We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and orientation restrictions. We show that already deciding feasibility of such approximation problems is NP-hard, and remains intractable even for very simple setups. We then devise an algorithmic framework that combines shape sampling with exact cardinality minimization to obtain good approximations using few components. As a particular application and showcase example, we discuss approximating shape contours using the classical Zometool construction kit and provide promising computational results, demonstrating that our algorithm is capable of obtaining good shape representations within reasonable time, in spite of the problem's general intractability. We conclude the paper with an outlook on possible extensions of the developed methodology, in particular regarding 3D shape approximation tasks.

我们考虑使用离散装配系统逼近二维形状轮廓（或曲线段）的问题，该系统允许基于受边缘长度和方向限制的有限节点和边缘类型集构建几何结构。我们表明已经决定这种近似问题的可行性是NP-hard，即使对于非常简单的设置也仍然难以处理。然后，我们设计了一个算法框架，将形状采样与精确基数最小化相结合，以使用很少的组件获得良好的近似值。作为一个特定的应用程序和展示示例，我们讨论了使用经典 Zometool 构建工具包近似形状轮廓并提供了有希望的计算结果，证明我们的算法能够在合理的时间内获得良好的形状表示，尽管该问题一般难以处理。我们总结了对已开发方法的可能扩展的展望，特别是关于 3D 形状近似任务。