Uniform convergence of discrete curvatures from nets of curvature lines

TL;DR

This paper proves that discrete curvatures derived from nets of curvature lines on smooth surfaces uniformly converge to the true principal curvatures, with explicit error bounds depending on surface properties and net regularity.

Contribution

It establishes the uniform convergence of discrete curvatures from curvature line nets to smooth principal curvatures, providing explicit error bounds based on surface and net properties.

Findings

Discrete curvatures converge uniformly to principal curvatures.

Explicit error bounds depend on surface smoothness and net regularity.

Results apply to nets of curvature lines on smooth surfaces.

Abstract

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.