A High-Speed CGH Calculation Method for Mirror Images on B\'ezier Surfaces using Optical Path Length Minimization

Abstract

Rendering reflections in curved mirrors is crucial for enhancing the realism in computer-generated hologram (CGH), yet it poses a fundamental challenge due to the unique computational principles of CGH. Conventional methods using B\'ezier clipping are computationally prohibitive, and a previously proposed mirror surface subdivision method suffered from the computation time increasing with mirror curvature. To address these limitations, this paper proposes a novel calculation method based on Fermat's principle that directly and efficiently determines the reflection point by minimizing the optical path length from a point light source to a hologram pixel via the mirror surface, using Newton's method for optimization. Experimental results demonstrate that this method significantly reduces computation time compared to previous approaches. Furthermore, it enables the rendering of multiple reflections from several mirrors, a capability that was challenging for conventional techniques.