A construction method for discrete constant negative Gaussian curvature surfaces

TL;DR

This paper presents a new construction method for discrete surfaces with constant negative Gaussian curvature using a nonlinear d'Alembert formula and Birkhoff decomposition, including an algorithm and visualizations.

Contribution

It introduces a simple algorithm for Birkhoff decomposition within the nonlinear d'Alembert framework for discrete negative curvature surfaces.

Findings

Developed a simple Birkhoff decomposition algorithm

Generated visual figures of discrete negative curvature surfaces

Validated the construction method through graphical examples

Abstract

This article is an application of the author's paper about a construction method for discrete constant negative Gaussian curvature surfaces, the nonlinear d'Alembert formula. The heart of this formula is the Birkhoff decomposition, and we give a simple algorithm for the Birkhoff decomposition. As an application, we draw figures of discrete constant negative Gaussian curvature surfaces given by this method.