Given a painting in one-point perspective, the method of finding the vanishing
point is well known. In addition, by finding the viewing distance, we can
determine where an observer can stand in relation to the painting to have the
greatest illusion of three-dimensionality. This talk will address whether that
determination can be made in Flatland. We will show how the inhabitants of a
two dimensional world could create and analyze works in perspective without the
benefit of intersecting lines. We will also show a Geometer's Sketchpad
application that illustrates the concepts of the talk.
Summary: This talk will cover the following items:
* A quick overview of the methods for finding the vanishing point and
viewing distance of a two-dimensional painting (illustrated with a work
in one-point perspective).
* A quick discussion of the underlying geometry.
* The introduction of the question: given a Flatland painting of an open
square room in one point perspective, how can we determine the vanishing
point and viewing distance?
* A method for finding optimal viewing locations: by carefully
parametrizing lines moving away from the picture plane, we can observe
that all points moving away from the picture plane reach the vanishing
point at the same time. Thus, we can use time to determine vanishing
points. A similar technique allows us to find viewing distances.
* A problem: depending on what general assumptions we make about where
the artist was standing, we find two possible optimal viewing locations
(unlike the two-dimensional case). With the stated problem, there is no
way to determine which one is correct, although that decision can be
made with more information about the painting.
If this talk is accepted, I will be using Geometer's Sketchpad to
illustrate the basic concepts and thus would like to use a computer
projector. This talk should be accessible to undergraduates. If
desired, a preprint of the paper is available at
http://personal.centenary.edu/~mschlat/flatpainting.pdf.