Handbook of mathematics (3rd ed.)
Handbook of mathematics (3rd ed.)
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Realistic human face rendering for "The Matrix Reloaded"
ACM SIGGRAPH 2003 Sketches & Applications
IEEE Transactions on Visualization and Computer Graphics
Visualization for the Physical Sciences
Computer Graphics Forum
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We present a methodical new approach to visualize the aspects of general relativity from a self-centered perspective. We focus on the visualization of the Gödel universe, which is an exact solution to Einstein's field equations of general relativity. This model provides astounding features such as the existence of an optical horizon and the possibility of time travel. Although we know that our universe is not of Gödel type, we can -- using this solution to Einstein's equations -- visualize and understand the effects resulting from the theory of relativity, which itself has been verified on the large scale in numerous experiments over the last century. We derive the analytical solution to the geodesic equations of Gödel's universe for special initial conditions. Along with programmable graphics hardware we achieve a tremendous speedup for the visualization of general relativity. This enables us to interactively explore the physical aspects and optical effects of Gödel's universe. We also demonstrate how the analytical solution enables dynamic lighting with local illumination models. Our implementation is tailored for Gödel's universe and five orders of magnitude faster than previous approaches. It can be adapted to manifolds for which an analytical expression of the propagation of light is available.