VoxelKei
@VoxelKei • 27,974 subscribers
VRでいろいろやってます。 作ったもの: ProjectJAPANELAND, 日本列島VR, 日本列島360, HoleLenz, HoleLenz Gate, SpatialGate, NailCanvasVR, HandParticle. TONEVOKのボク
Shorts
Videos
Thank you for taking the time to write this up — and for the pointer to your thesis; that figure is beautiful. You're right that classical sphere inversion is exactly the starting point: the feature is named "Sphere Inversion" in the tool for that reason. "Inversphere" is the name of the resulting object, not a claim of new mathematics. I should say up front that I'm not a mathematician, so please correct me if I get any of this wrong. My motivation was visual rather than mathematical: with the classical map, the entire far field piles up into a dense blob at the center (10× farther ⇒ 10× closer), and I simply wanted to control that density to balance the look of the finished object. To do that, the radial profile is generalized to f(r) = R·h(v), where v = (R/r − R/D)/(1 − R/D) is a normalized inverted depth and h is a μ-law log compression, h(v) = ln(1+μv)/ln(1+μ). Classical R²/r is the special case μ = 0, D = ∞. The footage here uses μ > 0, so — as far as I can tell — the map shown is outside the conformal family: the tangential scale f/r and radial scale |f′| agree only in the classical limit. If I understand Liouville's theorem correctly, this trade-off was unavoidable: staying conformal in 3D leaves no freedom to adjust the density, so angle preservation is given up deliberately in exchange for control over it. With μ > 0, mid-field depth below the sphere surface grows like log r, so distant scenery layers logarithmically inside the sphere. The 3DGS side also needed some care: each splat's covariance is carried by the Jacobian J = s·I + (f′−s)nnᵀ, depth sorting has to be re-keyed because inversion reverses the radial order, and the on/off transition is a linear blend whose Jacobian is exactly mix(I, J, t). Thanks again for taking the time — an expert eye on this is very welcome.
VoxelKei30,252 views • 6 days ago
Gaussian Splattingと制作中のSplats Voxelizerを使って「手を近づけた場所だけ現実が現れるボクセル体」が産まれた。
VoxelKei474,208 views • 11 months ago
制作中のVRChat「Spatialography」ワールドの新しい試作。額縁に入った青森県奥入瀬渓流の雲井の滝のGaussian Splatting、の中に入れるようになりました。
VoxelKei132,221 views • 1 year ago
