Outline
Voronoi Paintings
Article published in the Bulletin of the Puig Adam Society of Mathematics Teachers, vol. 112. Oct. 2021, pp. 32–53.
Looking at the paintings through Voronoi's eyes
Rafael Losada Liste
GeoGebra Institute of Cantabria
rafael.losada@gmail.com
Tomás Recio
Department of Industrial Engineering, Higher Technical School, Antonio de Nebrija University
trecio@nebrija.es
Abstract
We propose a protocol for the analysis of paintings (classic, modern, figurative or abstract) over GeoGebra, enhancing the perception of some of the characteristics (distribution of focal zones) of the artworks through the computation –using the dynamic color technique– of the Voronoi diagram of a collection of specific sites in the paintings.
Introduction
The artistic aspect of the Voronoi diagram (and its dual, the Delaunay triangulation) is well known, as the underlying geometric scheme in multiple works of art (see a simple description of this concept in Section 1 of this article and also, for a more detailed introduction, see [5, 14] and the references therein). Conversely, we believe that the role of the Voronoi diagram as a tool for the analysis of works of art has not been fully explored. This is our aim here.
The objective is to propose the recognition of certain characteristics of pictorial works: the distribution of focal zones in a painting (a concept introduced in sections 2, 4, and 5), with the use of dynamic color technique (briefly described in section 3 and, interactively, in the references mentioned there, as well as in [6] for a general introduction) applied to an image of such works located in a graphic window of the GeoGebra program (http://geogebra.org).
This protocol: calculation of the Voronoi diagram of focal zones using the dynamic color technique in GeoGebra, is applied in section 6 to different classical (The Creation of Adam, Las Meninas) or modern (Cristina's World, The Bedroom in Arles), figurative or abstract (Suprematist Painting) paintings, by classical (Michelangelo, Velázquez, Van Gogh...) or contemporary (Espejo Velasco) authors.
Finally, Section 7, Conclusions, mathematically argues (uniqueness of the set of objects that produce a certain Voronoi diagram) the value of the information obtained through this procedure, trying to answer the question: To what extent does the Voronoi diagram of a painting provide information about the silhouettes of its positive space? concluding that the Voronoi diagram adequately schematizes a significant part of the distribution of focal zones in a painting.
This is the interactive version of the article published in the Puig Adam Society Bulletin. It includes extensive Annexes with instructions so that the reader can apply, on their own and to the works they consider appropriate, the technique developed in this article, as well as an already configured application [13] for this purpose.
