GR 4D ray tracing

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An offline spacetime renderer focused on physical accuracy. The project aims to turn time-dependent numerical-relativity simulations, including binary black-hole mergers, into 4K movies by tracing light rays backward through the four-dimensional spacetime.

The 2MASS Galactic-center star field seen through Schwarzschild spacetime, from a camera at radius 100 M. Click the image for the full 4K render; rendering command below.

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.

Current status

The current implementation supports analytic Minkowski and Schwarzschild spacetimes, single images and observer-track image sequences, adaptive lens meshes, and reusable lens-map files. It is written primarily in C with OpenMP CPU parallelism; an optional HIP backend accelerates PSF accumulation.

The Nmesh numerical-spacetime backend and BBH rendering are still planned. The current scope is black-hole capture and distant stellar backgrounds; local matter emission, accretion disks, and plasma are outside this stage. See the design document for the architecture and development roadmap.

Build

The default build requires a C11 compiler with OpenMP support, GNU Make, and libpng development files. From the repository root:

make -j

This builds both build/Release/minkowski_sky and build/Release/schwarzschild_sky. For individual backends, Debug builds, optional HDR/FITS output, HIP support, and regression checks, see build.md.

Prepare the stellar catalog

The renderer accepts any stellar catalog converted to the supported CSV format: four columns containing ICRS right ascension and declination in degrees, temperature in kelvin, and amplitude, in that order. Use --catalog PATH to load a single CSV.

2MASS is the recommended survey catalog, with download and processing scripts provided by this project. Instructions are in assets/2mass/README.md. The full download takes approximately three to four days, so contact me for a compressed archive first if possible. Place the processed tile files under assets/2mass/processed/all_sky/ for the commands below.

The included assets/sky_grid_5deg.csv is a synthetic stellar grid for geometry and regression tests. It can be used directly with --catalog assets/sky_grid_5deg.csv, without downloading survey data; see the test-grid example below.

Rendering examples

The examples below illustrate a few choices of sky field, spacetime, and camera settings. After building and preparing the catalog, adapt these commands to your own field of view, observer position, and rendering settings. See usage.md for the available controls and workflows.

Example: Summer Triangle in flat spacetime

This example renders a field around the Summer Triangle:

mkdir -p output/imgs
./build/Release/minkowski_sky \
  --all-sky-catalog assets/2mass/processed/all_sky \
  --look-ra-deg 296 --look-dec-deg 27 --fov-deg 72 \
  --width 3840 --height 2160 --exposure 1e12 \
  --output output/imgs/summer_triangle.png

4K reference image with exposure 1e12. Click to view at full resolution.

Angles are in degrees; --fov-deg is the horizontal field of view. Exposure is an adjustable display multiplier. Use --verbose for progress during long renders.

Example: Galactic-center field through Schwarzschild spacetime

This example uses a camera at radius 100 M to render the lensed Galactic-center field shown at the top of this page:

mkdir -p output/imgs
./build/Release/schwarzschild_sky \
  --all-sky-catalog assets/2mass/processed/all_sky \
  --width 3840 --height 2160 \
  --look-ra-deg 262.5 --look-dec-deg -30 --fov-deg 45 \
  --observer-radius 100 --exposure 1e13 \
  --coarse-cell-pixels 16 --refine-max-level 4 --refine-jacobian-min 0.2 \
  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 \
  --psf-relative-tail 1e-8 --psf-min-y 0 --max-cache-psf-flux 1e8 \
  --catalog-load-workers 4 \
  --output output/imgs/schwarzschild_galactic_center.png

This uses the reference image's rendering settings, including its --max-cache-psf-flux 1e8 preview approximation, which clips bright PSF wings to the cache radius. The original benchmark record preserves the command and terminal output; the command above omits the optional HDR export.

The Schwarzschild camera points toward the hole. 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. Both binaries provide a complete option list with --help.

Example: Synthetic test grid with mesh overlay

This example uses assets/sky_grid_5deg.csv to inspect lensing and adaptive mesh refinement in Schwarzschild spacetime. --draw-mesh overlays the final image-plane triangles.

mkdir -p output/imgs
./build/Release/schwarzschild_sky \
  --max-cache-psf-flux 1e8 \
  --catalog assets/sky_grid_5deg.csv \
  --refine-max-level 3 --refine-jacobian-min 0.2 \
  --width 3840 --height 2160 \
  --look-ra-deg 0.1 --look-dec-deg 0.1 --fov-deg 45 \
  --coarse-cell-pixels 32 \
  --observer-radius 100 --exposure 0.2 \
  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --draw-mesh \
  --output output/imgs/schwarzschild_test_grid.png

4K test-grid reference image. Click to view at full resolution.

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