Book excerpt: Varieties of Realism argues that it is not possible to represent the layout of objects and surfaces in space outside the dictates of formal visual geometry, the geometry of natural perspective. The book examines most of the world's coherent representational art styles, both in terms of the geometry of their creation and in terms of their perceptual effects on the viewer. A lucid exposition of modern geometrical principles and relations, accessible to the nonmathematical reader, is followed by an analysis of all known styles as variants of natural perspective, as true varieties of realism. Delineating the physical and mechanical constraints that determine the act of visual representation in painting and drawing, the author traces the intimate relations among seemingly distant styles and considers the kind of perceptual information about the world each can carry. Margaret Hagen is a perceptual psychologist with an ecological point of view. Her rigorous but readable presentation of visual theory and research offers provocative new insights into the connections among vision, geometry, and art.