Perspective as a Symmetry Transformation

• Published in: Nexus network journal Vol. 5; no. 1; pp. 9 - 21
• Main Author: Darvas, György
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.04.2003
• Subjects: Artists; Origins; Projection; Representations; Symmetry; Transformations
• ISSN: 1590-5896; 1522-4600; 1522-4600
• DOI: 10.1007/s00004-002-0002-8

From the quattrocento to the end of the nineteenth century perspective has been the main tool of artists aiming to paint a naturalistic representation of our environment. In painters' perspective we find a combination of affine projection and similitude. We recognise the original object in the painting because perspective is a symmetry transformation preserving certain features. The subject of the transformation, in the case of perspectival representation, is visible reality, and the transformed object is the artwork. The application of symmetry transformations developed from the origin of perspective through the centuries to the present day. The single vanishing point could be moved (translated), and even doubled, developments that made it possible to represent an object from different points of view. In the twentieth century, the application of topological symmetry combined with similitude resulted in new ways of seeing, new tools for artists such as cubists and futurists.[PUBLICATION ABSTRACT]