スリットを含む平板素材の曲げ形状設計

概要

伸縮しない薄い素材を折り曲げてできる形状は可展面に限られ，自由曲面を含む形を作ることは本質的にできないが，素材に切り込みを入れることを許容すれば形状変形の自由度が増し，より意匠的な形を作ることが可能となる．しかしながら，実際に制作できる形には依然として厳しい幾何的な制約があり，この制約を満たしながら意図した形を設計することは難しい問題である．
本研究では，複数のスリット（細長い切りこみ）が入れられた長方形の素材を対象として，対話的に形を操作できるシステムを提案する．システムは，予め設定された折り線の位置と折れ角を最適化手法によって調整し，平面に展開できるという制約を維持しつつ意図した形のデザインを実現する．

Abstract

Most manufacturing materials, such as wooden boards, metal sheets, and paper, are planar and nearly inextensible. Bending such materials not only allows us to form objects, but also avoids wastes and reduces gluing costs. However, the resulting shape is limited to developable surfaces. Due to this limitation, this method lacks flexibility in design. This problem can be addressed by adding slits to the materials, thereby allowing the conformation of a single sheet into expressive surfaces with high flexibility. In this paper, we propose an interactive design system for flexible geometry. A rectangular sheet material containing parallel slits is used in this work. The regions between the slits are called strips, and by bending them, we can simulate the desired shape. Both flexibility and geometric constraints are satisfied by a numerical optimization approach. The proposed system optimizes a bending shape of the strips by considering the smoothness of the surface and the user input. We show the effectiveness of our system using evaluation experiments.

Video

Publication

  • Naoya Tsuruta, Jun Mitani, Yoshihiro Kanamori, Yukio Fukui, "Interactive Design of 3D Geometry Made by Bending Inextensible Sheet Material Containing Slits", International Journal of CAD/CAM, Vol. 13, No. 2, pp. 23-29 (2013). pdf
  • Naoya Tsuruta, Jun Mitani, Yoshihiro Kanamori, Yukio Fukui, "Interactive Design of 3D Geometry Made by Bending Inextensible Sheet Material Containing Slits", Asian Conference on Design and Digital Engineering (ACDDE2012), Hokkaido, Dec. 6-8, 2012.
  • 鶴田直也, 三谷純, 金森由博，福井幸男："スリット入り平板素材の折り曲げによる形状の設計支援システム"，Visual Computing/グラフィクスとCAD合同シンポジウム2012, 2012-6．
  • 鶴田直也, 三谷純, 金森由博，福井幸男, "スリット入り平板素材を折り曲げてできる形状の設計支援ツール", 第146回グラフィクスとCAD研究会, 2012-2. (優秀研究発表賞)