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.@en

We present a delta DLP 3D printer with large size in this paper. Compared with traditional DLP 3D printers that use a low-cost off-the-shelf consumer projector and a single vertical carriage, the platform of our delta DLP 3D printer can also move horizontally in the plane. We show that this structure allows the printer to have a larger printing area than the projection area of a projector. Our system can print 3D models much larger than traditional DLP 3D printers. The
major challenge to realize delta 3D printing with large size comes from how to partition an arbitrary planar polygonal shape (possibly with holes or multiple disjoint polygons) into a minimum number of rectangles with xed size, which is
NP-hard. We propose a simple yet efcient approximation algorithm to solve this problem. The time complexity of our algorithm is O(n3 log n), where n is the number of edges in the polygonal shape. A physical prototype system is built and
several large 3D models with complex geometric structures have been printed as examples to demonstrate the effectiveness of our approach.@en