Normal estimation
Surface normals are estimated as the smallest-eigenvalue direction of the covariance of
Result
| surfaces | plane (zero curvature), sphere (curvature 1.0), torus tube (curvature 2.857) |
| ground truth | analytic normals; error is the unsigned angle, so an unoriented PCA direction is scored fairly |
| swept | k from 4 to 2048, σ from 0 to 0.02, 2500 to 40000 points |
| estimators | PCA over k nearest · PCA over a fixed-radius ball · quadratic (jet) fit |
The finding
Three predictions from the geometry, three fitted exponents
Each regime has an exponent that follows from the geometry rather than from the data, so the run either reproduces it or contradicts it.
Figures
Elsewhere
Code and full results on GitHub
Every number is read from the file the run produced. github.com/hammasbuilds · kaggle.com/muhammadhammas13