黑洞光线追踪

For each pixel, build a ray from the camera and reduce it to a 2D problem in the plane containing the ray and the black hole centre. Integrate the Schwarzschild photon orbit equation d²u/dφ² = -u + 1.5u² (with u = 1/r and Schwarzschild radius 1) using a fixed-step RK4 or leapfrog loop of a few hundred steps in the fragment shader. At each step check for crossing the disk plane between inner and outer radii and for r < 1 (captured, black). Shade disk hits with blackbody colour adjusted by Doppler and gravitational redshift, and sample a sky cubemap or equirectangular texture with the final direction for escaped rays.