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Since nobody called it out in the comments, this “new way” to show 3D Gaussian splats is a basic 19th century construction, studied by Jakob Steiner and others, called a “sphere inversion” or “Möbius transformation”: https://en.wikipedia.org/wiki/Inversive_geometry It looks good because it is an example of a so-called conformal map, which preserves angles, but distorts scales. However, when you look at something up close, it doesn't really matter what its absolute scale is (whereas angular distortion is far more noticeable). Conformal maps, namely the 16th century Mercator projection (old as it is) remains the projection of choice in Google Maps and other mapping tools, since it is the unique map that (i) preserves angles, and (ii) keeps north pointing "up" everywhere on the globe. The 3DGS scheme shown here is just bumping up the usual approach up one dimension: apply a conformal projection; keep the "up" direction fixed. The specific choice of conformal maps (inversions in the sphere) are in fact the only choice available in 3D, due to Liouville's theorem on conformal mappings. [Orange illustration below is from my PhD thesis on conformal geometry: https://www.cs.cmu.edu/~kmcrane/Projects/ConformalGeometryProcessing/thesis.pdf]
3D Gaussian Splattingの新しい見せ方を作りました。その名も Inversphere. 2Dのリトルプラネットと違い、空間ごと球面反転しています。ガラス玉に入れる従来の見せ方は球で「切り取る」のに対して、これは球の中へ「折り込む」ので360度の景色が無限遠まで立体で入っています。 #3DGS