多面体を用いた縫合後の立体形状予測

摘要

To make 2D patterns of a garment, it must be noted that there are two types of parts. Some are flexible parts, for example drape in skirts, and others are stiff parts, for example collars. It is difficult to estimate the 3D form after sewing with 2D patterns in flexible parts. On the other hand, it is not so difficult to estimate that in stiff parts. Here, we focus on design of the stiff parts. We assumed that garments are made of paper, and have already predicted a continuous 3D form of a garment by using the theory of developable surfaces. Solutions were, however, usually differential equations these were not integrable. It was not general-purpose system. The aim of this paper is to make a general-purpose system for predicting the 3D form of garments after sewing. We approximate sewn curves to polygons, and seek the 3D form of garments after sewing and feasible region on the 2D patterns by using polyhedrons. At the same time, we considered the difference between the continuous system and proposed discrete system. We made the general-purpose prototype system by using an example, regular n th pyramid. As for the differences between the continuous system and the discrete system, the following three results were obtained. (1) Users can set up a first standing angle of regular n th pyramid. (2) The larger a difference between a standing angle corresponded with continuous system and a first standing angle become, the shorter a length of generating lines are. (3) The higher the accuracy of approximation becomes, the bigger the influence that the difference between the two angles gives the length of generating line is.%衣服の形には，型紙設計との関係に着目してみると，ドレープのように軟らかくて型紙設計の時点 からは完成形が予測しにくい部分と，衿のように硬くて型紙設計が完成形に反映される部分がある． 本論文では後者に着目した．材料を紙とし，可展面理論を用いて縫合後の立体形状予測をする場合， 解が一意に定まる点が長所であったが，解は一般に積分不可能な微分方程式であるため，実際に解く 場合には数値積分を用いる場合があるのが短所であった．つまり汎用システムではなかった．本論文 の目的は，汎用システムを作成すること，すなわち縫合線を折れ線に近似し，縫合可能な型紙の形状 と縫合後の立体形状を，多面体を用いて求めることである．同時に，既存の連続系システムと，本論 文で提案する離散系システムの違いを考察する． 最も簡単な正n角錐を例題として離散系システムを作成した．離散系システムにおいては，最初の 立ち上がり角を自由に設定できること，連続系システムに対応する立ち上がり角と離散系システムに おいて設定した立ち上がり角との差が大きくなるほど母線の制限長が短くなったこと，3次元縫合線 の分割数が大きくなるにつれて，この2つの角度の差が母線の制限長に大きな影響を与えることがわ かった．