Special cases of the discretization principle via permutability

TL;DR

This paper explores how permutability of transformations on smooth surfaces can generate discrete surfaces that preserve specific geometric properties, bridging continuous and discrete differential geometry.

Contribution

It introduces a method to derive discrete surfaces with preserved characteristics from smooth surfaces using permutability of transformations.

Findings

Discrete surfaces with continuous properties are constructed via permutability.

The approach links smooth and discrete differential geometry.

New classes of discrete surfaces are identified.

Abstract

We show how permutability of transforms of smooth surfaces with particular characteristics leads to discrete surfaces with discrete analogues of the same characteristics.