The patterns of many structural systems must fulfil a property of two-colourability to partition their elements into two groups. Such examples include top versus bottom layers of continuous beams in elastic gridshells, corrugated versus non-corrugated directions in corrugated shells or warp versus weft threads in woven structures. Complying with such constraints does not depend on the geometry but on the topology of the structure, and, more specifically, on its singularities. This paper presents a search strategy to obtain patterns that fulfil this topological requirement, which represent only a fraction of the general design space. Based on an algebra for the exploration of the topology of quad meshes, including a grammar and a distance, a topology-finding algorithm is proposed to find the closest two-colour quad-mesh patterns from an input quad-mesh pattern. This approach is expressed as the projection to the two-colourable subspace of the design space. The distance underlying the definition of the projection measures the similarity between designs as the minimum number of topological grammar rules to apply to modify one design into another. A design application illustrates how two-colour topology finding can complement workflows for the exploration of structural patterns with singularities informed by the system’s topological requirements.

许多结构系统的图案必须具有两种着色性，才能将其元素分为两组。这样的例子包括在弹性栅格壳中的连续梁的顶层与底层，在波纹壳中的波纹与非波纹方向或在编织结构中的经线与纬线。遵守这样的约束条件并不取决于几何形状，而是取决于结构的拓扑，更具体而言，取决于其奇异性。本文提出了一种搜索策略，以获取满足此拓扑要求的模式，这些模式仅代表一般设计空间的一小部分。基于用于探索四边形网格拓扑（包括语法和距离）的代数，提出了一种拓扑查找算法，以从输入的四边形网格图案中找到最接近的两色四边形网格图案。这种方法表示为对设计空间的两种颜色子空间的投影。投影定义所依据的距离衡量了设计之间的相似性，因为拓扑语法规则的最小数量适用于将一个设计修改为另一个设计。一个设计应用程序说明了两种颜色的拓扑查找如何以系统拓扑要求告知的奇异性补充工作流，以探索结构模式。投影定义所依据的距离衡量了设计之间的相似性，因为拓扑语法规则的最小数量适用于将一个设计修改为另一个设计。一个设计应用程序说明了两种颜色的拓扑查找如何以系统拓扑要求告知的奇异性补充工作流，以探索结构图案。投影定义所依据的距离衡量了设计之间的相似性，因为拓扑语法规则的最小数量适用于将一个设计修改为另一个设计。一个设计应用程序说明了两种颜色的拓扑查找如何以系统拓扑要求告知的奇异性补充工作流，以探索结构模式。