A Unified Architecture for N-Dimensional Visualization and Simulation: 4D Implementation and Evaluation including Boolean Operations

This paper proposes a unified software architecture for visualization and simulation based on a design targeting an $N$-dimensional space. The contribution of this work lies in presenting an architectural configuration that integrates multiple processes into a single software architecture: Quickhull-based convex hull mesh generation, Boolean operations, coordinate transformations for high-dimensional exploration (including orientation and view transformations), and hyperplane slicing for visualization. The proposed approach adopts an approximate implementation that tolerates numerical errors and prioritizes implementation transparency over guarantees of numerical rigor. The experimental results and evaluations presented in this paper are limited to a 4D implementation; no evaluation is conducted for $N>4$, and the discussion is restricted to stating that the architecture itself has a dimension-independent structure. This paper also proposes an interaction design for high-dimensional exploration based on FPS navigation. As an input example involving shape changes over time, a non-rigid body simulation based on XPBD (Extended Position Based Dynamics) is integrated into the 4D implementation. Experimental results confirm that the 4D implementation runs on a single PC.