1997 Perspective Systems Drawings

One-, two-, and three-point perspective projection systems,
developed during the Italian Renaissance to portray deep space,
are commonly used to describe the everyday experience of
our walk-around world. This geometric system is embedded in our
photographic lenses to make the pictures seem "right". We take
this system to be a true and acurate description of three-space.

In the drawings below, made only with points and
lines, this perspective system is altered to show
the possibility of describing three dimensional "spaces"
that are not the one we live in. But while we cannot imagine
walking around in these spaces, we can imagine flying or
somehow navigating through them.

The above drawing uses two points to which all the diagonal lines
receed to the imaginary horizon "line". This is a "normal" perspective
grid used to describe everyday walk-around space. But note that there are
areas that don't really describe the third dimension. Below the central
horizontal line, the space is not recessional, but frontal and flat.
Also, along the left and right broaders, the space stretches out to either
side in an inconsistant manner. Only a small area in the top, center
describes recessional space.

In a normal space grid, the regular units of space are measured in the
horzontal lines. Here, the curve that swings down from the top to the lower
left corner and the vertical line controls the spacing of the recessional lines.
And these in turn set up the space that we see. As the curved line descends and
move away from the vertical lines, the spacial grid opens up to larger and larger
units of space. We may describe this as the horizon gone vertical and curved.

This variation of one point perspective space doesn't read as a normal
perspective space. Only the small squares at each corner of this grid seem
undistorted. The ambiguity of the grid may be read as either contracting or as
receeding space.

In this drawing the one point perspective grid seems to radiate from the left.

Resume 1995 The Pythagorean Theorem 1992 In the Company of Men 1990 The Head Game 1975 Inverted Frames 1970 Perspective Grids