Pannini: A New Projection for Rendering Wide Angle Perspective Images

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Thomas K. Sharpless, Bruno Postle, Daniel M. Germán: Pannini: A New Projection for Rendering Wide Angle Perspective Images. In: Pauline Jepp, Oliver Deussen (Eds.): Eurographics Workshop on Computational Aesthetics, 2010. 9-16



The widely used rectilinear perspective projection cannot render realistic looking flat views with fields of view much wider than 70°. Yet 18th century artists known as 'view painters' depicted wider architectural scenes without visible perspective distortion.We have found no written records of how they did that, however, quantitative analysis of several works suggests that the key is a system for compressing horizontal angles while preserving certain straight lines important for the perspective illusion. We show that a simple double projection of the sphere to the plane, that we call the Pannini projection, can render images 150° or more wide with a natural appearance, reminiscent of vedutismo perspective. We give the mathematical formulas for realizing it numerically, in a general form that can be adjusted to suit a wide range of subject matter and field widths, and briefly compare it to other proposed alternatives to the rectilinear projection.

Extended Abstract


author = {Sharpless, Thomas K. and Postle, Bruno and German, Daniel M.},
title = {Pannini: A New Projection for Rendering Wide Angle Perspective Images},
booktitle = {Proceedings of the Sixth International Conference on Computational Aesthetics in Graphics, Visualization and Imaging},
series = {Computational Aesthetics'10},
year = {2010},
isbn = {978-3-905674-24-8},
location = {London, United Kingdom},
pages = {9--16},
numpages = {8},
url = {, },
doi = {10.2312/COMPAESTH/COMPAESTH10/009-016},
acmid = {2381315},
publisher = {Eurographics Association},
address = {Aire-la-Ville, Switzerland, Switzerland},

Used References

ADAMS O. S.: Elliptic Functions Applied to Conformal World Maps. Tech. Rep. Special publication No 112, Department of Commerce, U.S. Cost and Geodetic Survey, 1925.

AIKEN J. A.: The Perspective Construction of Masaccio's "Trinity" Fresco and Medieval Astronomical Graphics. Artibus et Historiae 16, 31 (1995), 171-187.

Margaret A. Hagen, How to make a visually realistic 3D display, ACM SIGGRAPH Computer Graphics, v.25 n.2, p.76-83, Apr. 1991

KUBOVY M.: The Psychology of Perspective and Renaissance Art. Cambridge University Press, 1986.

LEE: Conformal Projections Based On Jacobian Elliptic Functions. Cartographica 13, 1 (1976), 67-101. Monograph 16.

LIU B., TODD J. T.: Perceptual biases in the interpretation of 3D shape from shading. Vision Research 44, 18 (Aug. 2004), 2135-2145.

MELLUISH R.: The Mathematics of Map Projections. Cambridge University Press, 1931.

PEIRCE C. S.: A Quincuncial Projection of the Sphere. American Journal of Mathematics 2, 4 (Dec 1879), 394-396.

SNYDER J. P.: Map Projections-a working manual, Professional Paper 1395. U.S. Geological Survey, 1987.

SNYDER J. P.: Flattening the Earth, two thousand years of map projections. University of Chicago Press, 1993.

SNYDER J. P., VOXLAND P. M.: An Album of Map Projections, Professional Paper 1453. U.S. Geological Survey, 1989.

Denis Zorin , Alan H. Barr, Correction of geometric perceptual distortions in pictures, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, p.257-264, September 1995

Lihi Zelnik-Manor , Gabriele Peters , Pietro Perona, Squaring the Circles in Panoramas, Proceedings of the Tenth IEEE International Conference on Computer Vision, p.1292-1299, October 17-20, 2005


Full Text

intern file

Sonstige Links