Developing Algebraic Constraints for Reciprocal Polyhedral Diagrams of 3 D Graphic Statics
Developing Algebraic Constraints for Reciprocal Polyhedral Diagrams of 3 D Graphic Statics
复制标题
开发 3D 图形静力学倒多面图的代数约束
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Yi Guo
中科院分区：
文献类型：
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作者：
C. Mueller;M. Akbarzadeh;Márton Hablicsek;Yi Guo
基于倒多面体图的三维图形静力学是基于几何的结构找形领域的最新发展之一，是生成空间结构形式及其三维受力图的有力方法。然而，在三维空间中构建倒易多面体图形是非常具有挑战性的，而且该研究缺乏一个严格的数学定义来表达三维几何图形和力图形之间的几何关系和倒易关系。在过去的150年里，二维图形静力学已经被用代数表示出来，这使得人们能够更好地理解二维图形和力图之间的关系。这种代数公式在开发交互工具方面至关重要，使设计者和实践者能够通过计算绘制每个设计迭代的倒易图，从而开发使用形状图和力图的潜力，否则这是相当繁琐和繁琐的。本文初步建立了多面体形式与三维几何图形之间的倒易关系，为进一步研究三维几何图形的代数实现奠定了基础。
3D graphic statics using reciprocal polyhedral diagrams (3DGS) is one of the recent developments in the field of geometry-based structural form finding and is a powerful method in generating spatial structural forms and their force diagram in three dimensions. However, constructing reciprocal polyhedral diagrams in 3D is quite challenging and the research lacks a rigorous mathematical definition formulating the geometrical and reciprocal relationship between the form and force diagrams in 3DGS. Having been used for the past 150 years, 2D graphic statics has recently been formulated algebraically that allows better topological understanding the relationship between the form and the force diagrams in 2D. Such algebraic formulation is crucial in developing interactive tools enabling designers and practitioner to exploit the potentials of working with the form and force diagrams by computationally drawing the reciprocal diagrams for each design iteration which was otherwise quite tedious and cumbersome. This paper provides initial formulation of the reciprocal relationships between polyhedral form and the force diagrams in 3DGS and lays a foundation for further research in algebraic implementation of 3DGS.