Original scientific paper

Hyperbolic Perspective I

Ivanka Babić ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia
Branko Kučinić ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia

Abstract

In the hyperbolic space the central projection is considered, adjusted to the perspective, by defining the image plane and centre of projection, and the reference plane perpendicular to the image plane. This is the analogy of the so called piercing point method in the Euclidean space supplemented by indefinitely distant elements. The analogue of the method of Monge in H3-space realised on M-model enables necessary constructive procedures. The position and metric relations associated with the reference plane are also worked out thoroughly. Thus, the whole procedure is prepared to be applied.
Basic differences from the perspective of Euclidean space are: h-horizon is hyperbola, there is avoidable hyperbola instead of avoidable line, and the pencils of parallel lines in the plane (1 can be projected into the elliptic, parabolic and hyperbolic pencils (Theorem 3).

Keywords

hyperbolic space; H-model; central projection; perspective; piercing point method

Hrčak ID:

166349

URI

https://hrcak.srce.hr/166349

Publication date:

20.1.1998.

Article data in other languages: croatian german

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