Tri-Planar Orthogonal Complex Mapping (TP-OCM): A Convergent Framework for Spatial Computing, Robotics, and Simulation

This work introduces Tri-Planar Orthogonal Complex Mapping (TP-OCM), a novel mathematical framework for representing spatial states in robotics, artificial intelligence, and physical simulations. TP-OCM encodes 3D positions and orientations into a coupled 3-complex-plane manifold, preserving Cartesian linearity while allowing direct phase-based rotation synthesis. The framework bypasses computational overhead associated with quaternions, provides intrinsic drift correction, and serves as a structural prior for AI models and simulation engines. Benchmarks demonstrate significant speedup and numerical stability, making TP-OCM a practical and versatile tool for high-fidelity spatial computing applications.