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Metric characters of spherical perspective. (English) Zbl 1057.51018

Pretorius, Johann, Proceedings of the 9th international conference on geometry and graphics, Johannesburg, South Africa, July 28–31, 2000. Vol. 1. Johannesburg: Rand Afrikaans University (ISBN 0-620-26255-9/hbk). 57-62 (2000).
Summary: The graphical constructive models which are applied to derive the solutionts of such metric problems as the measurements and perpendicularities through the spherical perspective, are introduced in this paper. The spherical perspective images are developed through a double projection consisting of the gonomonic projection and stereographic projection. The present spherical image is a mode of the Fish-Eye perspective which is called the true perspective of an object. One of the characteristic features of the spherical perspective is that any line in space is transformed into a part of circular arc limited by two vanishing points. Because the images are constructed on the undevelopable surface of sphere, the perspective is curvilinear and the solutions of the metric problems become difficult than those are solved in linear perspective. The curvilinear perspective is generally used to avoid the wrongs and distortion that may be caused by linear perspective. The geometric analysis of the metric problems on the curvilinear perspective is very useful in photogrametry when the photograph is picked up via a camera of spherical lens. In this case, the spherical image resembles a photograph like to that can be carried out by camera of the sense of wide-angle lens. The inverse projection is the main our device for developing the graphical constructions which are used to facilitate the complexity of the metric characters of the spherical perspective. The inverse projection of the spherical perspective is utilized to get the pectoral description of the objects that are used directly to assess the proposed measurements.
For the entire collection see [Zbl 1005.00036].

MSC:

51N05 Descriptive geometry
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