From graphs to tensegrity structures: Geometric and symbolic approaches
From graphs to tensegrity structures: Geometric and symbolic approaches
复制标题
从图到张拉整体结构：几何和符号方法
DOI：
10.5565/publmat_50206_02
复制
发表时间：
2004
影响因子：
1.1
通讯作者：
David Orden
中科院分区：
文献类型：
--
作者：
Miguel de Guzm'an;David Orden
本文研究了张拉整体结构的形状确定问题，给出了一个算法，给出了一个抽象图成为Rd（d = 2，3）中顶点处于一般位置的张拉整体结构的基础图的必要条件。此外，对于某一类图，我们的算法允许获得必要的和succientconditions上的顶点的相对位置，以根据张拉整体，为什麽我们提出了一个几何和符号的approach.Subject classification：05C85，Graph algorithms.Key words：Form finding problems，Tensegrity，Graphs，Polynomial elimination. 1引言在本文中，我们研究了张拉整体结构的所谓找形问题的一个实例。自1948年左右Kenneth Snelson的开创性著作以来，这些都引起了数学家和工程师的特别关注（见[15]）。粗略地说，张拉整体结构的形状确定问题要求确定R中点和直边的几何构型
AbstractA form-finding problem for tensegrity structures is studied; given an abstract graph,we show an algorithm to provide a necessary condition for it to be the underlying graphof a tensegrity in R d (typically d = 2,3) with vertices in general position. Furthermore,for a certain class of graphs our algorithm allows to obtain necessary and sufficientconditions on the relative position of the vertices in order to underlie a tensegrity, forwhat we propose both a geometric and a symbolic approach.Subject classification: 05C85, Graph algorithms.Key words: Form-finding problems, Tensegrity, Graphs, Polynomial elimination. 1 Introduction In this paper we study an instance of the so-called form-finding problems for tensegritystructures. These have brought special attention both among mathematicians and engineerssince the seminal works of Kenneth Snelson around 1948 (see [15]). Roughly speaking, aform-finding problem for a tensegrity structure asks to determine a geometric configurationof points and straight edges in R