Towards an Aesthetic Invariant for Graph Drawing
Adamec, Jan and Nesetril, Jaroslav (2002) Towards an Aesthetic Invariant for Graph Drawing. In: Graph Drawing 9th International Symposium, GD 2001, September 23-26, 2001, Vienna, Austria , pp. 287-296 (Official URL: http://dx.doi.org/10.1007/3-540-45848-4_23).
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In this paper we do not address the question of visualization, of picture processing of visual information. The information for us is already processed and ,typically, it is of a very simple type such as drawing (however not necessary a graph drawing). What we would like to answer is how to formalize the fact that such a picture (drawing) is harmonious. Harmonious we mean in the sense of aesthetic pleasing. We prefer the word harmonious to aesthetic (which is probably more in common usage) as an aesthetic feeling is probably highly individual and we cannot have an ambition to define (or even approach that). We propose an approach which should capture some features of a harmonious picture by means of the notion Hereditary Fractional Length (HFL). This approach is based on the analysis of curves  which in turn goes back to Steinhaus and Poincaré. The hereditary approach is based on the dual approach (it may be viewed as an approach dual to the Piaget's analysis of intelligence), . The Hereditary Fractional Length is preserved by scaling and rotations and it is a very robust parameter which can be computed for a large class of drawings and pictures. This is an important feature as a perception of harmony (and aesthetic pleasure) is a robust feeling. Perhaps this parameter could aid in the hierarchical approach to graph visualization and graph drawing in particular.
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