Ruler, compass, and nail: constructing a total spherical perspective. Issue 2 (3rd July 2018)

• Record Type: Journal Article
• Authors: Araújo, António Bandeira
• Is Part Of: Journal of mathematics and the arts. Volume 12:Issue 2/3(2018)
• Page Start: 144
• Page End: 169
• Publication Date: 2018-07-03
• Subjects: Visual arts -- geometry -- anamorphosis -- spherical perspective -- ruler and compass; 51N05 -- 68U05; Arts -- Mathematics -- Periodicals; 700.151
• DOI: 10.1080/17513472.2018.1469378
• Languages: English
• ISSNs: 1751-3472

Abstract

ABSTRACT: We describe a construction of a total spherical perspective using a 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 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 to the problem of reflection on a sphere. GRAPHICAL ABSTRACT: