The Folded Shape Restoration and the Rendering Method of Origami from the Crease Pattern

Recently, it is not uncommon to use a computer to research on Origami. We developed a dedicated editor, ORIPA, for designing the crease pattern of Origami intending to establish the basis of the future research on Origami. The editor has unique features that the folded shape of flat Origami (Origami which is folded flat) is restored from the crease pattern and the CG image of that can be generated. The users can input crease patterns by using a simple user interface. We expect that this editor can have beneficial influence on Origami researches. In this paper, we introduce the user interface of this system and the inner algorithms of rendering. Restoring the folded shape of Origami from the crease pattern can be replaced by the problem of finding valid overlap relations between all two faces. This relation can be represented by a matrix. To define the matrix is not a simple problem because it is proven that this problem belongs to a class of NP-complete. Although ORIPA finds the valid overlap relations by using brute-force approach, the answers are found in reasonable time due to the elimination of the invalid overlap relations at the early stage of estimation. After a valid overlap order of folded Origami is found, there is another problem; how to display it. In flat Origami, some cases exist that have a closed loop in the overlap order of faces after they are folded. It is difficult to display this shape correctly on the screen because Origami is usually represented by a set of plane polygons of zero thickness as is generally used in CG and all faces are placed on the same plane. In the proposed method, we use the matrix that represents the overlap relation and a face ID buffer and the concept of which is similar to a Z buffer in the z-buffer algorithm. With this buffer, the face located in the uppermost is monitored in each pixel at the rendering stage. By using this buffer, we propose three rendering styles. Lastly, we introduce applications that use the exported data from ORIPA.