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首页> 外文期刊>International Journal of Computer Integrated Manufacturing >Aiding design with constraints: an extension of quad trees in order to deal with piecewise functions
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Aiding design with constraints: an extension of quad trees in order to deal with piecewise functions

机译：有约束的辅助设计：四叉树的扩展以处理分段函数

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This paper deals with aiding preliminary design when considered as a constraint satisfaction problem (CSP). In this case, constraint filtering techniques provide some kind of interactive assistance to the designer. However, some kinds of numerical constraints corresponding with numerical relations cannot be filtered precisely with classical analytical filtering techniques such as interval arithmetic or box-consistency; it is therefore necessary to discretize them in order to include them in the CSP. To this end, quad trees (QT) have been proposed for binary constraints, or 2{sup}k trees when more than two variables are considered; but QT assume that a constraint must be defined by a single numerical function. The aim of this paper is to show that QT techniques can be extended when a constraint is defined by a piecewise function or by a set of numerical functions defined on intervals. The first section recalls some basics relevant to the preliminary design problem and the interests of the CSP assistance. The second section presents the principles of the QT. The last section describes our contributions relevant to QT extensions dealing with piecewise functions.
机译：当被视为约束满足问题（CSP）时，本文旨在协助初步设计。在这种情况下，约束过滤技术为设计人员提供了某种交互式帮助。但是，某些与数值关系相对应的数值约束无法使用经典的分析滤波技术（例如区间算术或框式一致性）精确地进行滤波;因此，有必要对它们进行离散化处理，以便将其包含在CSP中。为此，已经提出了针对二元约束的四叉树（QT），或者当考虑两个以上的变量时建议使用两千棵树。但是QT假设约束必须由单个数值函数定义。本文的目的是表明，当通过分段函数或间隔上定义的一组数值函数定义约束时，可以扩展QT技术。第一部分回顾了一些与初步设计问题和CSP协助的利益相关的基础知识。第二部分介绍了QT的原理。最后一部分描述了我们与处理分段函数的QT扩展相关的贡献。

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