Feat: support general single-frame cameras and add a near-horizon example

README.md

@@ -17,7 +17,13 @@ Stars are individual catalog point sources with direction, temperature, and
 amplitude. The renderer maps them into the camera image, accounting for
 multiple images, gravitational lensing magnification, and frequency shifts,
 then accumulates their sub-pixel point-spread functions (PSFs) into an HDR
-image. Moving cameras are described by worldline and tetrad tracks.
+image. Movie cameras are described by worldline and tetrad tracks.
+
+Single images support independent coordinate position and look direction,
+coordinate velocity, and camera roll in both backends. For example,
+`--observer-position 1.75 0 0 --observer-velocity -0.5 0 0 --look-ra-deg 0 --look-dec-deg 0`
+specifies an inward-moving Schwarzschild camera looking outward from inside
+the horizon. See [single-frame camera parameters and complete commands](usage.md#single-frame-camera).
 
 ## Current status
 
@@ -119,12 +125,43 @@ to the cache radius. The [original benchmark record](benchmarks/2mass_galactic_c
 preserves the command and terminal output; the command above omits the optional
 HDR export.
 
-The Schwarzschild camera points toward the hole. Adaptive refinement should
+This example infers a position facing the hole from its look direction and radius. Adaptive refinement should
 be configured for the desired image accuracy; it is disabled by default.
 Camera controls, movie sequences, lens-map reuse, PSF settings, and HDR output
 are described in [usage.md](usage.md). Both binaries provide a complete option
 list with `--help`.
 
+### Example: Looking outward just above the Schwarzschild horizon
+
+This camera is static at `(2.1, 0, 0)` in Cartesian Kerr–Schild coordinates,
+just outside the horizon at `r=2M` (`M=1`). RA=0°, Dec=0° points along +X,
+radially outward. Its coordinate velocity is zero: this is a static
+observer, not a freely falling one. The scene uses the bundled synthetic
+stellar grid, so no survey download is needed.
+
+```sh
+mkdir -p output/imgs
+./build/Release/schwarzschild_sky \
+  --catalog assets/sky_grid_5deg.csv \
+  --observer-position 2.1 0 0 \
+  --observer-velocity 0 0 0 \
+  --look-ra-deg 0 --look-dec-deg 0 \
+  --camera-roll-deg 0 \
+  --width 3840 --height 2160 --fov-deg 90 \
+  --coarse-cell-pixels 16 --refine-max-level 3 \
+  --exposure 0.01 \
+  --output output/imgs/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png
+```
+
+[![Synthetic stellar sky seen outward by a static observer at r=2.1M](assets/images/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png)](assets/images/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png)
+
+*4K render with a 90° horizontal field of view, exposure `0.01`, and maximum
+refinement level 3. Click to view at full resolution.*
+
+The distant sky occupies a bounded angular region around the outward
+direction, with repeated images crowded near its edge. Strong gravitational
+blueshift pushes both the 3000 K and 12000 K test stars toward blue-white.
+
 ### Example: Synthetic test grid with mesh overlay
 
 This example uses `assets/sky_grid_5deg.csv` to inspect lensing and adaptive