6.) Spheres in space also project to ellipses in the picture plane, although generally with much less distortion than for circles (Fig. 7). Spheres always project to circles when at the center of projection. The elongation arises only because of marginal distortion, the stretching of the image as the picture plane itself recedes from the viewer at increasing angles of view.
In conclusion, perspective proves to be a rich paradigm for revealing the interplay of the mind with the space that it inhabits. Its problems posed in Greek antiquity have challenged the human intellect up through the 20th century. Some issues, indeed, still resist a geometric solution. Moreover, virtually nothing is known about the representation of perspective in the brain itself. It will be fascinating to follow the investigation of the neural processing structure and dynamics of this profound modality of space representation by present and future brain imaging techniques.
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Fig. 7. Projection of spheres. Spherical objects always form a circular cone projecting to the eye, whatever the angle of view. Unless this cone is perpendicular to the picture plane, the sphere will project as an ellipse in the picture plane.
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