As a ubiquitous paper folding art, origami has promising applications in science and engineering. Many software and parameterized methods have been proposed to draw, analyze and design origami patterns. Here we focus on the shape grammar formalism and the Shape Machine, a shape grammar interpreter that has managed to automate the seamless shape calculations that the shape grammar formalism advocates. Different from other origami pattern generation methods, shape grammars generate origami patterns through recursive applications of shape rewriting rules using lines and curves. Based on this concept, the transformations between some common origami patterns are reorganized following visual cues and reasoning. Four examples of generating origami pattern are presented to show the capability of Shape Machine in origami design, including construction, modification and programming of an origami pattern. The new origami designs inspired by this work prove that shape grammars and Shape Machine provide a perspective and modeling technique for creating origami tessellation patterns.

折纸作为一种普遍存在的折纸艺术，在科学和工程领域具有广阔的应用前景。已经提出了许多软件和参数化方法来绘制，分析和设计折纸图案。在这里，我们集中讨论形状语法形式主义和形状机器，这是一个形状语法解释器，已成功实现了形状语法形式主义提倡的无缝形状计算的自动化。与其他折纸模式生成方法不同，形状语法通过使用直线和曲线递归应用形状重写规则来生成折纸模式。基于此概念，一些常见的折纸样式之间的转换会根据视觉提示和推理进行重组。给出了四个产生折纸图案的示例，以展示Shape Machine在折纸设计中的功能，包括构造，折纸样式的修改和编程。受这项工作启发的新折纸设计证明，形状语法和Shape Machine提供了用于创建折纸镶嵌图案的透视图和建模技术。