This paper presents a 3-D printing system that uses a low-cost off-the-shelf consumer projector to fabricate large models. Compared with traditional digital light processing (DLP) 3-D printers using a single vertical carriage, the platform of our DLP 3-D printer using delta mechanism can also move horizontally in the plane. We show that this system can print 3-D models much larger than traditional DLP 3-D printers. The major challenge to realize 3-D printing of large models in our system comes from how to cover a planar polygonal domain by a minimum number of rectangles with fixed size, which is NP-hard. We propose a simple yet efficient approximation algorithm to solve this problem. The key idea is to segment a polygonal domain using its medial axis and afterward merge small parts in the segmentation. Given an arbitrary polygon Q with n generators (i.e., line segments and reflex vertices in Q), we show that the time complexity of our algorithm is O(n2 log2 n) and the number of output rectangles covering Q is O(Kn), where K is an input-polygon-dependent constant. A physical prototype system is built and several large 3-D models with complex geometric structures have been printed as examples to demonstrate the effectiveness of our approach.

中文翻译：

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Delta DLP 3D 打印大型模型


本文介绍了一种 3D 打印系统，该系统使用低成本现成的消费级投影仪来制造大型模型。与使用单个垂直滑架的传统数字光处理（DLP）3D打印机相比，我们使用Delta机构的DLP 3D打印机的平台还可以在平面内水平移动。我们证明该系统可以打印比传统 DLP 3D 打印机大得多的 3D 模型。在我们的系统中实现大型模型3D打印的主要挑战来自于如何用最少数量的固定尺寸的矩形覆盖平面多边形域，这是NP难的。我们提出了一种简单而有效的近似算法来解决这个问题。关键思想是使用多边形域的中轴来分割多边形域，然后合并分割中的小部分。给定一个具有 n 个生成器的任意多边形 Q（即 Q 中的线段和反射顶点），我们表明算法的时间复杂度为 O(n2 log2 n)，覆盖 Q 的输出矩形的数量为 O(Kn)，其中 K 是与输入多边形相关的常数。构建了一个物理原型系统，并打印了几个具有复杂几何结构的大型 3D 模型作为示例，以证明我们方法的有效性。