Search Results (2)

Performing accurate and precise collision detection is a key to real-time applications in computer graphics, games, physical-based simulation, virtual reality, augmented reality, and research and development. Researchers have developed numerous methods to minimize computation time and enhance the accuracy of collision detection for pair-object collisions. Although the performance of the central processing unit (CPU) has significantly improved in recent years, it is still insufficient for many applications. In this study, we have developed an improved algorithm for geometric bounding volume hierarchy (BHV) in 3D spatial subdivisions using an Octree-based axis-aligned bounding box (AABB) structure. The AABB structure is used for collision detection and its computation by the central processing unit and graphic processing unit (GPU), which is implemented on the compute shader in Unity3D. AABB was defined as the maximum and minimum hexahedron within an object that is parallel to the coordinate axis. While GPU computing is essential for enhancing the object’s performance. The proposed algorithm approaches Octree AABB-based GPU parallel processing to reduce the calculation or process of simulation for real-time collision detection and handles multiple computations. In the CPU environment, the algorithm spent 2.9 fps when simulating up to 20 objects of the Torus Model that contains 2.3 K vertices and 4.6 K triangles. In the GPU environment, it spent 635.62 fps with 20 objects, and the maximum number increased to 180 objects in real-time. Full article

In this article, we study the intersection of a finite collection of disks in Euclidean space by examining spheres of various dimensions and their poles (extreme values with respect to canonical projections) contained within the intersection’s boundary. We derive explicit formulae for computing these extreme values and present two applications. The first application involves computing the smallest common rescaling factor for the radii of the disk system, which brings the system to a single point of intersection. This calculation allows us to compute the generalized Čech filtration, a crucial tool for the topological data analysis of weighted point clouds. The second application focuses on determining the minimal Axis-Aligned Bounding Box (AABB) for the intersection of a finite collection of disks in Euclidean space, addressing a significant problem in computational geometry. We consider that this work aims to contribute to the fields of topological data analysis and computational geometry by providing new tools for analyzing complex geometric structures. Full article