We implement an efficient pipeline to create realistic visual renders of Schwarzschild black holes with negligible charge and zero angular momentum while modeling various physical effects on the structure and behavior of the black hole.

Our approach augments the traditional raytracing pipeline by utilizing Euler integration to map out the path of light traveling through the immensely strong gravitational field induced by the presence of black holes. Additionally,  we simulate what an ideal black body's accretion disk would look like by calculating the density and temperature of matter at every intersection point and converting that to the color and relative intensity of emitted thermal radiation. Furthermore, we model the effects of redshifting, which is the result of light being doppler-shifted due to the expansion of space itself.

We further improve upon the quality and speed of the renders by utilizing various computer graphics methods such as supersampling, anti-aliasing, adaptive sampling, bezier curve interpolation, texture mapping, and most importantly Euler integration.

We iterate over each pixel in the image and trace a ray emitted from the camera's location. Because of the black hole's strong gravitational field, we simulate the nonlinear path of light rays over a certain number of steps through Euler Integration. At each step, we update the location of the photon using the prior velocity and position, along with calculating the force acting on the particle at that point in space which is then used to update the velocity. We define the step size and total ray depth before the start of the render and use the last calculated velocity at the end of the ray depth in order to continue the ray and intersect with the background texture. Due to this process, rays will curve as they move through time, which is an effect commonly referred to as gravitational lensing where gravitational forces create a so-called lens in space, spacially distorting the light incident to it. The region around the black hole with the most extreme distortion is called the Einstein ring and is actually a superimposed circular image of a point far away in space behind the black hole.

As our scene essentially only contains 2 objects, the black hole, and accretion disk, we only have to do 2 intersection tests at each point along the ray integration. At each intersection, we calculate the light being emitted at that point in space in order to integrate over the ray's path and compute the total amount of light being received on the camera sensor. If the ray is intersecting the event horizon, it has entered the black hole and has no chance of exiting the gravitational pull thus is displayed as pure black from that point onwards. If it is crossing the accretion disk, we can calculate the color according to what material style we have set. If we are using blackbody radiation, we can calculate the temperature and then map that temperature to its corresponding color. If we are using texture mapping, we calculate the current point's texture coordinates and map it to a given texture. Additionally, we implemented an optional redshift, which shifts the wavelength of the particles toward the red end of the spectrum due to their velocity.

The initial challenge we encountered was with understanding the technical details in the paper we used as a reference. The lack of a physics background of our team meant it took a considerable amount of time to parse through all the dense information and fully understand the key parts of the paper while leaving behind the more complicated and unnecessary parts. We additionally used the blog post Raytracing a Black Hole as it did a great job of simply explaining the overall concepts to the point where we were able to use that as a starting point for our implementation

Other problems with the quality and speed of our renders are addressed in the above section.

Additionally, we encountered some issues in implementing the GUI. To start off with, we knew we wanted something with various sliders and input fields on the screen that allows the user to change different simulation properties. However, adding the NanoGui library to our existing code proved to be quite difficult, as there were some dependency issues. Then, we decided to use the ImGui library instead. However, there were also some issues here when trying to add it into the main window, so we instead had to build visual debugging code because that was the section that was already using the ImGui library.

Overall, we were able to get a strong grasp of the physical attributes and properties of black holes along with a keen understanding of how to create high-quality visual renders of them. Throughout the process, integrating various computer graphics algorithms and tools in order to improve the quality and efficiency of our pipeline allowed us to appreciate how these concepts are implemented and used in real life in ways which we would have not necessarily previously imagined.