Explore the renderer and the geometric part of the tracker using small synthetic scenes.
Try this Lower opacity and click the range image. The rear splat contributes more to each ray.
| Hit order | Range d | α = oG | Weight w |
|---|
wᵢ = αᵢ ∏ⱼ₍ⱼ<ᵢ₎ (1 − αⱼ). Dacc is unnormalised; D/O is undefined without a hit.
rᵢ = nᵢᵀ(Rqᵢ + t − pᵢ). Robust Gauss–Newton recomputes matches each step. *Truth is used only to evaluate error.
Rendering: rotate and resize the front Gaussian, lower its opacity, then select a ray in the image. Compare each intersection's range, opacity, and front-to-back weight. Switch between accumulated range, opacity-normalised expected range, and opacity.
Registration: run the room-corner case, then switch to a corridor. The geometric residual can become very small while motion along the corridor remains unobservable. Increase the synthetic noise along surface normals to see an actual residual floor.
Scope: this is an explanatory simulation. It uses three planar 3D Gaussians and per-ray sorting, not the paper's GPU tile rasteriser. Its registration lab implements only the geometric point-to-line SE(2) analogue. Splat-LOAM uses SE(3), rendered-keyframe geometry, and a joint geometric plus range-image warping objective; Gaussian map optimisation is a separate operation. The repository's optional median-depth mixture is omitted.