Delta DLP 3-D printing of large models

Abstract

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 Ω with n generators (i.e., line segments and reflex vertices in Ω), we show that the time complexity of our algorithm is O(n²log² n) and the number of output rectangles covering Ω 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.