Flat-Sphere Perspective

Abstract

In this paper, a new system of visual representation, Flat-Sphere Perspective, is developed. With Flat-Sphere Perspective, an image of the entire visual space around an observer can be represented on a flat surface. The system integrates in a coherent and continuous image the many instantaneous views a human observer perceives as he turns his head.

This new perspective system furnishes the contemporary artist with a new representational format that corresponds more closely to the geometrical and perceptual principles governing visual perception than any other system hitherto devised.


I. Introduction 

For the last 500 years, human beings have been creating two-dimensional representations of the visual three-dimensional world guided by a system of representation called Central Convergent Perspective (CCP).

Developed primarily during the Renaissance, CCP has come to us as a set of concepts and principles which provide:

  1. A geometrical analysis of the human visual field.
  2. A way to represent that visual field on a surface.

The considerable success of CCP in representing the visual world is evident in the fact that many pictures constructed with CCP can actually fool the eye of an observer.


Shortcomings of CCP

Although the merits and usefulness of CCP as a system of visual representation are undeniable, it has become increasingly clear that the system is both limited and flawed.

In this paper, a new system of perspective—Flat-Sphere Perspective—will be developed which, it will be argued, captures more adequately than CCP the range and geometrical nature of the visual world.


The Development of Flat-Sphere Perspective

In the first section of this paper, some of the shortcomings of CCP are briefly examined.

In the following sections:

  • Spherical Perspective will be developed.
  • Then Flat-Sphere Perspective will be introduced as a system that overcomes CCP’s flaws.

Toward Polar Perspective

In a second study, Flat-Sphere Perspective will be refined and developed further into Polar Perspective.

With Polar Perspective, it is possible to create perspective images of more than three dimensions, which are perfectly coherent and non-ambiguous.

Read the full Publication here:

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In Memoriam
Fernando Casas March 25, 1946 - May 28, 2026

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