# Mathematical Progress in Expressive Image Synthesis IIIA Construction Method for Discrete Constant Negative Gaussian Curvature Surfaces

Mathematical Progress in Expressive Image Synthesis III: A Construction Method for Discrete... [This article is an application of the author’s paper (Kobayashi, Nonlinear d’Alembert formula for discrete pseudospherical surfaces, 2015, [9]) 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 in Lemma 3.1. As an application, we draw figures of discrete constant negative Gaussian curvature surfaces given by this method (Figs. 1 and 2).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Mathematical Progress in Expressive Image Synthesis IIIA Construction Method for Discrete Constant Negative Gaussian Curvature Surfaces

Part of the Mathematics for Industry Book Series (volume 24)
Editors: Dobashi, Yoshinori; Ochiai, Hiroyuki
12 pages

/lp/springer-journals/mathematical-progress-in-expressive-image-synthesis-iii-a-construction-4uaASpx2is
Publisher
Springer Singapore
ISBN
978-981-10-1075-0
Pages
21 –33
DOI
10.1007/978-981-10-1076-7_3
Publisher site
See Chapter on Publisher Site

### Abstract

[This article is an application of the author’s paper (Kobayashi, Nonlinear d’Alembert formula for discrete pseudospherical surfaces, 2015, [9]) 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 in Lemma 3.1. As an application, we draw figures of discrete constant negative Gaussian curvature surfaces given by this method (Figs. 1 and 2).]

Published: May 22, 2016

Keywords: Discrete differential geometry; Pseudospherical surface; Loop groups; Integrable systems