Discrete geometry and creation of 3 dimensional geometric models

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13434
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: The University of Tokyo
• Principal Investigator: KOHNO Toshitake 東京大学, 大学院数理科学研究科, 教授 (80144111)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 離散幾何学 / 定曲率曲面 / 極小曲面 / 代数曲面 / 特異点理論 / 可積分系 / 極限集合 / 離散データ

Outline of Final Research Achievements

In this research we developed a method to create extremely accurate 3 dimensional models of surfaces appearing in geometry and topology by curving metals. This method realized models much more accurate than those created by 3D printers. We also developed techniques realizing limit sets of discrete group and objects in singularity theory, foliation theory and integrable systems, which were difficult to create by previous methods. By adding data of normal direction to discrete point data sets and mesh, we realized accuracy of less than 1/100mm. Our research established a new interface for creating accurate 3 dimensional models.

Free Research Field

位相幾何学，数理物理学