Simulation of Perspective by Nonlinear Transformations

Abstract

A feature of the brain processing the visualization of objects is such that objects that are much farther away from the eye look smaller than closer objects to the eye. We show that a family of nonlinear transformations, also to be called compactifications, simulate qualitatively this property of keeping objects in perspective. These transformations project objects in a plane on a spherical shell. It is shown then that an observer located at a fixed point on the axis of the sphere visualizes the projected objects on the sphere in perspective. Namely, that objects that are farther away from the observation point seem smaller. Examples are provided. This is a departure from the traditional approaches using linearity and projections of objects from one plane into another plane.

Keywords:

• perspective
• compactification
• nonlinear transformations
• sphere
• infinity

AMS Subject Classification:

• 14M27