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Journal for Geometry and Graphics 18 (2014), No. 2, 225--238
Copyright Heldermann Verlag 2014

Perspective Concepts - Exploring Seeing and Representation of Space

Cornelie Leopold
Descriptive Geometry and Perspective, Faculty of Architecture, Technical University of Kaiserslautern, Pfaffenbergstr. 95, 67663 Kaiserslautern, Germany

There had been a long tradition in analyzing the human seeing and conditions of perception in order to represent space and spatial objects similar to the way, we are seeing. Euclid tried already to describe the characteristics of perspective in his 'Optics'. Later in the Renaissance period Alberti referred to the ideas of Euclid and explained linear perspective as the section of the pyramid of vision. He described the image as practically received by the device 'velum', the image plane, set between the eye and the object to be represented. There had been various seeing or perspective machines, which are able to represent the concept of perspective as a practical way to produce images of spatial objects according to the process of seeing.
Our students of architecture rebuilt some of these machines. The approach to perspective by the seeing machines explains the origin of the perspective concept from simulating the seeing process. The knowledge of optics and physiology of the eye had been part of the foundations of perspective. In this tradition can be analyzed the work of Guido Hauck, who tried to develop another concept of perspective, the primarily by Hermann von Helmholtz.
Following the geometric background of perspective we will observe the development of the comprehension of vanishing points. The clear concept of points of infinity and vanishing points initialized the development of projective geometry. Only then it was possible to develop the representation method 'Relief Perspective' systematically, where half space is projected to a spatial layer. We will ask and discuss, how the comprehension and concept of perspective had been developed in geometry and what had been the influences between theory and practice from various disciplines like geometry, art, architecture, physiology and perception theory.

Keywords: Perspective, space, representation, seeing, perspective machine, relief perspective.

MSC: 51N05; 01A99, 97G80

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