Four-dimensional collision detection and behaviour based on the physics-based calculation

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.