Curvature measures for discrete surfaces

It has been recently discovered that a certain class of nanocarbon materials has geometrical properties related to the geometry of discrete surfaces with a pre-constant discrete curvature, based on a discrete surface theory for trivalent graphs ...

Examples of constant principal curvature surfaces in R 3 on a full 3-ary oriented tree.

• Full 3-ary oriented trees are investigated as a covering of closed trivalent graphs.
• A discrete analogue of the principal directions is defined.
• Several discrete constant principal curvature surfaces are demonstrated.

Intrinsic curvature flows can be used to design Riemannian metrics by prescribed curvatures. This chapter presents three discrete curvature flow methods that are recently introduced into the engineering fields: the discrete Ricci flow and discrete ...

The curvatures of a smooth curve or surface are local measures of its shape. Here we consider analogous measures for discrete curves and surfaces, meaning polygonal curves and triangulated polyhedral surfaces. We find that the most useful analogs are ...