Introduction
How do the three spatial dimensions of the visual world project (or map) on a surface (or picture)?
Imagine a structure of three wooden poles that intersect each other perpendicularly. Each pole represents one of the three spatial dimensions of the world. The person interested in perspective wants to find out what kind of image these three poles create on the visual field of a human observer.
Classical Perspective
Classical perspective (also called central convergence perspective), developed mainly during the Renaissance, gives one explanation.
According to classical perspective, the visual image that an observer has in his visual field at a given moment is identical to the image that would be created on a flat window placed between the observer and the object observed. This setup, illustrated in Fig. 1a, is classical perspective’s model of visual perception.
This model likens the visual field of the observer to a flat surface called the picture plane. For the last 400 years, classical perspective has allowed the artist to create remarkably “realistic” images of the world that, when placed in appropriate circumstances, were able to fool the eye.
Examining Fig. 1a, we can see that the three spatial dimensions of the visual world (axes X, Y, Z) project onto the picture plane a perspective grid with one and only one vanishing point. This is point V, where the projected lines of axes X, Y, and Z intersect.
Limitations of Classical Perspective
In spite of its remarkable realism, classical perspective creates anomalous images. When we strictly follow the rules of image construction according to classical perspective, we end up creating images that do not accord with the way we actually see the world.
This disparity is more evident in some images than others. The notorious column paradox is one example [1].
Such anomalies can be avoided by altering the model of visual perception offered by classical perspective. This can be accomplished by conceiving of the human visual field not as a flat surface, but as a concave surface [2].
The Surrounding Visual World
We are completely surrounded by the visual world. We can turn our gaze in any direction and see a different portion of it. This is illustrated in Fig. 1b as a spherical surface with an observer at its center.
The spherical surface, which replaces the flat picture plane model of the visual field, carries on its surface the image of the entire surrounding visual world. Regardless of how narrow our instantaneous visual field, our sphere of vision includes all the visual data of our surroundings.
This raises two questions:
- What kind of image do the three dimensions of the visual world project onto this spherical visual field?
- Imagine that we could see all around ourselves at once. How might we represent on a flat surface this visual experience?
I have answered the first question with spherical perspective, and the second with flat-sphere perspective.
Spherical Perspective
Figure 1b illustrates an observer surrounded by his spherical visual field. The three spatial dimensions are represented by axes X, Y, and Z.
When these axes are mapped onto the spherical visual field of the observer, they create a perspective grid—the group of lines that organize on the spherical surface the appearance of the three spatial dimensions presented to the observer.
This grid has six fundamental points of convergence.
Spherical perspective has two advantages over classical perspective:
- It dissolves the anomalies that classical perspective gives rise to.
- It organizes, in a single continuous image, the whole surrounding visual world rather than only a portion of it.
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