3D Image Rendering for HUDs via Catadioptric Optical Transformations

The patent changes the calculation parameters from using approximated refractive indices to using precise optical transformation parameters that account for the actual optical paths through the catadioptric system. This involves calculating ray directions based on accurate refraction and reflection models rather than simplified approximations, thereby improving image accuracy while managing computational complexity through efficient rendering algorithms.

The patent replaces the traditional mechanical/optical approximation methods with a computational approach that uses precise optical transformation calculations. Instead of relying on simplified physical models, the system uses computer-based ray tracing and optical path calculations that accurately model the catadioptric system's behavior, substituting physical approximation with computational precision.

The patent applies preliminary optical transformation calculations to determine the mapping between display panel pixels and optical images before actual image rendering. By pre-calculating ray directions and optical paths based on the catadioptric system's optical characteristics, the system establishes accurate correspondence relationships in advance, which then guides the rendering process and reduces real-time computational complexity.

The patent creates a computational model (optical transformation model) that copies and simulates the physical optical paths through the catadioptric system. This virtual model allows the system to calculate ray directions and pixel mappings without performing complex physical measurements during rendering, replacing physical complexity with computational efficiency while maintaining accuracy.