Yin-Yang grid shallow water equations using virtual pipes method (WebGPU)

A fully WebGPU-driven Yin-Yang shallow-water planet: stable overlap exchange, realtime cubemap synthesis, and live displaced-sphere rendering. Steps: 1. Generate terrain independently on Yin and Yang spherical patches (PSRDNoise 3D). 2. Simulate shallow-water dynamics on each patch with MAC-style face flows (virtual pipes method). 3. Build compact overlap exchange tables once (flag, scan, compact, weight build). 4. Exchange seam data every step: - MAC U and V face fields are interpolated and rotated into the target patch. - Scalar water field uses target-space relaxation to reduce one-pass seam mismatch. 5. Convert live Yin/Yang state to runtime cubemap textures on the GPU. 6. Render a displaced sphere from those textures in the same process. Why it works: - Yin-Yang patches avoid polar singularities of a single lat-lon grid. - Precomputed compact exchange tables make overlap coupling fast at runtime.