AUnified Framework for N-Dimensional Visualization and Simulation: Implementation and Evaluation including 4D Boolean

Abstract: This study proposes a unified framework for simulation and visualization of intuitive exploration of phenomena in N-dimensional space. While specialized libraries offer powerful geometric algorithms, they typically lack integrated environments for interactive trial and error, creating a barrier for researchers. The contribution of this research is the integration of Quickhull-based mesh generation, visualization via hyperplane slicing, and computationally expensive Boolean operations into a single, extensible platform, while maintaining interactivity. To validate its effectiveness, this paper presents a 4-dimensional implementation and introduces a new interaction design, termed `High-Dimensional FPS,' to enable intuitive high-dimensional exploration. Furthermore, as a case study to demonstrate the framework's high extensibility, I also integrated a non-rigid body physics simulation based on Extended Position Based Dynamics (XPBD). Experimental results confirmed the effectiveness of the proposed method, achieving real-time rendering (80 fps) of complex 4D objects and completing Boolean operations within seconds in a standard PC environment. By providing an accessible and interactive platform, this work lowers the entry barrier for high-dimensional simulation research and enhances its potential for applications in education and entertainment.