Gaussian Sphere for Polyhedron Made from Paper Pattern and Recoverable Information

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  • 型紙から作成される多面体のガウス球表現と保持情報
  • カタガミ カラ サクセイ サレル タメンタイ ノ ガウスキュウ ヒョウゲン ト ホジ ジョウホウ

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Abstract

<p>Because a paper pattern has two dimensions, it is easier to handle than a three-dimensional object. In contrast,it is difficult to assume the three-dimensional shape of a garment based on a paper pattern alone. Its shape must be confirmed by manufacturing a sample or by simulating the garment. In this paper, we propose a method using a Gaussian sphere to visualize “Gaussian curvature” and “meancurvature,“ which are geometric quantities of a three-dimensional shape. Angular defects,i.e., the Gaussian curvature of a polyhedron, are visualized as areas on the Gaussian sphere. This visualization relates to “conversion to the area of the Gaussian curvature“ directly, and provides information on the mean curvature of the Gaussian sphere. In addition, the examples are shown of the basic paper pattern and development charts of the polyhedron, polyhedral model, and Gaussian spheres.</p>

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