A Construction of the Total Spherical Perspective in Ruler, Compass and Nail
Abstract
We obtain a construction of the 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
Cite
@article{arxiv.1511.02969,
title = {A Construction of the Total Spherical Perspective in Ruler, Compass and Nail},
author = {António Araújo},
journal= {arXiv preprint arXiv:1511.02969},
year = {2018}
}
Comments
Major revision of the 2015 version, with many changes, including and a new title. Main results unaltered, but important changes to the definitions, to notation and organization, and correction of minor errors. Illustrations revised/added, including a major illustration of spherical perspective on page 22. Added references to several works previously unknown. 25 pages, 12 figures