论文标题
确定形状的布置的几何形状
Geometry of Arrangements that Determine Shapes
论文作者
论文摘要
形状语法计算在宇宙$ u^*$中定义的形状上计算。宇宙中的形状$ u^*$类似于可以在飞机上物理实现的线图。任何形状都嵌入或包含在平面的点和线排列中，分别称为登记标记和构造线，以满足特殊发病率法律。在这篇说明性文章中，将包含形状的布置研究为发病率结构和产生的有限几何形状的特征。特别是，包含形状的布置被区分为产生有限的接近线性和线性空间的排列，以及那些不会产生任何适当形式的几何形状的排列（从严格的数学意义上讲）。构成有限几何形状（接近线性和线性空间）的布置给出了形状语法中确定规则的替代表征。本文有助于与形状语法理论领域形状数学有关的工作体系。
Shape grammars compute over shapes which are defined in the universe $U^*$. Shapes in the universe $U^*$ are analogous to line drawings that can be physically realized in the plane. Any shape is embedded or contained in an arrangement of points and lines in the plane called, respectively, registration marks and construction lines, that satisfy special incidence laws. In this expository article, arrangements that contain shapes are studied as incidence structures and the finite geometries they give rise to are characterized. In particular, arrangements that contain shapes are distinguished into those that give rise to finite near-linear and linear spaces, and those that do not give rise to any proper form of geometry (in the strict mathematical sense). Arrangements that constitute finite geometries (near-linear and linear spaces) give an alternative characterization of determinate rules in shape grammars. This paper contributes to the body of work related to the mathematics of shapes in the area of shape grammar theory.
