Space-time integrated approach for design and planning based on four-dimensional geometry

本研究的主题是表示动态对象的位置，方向和形式，并在设计和规划中利用这些表示。在表示时空空间的四维空间中，用确定四维物体边界的四面体构造四维几何模型。在此基础上，开发了一个四维几何造型系统。所提出的方法和开发的系统进行了评估，适用于三个问题：碰撞避免问题的移动物体，代表5自由度切割与球头铣削，和水位变化的海啸灾害。

The subject of this study is to represent the positions, orientations, and forms of dynamic objects and to utilize the representations in design and planning with respect to them. In a four-dimensional space representing a spatio-temporal space, four-dimensional geometric models are constructed with tetrahedrons which determine the boundary of 4D body. Based on this shape data schema, a four-dimensional geometric modeling system has been developed. The proposed method and the developed system were evaluated by applying to three problems: collision avoidance problem of moving objects, representing 5DOF cutting with ball-end milling, and water-level changes in the tsunami disaster.