Curvilinear perspective

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"[citation needed]).

It was formally codified in 1968 by the artists and art historians André Barre and Albert Flocon in the book La Perspective curviligne,[1] 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.

An early example of approximated five-point curvilinear perspective is within the Arnolfini Portrait (1434) by the Flemish Primitive Jan van Eyck.

They started a long correspondence, in which Escher called Flocon a "kindred spirit".

[2][page needed] 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.

Curvilinear barrel distortion
Curvilinear pincushion distortion
Curvilinearity in photography: Curvilinear (above) and rectilinear (below) image. Notice the barrel distortion typical for fisheye lenses in the curvilinear image. While this example has been rectilinear-corrected by software, high quality wide-angle lenses are built with optical rectilinear correction.