The recent success of a class of mechanical applications of shape rules in CAD shape grammar interpreters has produced a renewed interest in the design and support of shape embedding and shape rewrite technologies. Despite this, some fundamental constructions in rule-based modeling, namely, any of Euclid's straightedge and compass constructions, appear awkward to simulate within the fuse-embed cycle of a shape grammar interpreter. It is suggested here that this problem of modeling Euclid's straightedge and compass constructions can be efficiently addressed with the introduction of a new schema rule leveraging symbolic representations of shape. Two applications based on the usage of three instances of this schema rule are given to show the simulation of straightedge and compass constructions in a general purpose 2D CAD shape grammar interpreter, the Shape Machine for Rhino. A reflection upon the usage of rule schemas in shape grammar interpreters is given in the end.

中文翻译：

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形状遇见欧几里得：将形状计算与标尺和指南针程序集成


最近，一类形状规则在 CAD 形状语法解释器中的机械应用取得了成功，这引起了人们对形状嵌入和形状重写技术的设计和支持的新兴趣。尽管如此，基于规则的建模中的一些基本构造，即任何欧几里得的直尺和圆规构造，在形状语法解释器的熔丝嵌入循环中进行模拟似乎很困难。这里建议，通过引入利用形状符号表示的新模式规则，可以有效地解决欧几里得直尺和圆规构造建模的问题。给出了基于此模式规则的三个实例的使用的两个应用程序，以显示通用 2D CAD 形状语法解释器（Rhino 形状机）中直尺和圆规结构的模拟。最后对规则模式在形状语法解释器中的使用进行了反思。