A Real-time High-quality Black Hole Shader

Eric Bruneton, 2020

A black hole near Orion, with 2 opposite images of a star around it [demo].

We propose a real-time method to render high-quality images of a non-rotating black hole with an accretion disc and background stars. Our method is based on beam tracing, but uses precomputed tables to find the intersections of each curved light beam with the scene in constant time per pixel. It also uses a specific texture filtering scheme to integrate the contribution of the light sources to each beam.

Gallery

Here are some images obtained with our method.

The Large Magellanic Cloud forming an Einstein ring around the black hole [demo].

Near the speed of light lengths are contracted in the direction of motion (from left to right), colors are blue-shifted ahead and red-shifted behind (due to relativistic Doppler effects) and their intensity increases ahead and decreases behind (due to relativistic beaming effects) [demo].

Same conditions as above, but with an accretion disc too [demo].

A static observer represented with a rocket. To keep its position fixed instead of falling into the black hole, the rocket engine must be on [demo].

A freely falling observer orbiting around the black hole, represented with a rocket. By definition of free fall, the rocket engine must be off [demo].

A demo illustrating our method is available online. To recompile it and precompute all the data from the source code, clone the git repository, init the submodules, and type make (this requires GNU make, the GNU C++ compiler, the sed, curl and gunzip command line tools, and the libcurlpp-dev, libpng-dev, zlib1g-dev libraries).

Structure

The generic part does not depend on the rest of the code, and is divided in two subparts: preprocessing and rendering. The preprocessing, in black_hole/preprocess/, implements the Precompute procedure in Algorithm 1 of our model. The rendering part, in the black_hole/*.glsl files, provides a library of GLSL functions implementing the TraceRay procedure in Algorithm 1 of our model, but also our custom texture filtering method for stars, our accretion disc shading model, the gravitational lensing effect, and the relativistic Doppler and beaming effects.

The demo is also divided in a preprocessing part and a rendering part. The preprocessing code is used to generate

• parameters for the bloom shader effect (in bloom/),
• textures for the stars, the Doppler effect, etc (in gaia_sky_map/ and color_maps/),
• a 3D model for the rocket (in rocket/).

The rendering part, in black_hole/demo/, is a WebGL 2 application organized into several UI components interacting via a shared model:

• The model/ component manages the state of the system, and notifies its listeners when this state changes. In particular, it updates the camera position along its orbit, and the camera Lorentz transform, as described in Appendix C of our model.
• The orbit_panel/ component presents a read-only, partial view of this state in the top-right panel of the UI.
• The settings_panel/ component presents another part of this state, in the top-left panel of the UI. This component allows the user to modify some state parameters via checkboxes and range sliders.
• The url_params/ component presents the state as URL parameters, so that the current view can be shared via URLs.
• Finally, the camera_view/ component renders the view from the camera with WebGL 2, by using a small wrapper around our generic black hole rendering functions (and the rocket/ component to render the 3D rocket).

The documentation of the generic black hole shader functions consists of a general overview of our method and algorithms, and a detailed description of their implementation:

• black_hole/
  • preprocess/
    • definitions.h
    • functions.h
    • functions.cc
    • functions_test.cc
    • preprocess_main.cc
  • definitions.glsl
  • functions.glsl
  • model.glsl

The demo code is simpler and is documented with inline comments.