Perspective with Six Vanishing Points - an Alternative Method


  • Ágnes Urbin

    Department of Mechatronics, Optics and Mechanical Engineering Informatics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics

  • Brigitta Szilágyi

    Department of Geometry, Faculty of Natural Sciences, Budapest University of Technology and Economics


The purpose of this paper is to describe perspective with six vanishing points. The line opened by axonometry and continued by one, two, three vanishing points and spherical perspectives, one became complete with the sixth vanishing point. Linear perspectives are often used, well known systems. Introducing new vanishing points doubles the represented part of space. The question of representing the half-space, hence the definition of the first five vanishing points can be found in literature. However, there was no useful solution for the representation of the whole space for a long time. This paper introduces a new definition of the sixth vanishing point that resulted a well applicable system. A short historical introduction looks at some of the interactions between mathematics and arts of western culture. Afterwards we formulate the new alternative perspective and give some methods of construction for notable lines and planes. Finally we write about possible applications.


linear perspective, curvilinear perspective, vanishing point, space representation

Published Online


How to Cite

Urbin, Ágnes, Szilágyi, B. “Perspective with Six Vanishing Points - an Alternative Method”, Periodica Polytechnica Civil Engineering, 59(4), pp. 591–601, 2015.



Research Article