct a comparative structural analysis of GATs as individual shapes as well as tiled assemblies for three different fabric patterns using plain and twill weave patterns. Our analysis reveals interesting relationship between the choice of fabric symmetries and the corresponding distribution of stresses under loads normal to the tiled assemblies.
This paper explores how computational methods of representation can support and extend kagome handcraft towards the fabrication of interlaced lattice structures in an expanded set of domains, beyond basket making. Through reference to the literature and state of the art, we argue that the instrumentalisation of kagome principles into computational design methods is both timely and relevant; it addresses a growing interest in such structures across design and engineering communities; it also fills a current gap in tools that facilitate design and fabrication investigation across a spectrum of expertise, from the novice to the expert. The paper describes the underlying topological and geometrical principles of kagome weave, and demonstrates the direct compatibility of these principles to properties of computational triangular meshes and their duals. We employ the known Medial Construction method to generate the weave pattern, edge 'walking' methods to consolidate geometry into individual strips, physics based relaxation to achieve a materially informed final geometry and projection to generate fabrication information. Our principle contribution is the combination of these methods to produce a principled workflow that supports design investigation of kagome weave patterns with the constraint of being made using straight strips of material. We evaluate the computational workflow through comparison to physical artefacts constructed ex-ante and ex-post.
Computers & Graphics, 2011
Classical (or biaxial) twill is a textile weave in which the weft threads pass over and under two or more warp threads, with an offset between adjacent weft threads to give an appearance of diagonal lines. This paper introduces a theoretical framework for constructing twill-woven objects, i.e., cyclic twill-weavings on arbitrary surfaces, and it provides methods to convert polygonal meshes into twill-woven objects. It also develops a general technique to obtain exact triaxial-woven objects from an arbitrary polygonal mesh surface.
SIGGRAPH Asia 2022 Technical Communications
A printed single VoroNoodle. (c) Assembly of two printed VoroNoodles. (d) Assembly of three printed VoroNoodles. (e) 2 × 2 Assembly of printed VoroNoodles. (f) 2 × 2 Assembly of printed VoroNoodles. Figure 1: An example of congruent VoroNoodles that provide strong topological interlocking. Each layer is translated into a parametric equation in the form of = (3) and = (3) to produce a helix. To obtain the helical ruled surface shown in 1a, we rotated and scaled a 2D vector along this helix. Translated versions of these ruled surfaces are used as Voronoi sites to obtain Corrugated Bricks, which we call VoroNoodles.
Architectural Design, 2006
View from the Turbine Hall entrance. Woven Surface and Form The Advanced Geometry Unit (AGU) at Arup, founded by Cecil Balmond and Charles Walker, has become synonymous with a highly mathematical, topological approach to architecture. It has, however, collaborated on some of the most exciting experimental fabric structures of recent years, including Anish Kapoor's Marsyas at Tate Modern and Rem Koolhaas's Cosmic Egg at the Serpentine Gallery. Here, the unit's Tristan Simmonds, Martin Self and Daniel Bosia describe how the AGU has progressed research into textile techniques that encompass tailored biomorphic forms alongside knot diagrams. 84 Arup AGU, Geometry research, 2005 Straight lines drawn over toroidal and catenoidal meshes show possible trajectories for structural ribbons. Arup AGU, Geometry research, 2005 Draping of an equal-link-length grid over an arbitrary meshed surface using ELM. Arup AGU, Geometry research, 2002 Form-finding of a cylindrical mesh. Anticlockwise from top left: starting mesh; collapsed catenoid form resulting from equal tension in warp and weft directions; catenoid form produced using 7:1 warp to weft tension; addition of hydrostatic pressure; addition of internal pressure.
Weaving Double-Layered Polyhedra
2018
At Bridges 2016 I showed single sheet folding nets of some of the Platonic double layer single surface polyhedra. Having real physical models helps to understand the complex structure of these double layer single surface polyhedra. Therefore I developed more simple ways to create these models. In this paper I want to introduce weaving as a technique for creating models of double layer single surface polyhedra.
Effect of Geometric Arrangement on Mechanical Properties of 2D Woven Auxetic Fabrics
Textiles
Textiles-fibres, yarns and fabrics are omnipresent in our daily lives, with unique mechanical properties that fit the design specifications for the tasks for which they are designed. The development of yarns and fabrics with negative Poisson’s ratio (NPR) is an area of current research interest due to their potential for use in high performance textiles (e.g., military, sports, etc.). The unique braiding technology of interlacement for preparation of braided helically wrapped yarns with NPR effect with later development of auxetic woven fabric made it possible to avoid the slippage of the wrapped component from the core. The applied geometrical configuration and NPR behaviour of the braided helical yarn structure with seven different angles comprising of monofilament elastomeric polyurethane (PU) core with two wrap materials that include multifilament ultra-high molecular weight polyethylene (UHMWPE) and polyethylene terephthalate (PET) fibres were investigated and analysed. The mec...
Mathematical Design for Knotted Textiles
Handbook of the Mathematics of the Arts and Sciences, 2019
This chapter examines the relationship between mathematics and textile knot practice, i.e., how mathematics may be adopted to characterize knotted textiles and to generate new knot designs. Two key mathematical concepts discussed are knot theory and tiling theory. First, knot theory and its connected mathematical concept, braid theory, are used to examine the mathematical properties of knotted textile structures and explore possibilities of facilitating the conceptualization, design, and production of knotted textiles. Through the application of knot diagrams, several novel two-tone knotted patterns and a new material structure can be created. Second, mathematical tiling methods, in particular the Wang tiling and the Rhombille tiling, are applied to further explore the design possibilities of new textile knot structures. Based on tiling notations generated, several two- and three-dimensional structures are created. The relationship between textile knot practice and mathematics illuminates an objective and detailed way of designing knotted textiles and communicating their creative processes. Mathematical diagrams and notations not only reveal the nature of craft knots but also stimulate new ideas, which may not have occurred otherwise.