If you warp a Euclidean plane like a Pringle’s potato chip, giving it hyperbolic curves, you get an idea of hyperbolic geometry. We recognize this geometry when we look at buildings, desks or coffee cups. There are triangles, rectangles, circles, spheres, cubes, etc. The basics are: Points, straight lines, angles, and planes that are flat and extend infinitely. Some 2,300 years ago, mathematician Euclid of Alexandria developed the geometry commonly taught today in high school. That’s fiction, but it makes for a nice bridge to hyperbolic geometry and how this new VR program takes viewers hyperbolic from the much more customary Euclidean geometry experience of everyday life. Meanwhile, inside the ship, everything is shaped and moves “normally.” Sci-fi fans may remember hyperspace, created when “warp drive” engines curve spacetime so that the Starship Enterprise can travel at multiples of the speed of light. The researchers have posted papers on the math and perceptual considerations behind their work on. “The virtual reality takes something that would normally live in a set of equations, and makes something you can interact with.” “Visualizations can help to prove theorems that are purely abstract, and physicists want to get an intuition for what’s going on,” said Matsumoto, an assistant professor in Georgia Tech’s School of Physics. Segerman and Matsumoto collaborated on the hyperbolic virtual reality experience with a collective of mathematician-artists called eleVR to make the work of the geometry experts easier and more productive. That weirdness can give the non-mathematician an idea of how picturing non-Euclidean geometries mentally can strain even the minds of mathematicians and physicists. photo of Henry Segerman (OSU).īut be a little careful walking around the 3D version, as the hyperbolic space doesn’t have a floor to provide visual balance orientation, and turning corners is very different from in everyday life. Sabetta Matsumoto, physicist and applied mathematician at Georgia Tech’s School of Physics. “It never stops, just keeps going, and you never get to the back side of it.” He slid around a diamond-like shape in VR hyperbolic space, describing it. “If you walk around in this space, things that started out horizontal and vertical become twisted and weird,” Segerman said, as he donned a VR headset. When Matsumoto or her collaborator, mathematician Henry Segermanfrom Oklahoma State University, do that, they’re actually exploring particular geometric nooks. Splashed in color, the virtual space’s graphics can seduce even the most math-phobic mind to roam, crawl or slither about. The program was co-created by Sabetta Matsumoto, a physicist and applied mathematician at the Georgia Institute of Technology as a visual aid to researchers exploring geometries that deviate from the everyday norm. Math just met “warp drive” in a virtual reality headset to transport anyone who dons the visor to a reality twisted by hyperbolic geometry. Furthermore, our method is not restricted to static scenes and provides an acceleration structure for post-processing passes.Hold tight for a psychedelic trip to hyperbolic space, where the floor drops out from beneath your feet. Evaluated against regular rendering as well as established foveated rendering methods, our approach shows increased performance in both cases. Hence, the average primitive processing and shading costs are lowered dramatically. The foveal region, as well as areas with low confidence values, are redrawn efficiently, as the confidence value allows for the delicate regulation of hierarchical geometry and pixel culling. Artefacts and disocclusions caused by this reprojection are detected and re-evaluated according to a confidence value that is determined by a newly introduced formalized perception-based metric, referred to as confidence function. Our method comprises recycling pixels in the periphery by spatio-temporally reprojecting them from previous frames. To this end, we propose a novel foveated rendering method for virtual reality headsets with integrated eye tracking hardware. Eye tracking-based foveated rendering presents an opportunity to strongly increase performance without loss of perceived visual quality. Rendering in real time for virtual reality headsets with high user immersion is challenging due to strict framerate constraints as well as due to a low tolerance for artefacts.
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