Nonlinear Projections - Transformations and Projections in Computer Graphics - page 178

Figure 4.32: Cubic Panoramic Perspective (color version on page 239).
(Courtesy of Professor Shinji Araya, Fukuoka Institute of Technology.)
4.8 Six-Point Perspective
Chapter 3 introduces the concept of n -point perspective, where n can be 1, 2, or 3. This
section extends the term “ n -point” and discusses n values up to 6. The discussion is
based on the work of and terms coined by Dick Termes, who also created the images,
art, and grids in this section.
Figure 3.14 shows Alberti's method of traversals in one-point perspective. The
important feature of this figure for our present discussion is the converging grid. Certain
lines in this grid converge to a vanishing point and thereby turn the grid into an aid
to the artist. Such a one-point grid becomes a tool that helps to draw any image in
one-point perspective. Section 3.3 discusses perspective in curved objects and employs
a similar grid (Figure Ans.6).
Figure 4.33 shows grids for 1, 2, and 3 vanishing points and artistic drawings based
on them. It is natural to accept these drawings. They look familiar and don't seem
distorted or unusual (although the viewpoint in some of them may be unusual). They
are drawn in linear perspective.
In contrast, drawings based on similar grids with more than three vanishing points
are distorted. They belong in the realm of nonlinear projections. Figure 4.34 shows
grids for four and five vanishing points, and it is immediately clear that they must