thumb|Curvilinear barrel distortion
thumb|right|Curvilinear pincushion distortion
Curvilinear perspective, also five-point perspective, is a graphical projection used to draw 3D objects on 2D surfaces, for which (straight) lines on the 3D object are projected to curves on the 2D surface that are typically not straight (hence the qualifier "curvilinear"). 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.
History
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".