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Concept
Curvilinear perspective
Summary
Curvilinear perspective, also five-point perspective, is a graphical projection used to draw 3D objects on 2D surfaces. It was formally codified in 1968 by the artists and art historians André Barre and Albert Flocon in the book La Perspective curviligne, which was translated into English in 1987 as Curvilinear Perspective: From Visual Space to the Constructed Image and published by the University of California Press.
Curvilinear perspective is sometimes colloquially called fisheye perspective, by analogy to a fisheye lens. In computer animation and motion graphics, it may also be called tiny planet.
An early example of approximated five-point curvilinear perspective is within the Arnolfini Portrait (1434) by the Flemish Primitive Jan van Eyck. Later examples may be found in mannerist painter Parmigianino Self-portrait in a Convex Mirror (c. 1524) and A View of Delft (1652) by the Dutch Golden Age painter Carel Fabritius.
In 1959, Flocon had acquired a copy of Grafiek en tekeningen by M. C. Escher who strongly impressed him with his use of bent and curved perspective, which influenced the theory Flocon and Barre were developing. They started a long correspondence, in which Escher called Flocon a "kindred spirit".
The system uses both curved perspective lines and an array of straight converging ones to approximate the image on the retina of the eye, which is itself spherical, more accurately than the traditional linear perspective, which only uses straight lines but is very distorted at the edges.
It uses either four, five or more vanishing points:
In five-point (fisheye) perspective: Four vanishing points are placed around in a circle, they are named N, W, S, E, plus one vanishing point in the center of the circle.
Four, or infinite-point perspective is the one that (arguably) most approximates the perspective of the human eye, while at the same time being effective for making impossible spaces, while five point is the curvilinear equivalent of one point perspective, so is four point the equivalent of two point perspective.
Official source
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