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

本研究的主题是表征动态物体的位置、方向和形式，并在设计和规划中利用这些表征。在代表时空空间的四维空间中，用四面体构造四维几何模型，四面体确定四维体的边界。基于该形状数据模式，开发了一个四维几何建模系统。将所提出的方法和开发的系统应用于三个问题：运动物体的避碰问题、球头铣五自由度切削问题和海啸灾害中的水位变化问题。

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.