Four‐dimensional collision detection and behaviour based on the physics‐based calculation
Yuki Nakai, Takanobu Miwa, Hiroki Shigemune, Hideyuki Sawada · Expert Systems · 2021
Abstract In the field of 4‐D space visualization, the information of 4‐D space is obtained by projecting 4‐D data onto 3‐D space. Most of the previous research has been aimed at the recognition of 4‐D space, whereas the target of the recognition has been limited to the geometrical information of 4‐D objects in 4‐D space or static spatial information without dynamics. Our research aims to develop a visualization system for providing the human experience of the physics‐based environment in 4‐D space. In this research, we mainly focus on collision detection and the behaviour of 4‐D objects in 4‐D space in order to construct the physics‐based environment of 4‐D space. Our contribution in this paper is the development of a collision detection algorithm for 4‐D objects and a calculation method for physics based behaviour of 4‐D objects. Our proposed collision detection algorithm is based on the intersection test of tetrahedrons in 4‐D space, so that 4‐D objects in our system is represented as tetrahedral meshes. The tetrahedron‐based collision detection algorithm is performed by a combination of half‐space tests with the use of 5‐D homogeneous processing to enhance the calculation accuracy of the collision detection. Our proposed method calculates the behaviour of the 4‐D objects after the collision by solving the motion equation based on the principle of physics. Consequently, the visualization system with the proposed algorithm allows us to observe the physics‐based environment in 4‐D space.