Research on the generation of Escher-like tilings based on the generalization of Procrustes distance

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K11695
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60020:Mathematical informatics-related
• Research Institution: The University of Tokushima
• Principal Investigator: NAGATA Yuichi 徳島大学, 大学院社会産業理工学研究部(理工学域), 教授 (70334795)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: エッシャータイリング

Outline of Final Research Achievements

In this study, a method was developed to generate one type of shape that are similar to a given target shape and can tile the plane. In conventional methods, the similarity between the target shape and the tile shape was evaluated using Procrustes distance. This study introduced the concept of as-rigid-as-possible deformation to Procrustes distance, which made it possible to achieve satisfactory results even for complex target shapes that were difficult to obtain satisfactory results with using previous methods. Additionally, the scope of this method was expanded to encompass the tiling of the plane using two distinct types of shapes for two different target shapes. These achievements were published in the top journal in the field of computer graphics, ACM Transactions on Graphics.

Free Research Field

数理最適化

Academic Significance and Societal Importance of the Research Achievements

本研究で開発した手法により，クモのような複雑な目標図形に対しても，目標図形の自然な変形により得られる図形を敷き詰めた平面タイリングを生成することが可能となった．一見，無謀に思える複雑な目標図形に対して満足度の高いタイリングを自動生成できることは，多くの人に驚きを与えるものであり，本研究は数理最適化と芸術が融合した応用研究の成功例の一つと言えるだろう．また，数理最適化を応用してこのような芸術作品を自動生成できることを示したことは，多くの人に数理最適化に興味を持ってもらうための契機となるもである．