Ruler, compass, and nail: constructing a total spherical perspective

Araújo, António

http://hdl.handle.net/10400.2/7853

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Authors

Araújo, António

Abstract(s)

We obtain a construction of a total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360-degree field of view. Since the 1960s, several generalizations of this perspective have been proposed, but they were either works of a computational nature, inadequate for drawing with simple instruments, or lacked a general method for solving all vanishing points. We establish a general setup for anamorphosis and central perspective, define the total spherical perspective within this framework, study its topology, and show how to solve it with simple instruments. We consider its uses both in freehand drawing and in computer visualization, and its relation with the problem of reflection on a sphere.

Keywords

Art and Mathematics Perspective Anamorphosis Fisheye Azimuthal equidistant 6-Point perspective 5-Point perspective Drawing Descriptive geometry Geometry Spherical perspective Curvilinear perspective Computer graphics

URI

http://hdl.handle.net/10400.2/7853

Citation

António Araújo - Ruler, compass, and nail: constructing a total spherical perspective. "Journal of Mathematics and the Arts" [Em linha]. ISSN 1751-3472 (Print) 1751-3480 (Online). 12, nº 2, 3 (2018), 22 p.