Cut & Unfold 

2022, University of Kansas
Cutting (sub-dividing) object is commonly seen in daily life, however, cutting can be complicated with constraints. In this study, an algorithm is developed to cut a three-dimensional box into pieces with two constraints: 1) any vertex has three valencies, that is, three edges are connected to each vertex; and 2) all surfaces are planar surfaces after cutting. After cutting, the second phase of this application is to unfold every piece and generate the cutting files for fabrication. The algorithm is to unfold the polysurfaces on the zero plane without overlapping the unfold surfaces. Also, cutting file should have two different line types: cutting lines and folding lines so that fabricator can put them back.