Exploiting lattice structures in shape grammar implementations
Exploiting lattice structures in shape grammar implementations
复制标题
DOI：
10.1017/s0890060417000282
复制
发表时间：
2018-05
期刊：
影响因子：
--
通讯作者：
H. Chau;A. McKay;C. Earl;A. Behera;A. de Pennington
中科院分区：
文献类型：
--
作者：
H. Chau;A. McKay;C. Earl;A. Behera;A. de Pennington
摘要形状语法的独特优势是能够处理歧义，并基于已定义和新出现的形状计算新的设计。要在设计实践中实现这些好处，需要实现通用形状语法解释器，其支持：(A)检测任意形状中的任意子形状，以及(B)应用使用这些子形状来创建新形状的形状规则。目前可用的解释器的复杂性源于它们将形状计算(用于子形状检测和规则的应用)与计算几何(用于需要生成新形状的几何操作)相结合。本文提出了一种基于格论的表示为有理二次Bézier曲线的三维圆弧的形状语法实现方法，通过将形状计算过程中的步骤与与特定语法和形状相关的几何操作分开来降低这种复杂性。通过对两个著名的形状文法：Stiny的三角形文法和Jowers和Earl的三叶文法的应用，证明了该方法的有效性。建立了一个解释程序内核的原型计算机实现，并给出了它在这两种文法中的应用。三维贝塞尔曲线的使用为扩展形状语法实现提供了可能性，以覆盖在实际产品设计和开发过程中使用的实际实现变得可行之前所需的更广泛的应用。
Abstract The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible.