Computational Aesthetics in Graphics, Visualization, and Imaging (2010) O. Deussen and P. Jepp (Editors) Pannini: A New Projection for Rendering Wide Angle Perspective Images Thomas K. Sharpless 1 , Bruno Postle, and Daniel M. German 2 1 tksharpless@gmail.com 2 dmg@uvic.ca, Dept. of Computer Science, University of Victoria. Abstract 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. 1. Introduction Modern photographic and computer technology make it easy to acquire wide angle images of the world, even up to fully spherical 360 ◦ images, and to synthesize wide images of imaginary worlds. But we still have trouble displaying those images on a flat surface [GBDL * 07]. The rectilinear per- spective projection, universally used for rendering realistic images at moderate fields of view, is simply not suitable for very wide angle views. Its magnification increases too rapidly with the view angle, with the result that objects near the edges of wide field images appear too large, and are stretched radially. These effects are known as rectilinear per- spective distortion. Modern manuals of perspective drawing suggest that to avoid rectilinear perspective distortion, fields of view should be limited to no more than 60 to 70 ◦ . Renaissance artists ob- served smaller limits – 30 to 40 ◦ [Kub86]. Today the “mar- ket limit” on the rectilinear field of view appears to be near 90 ◦ . Drawings and photographs that wide are published reg- ularly. The widest broadcast television lenses cover 94 ◦ , and some rectilinear still camera lenses can take pictures over 100 ◦ wide. It is easy to see the perspective distortion in such wide images. The availability of tools to create photographic panoramas (which can have fields of view of up to 360 ◦ ) in- creases the need for realistic alternatives to the rectilinear projection. Certain artists of the Baroque period (1650-1800) pro- duced pictures with wide fields of view, in what looks like correct perspective, without any visible sign of rectilinear perspective distortion. Their style, called vedutismo in Ital- ian, view painting in English, is highly recognizable. How- ever there are no written records of how these remarkable perspectives were constructed. In this paper we describe a simple but effective alterna- tive to the rectilinear perspective projection, derived from an analysis of vedutismo perspective, that we call the Pannini projection. 2. Related Work Digital panoramic photographers now use many alternative projections to render wide views of their work [GdGP07]. Most of those cannot be considered replacements for the rec- tilinear projection, because they produce images that violate our sense of correct perspective by curving lines we expect to be straight. However several methods have been devel- oped that can, in favorable circumstances, render wide views that resemble rectilinear perspectives. Zorin and Barr [ZB95] described the first such method in 1995. It uses nonlinear optimization to find a locally varying c  The Eurographics Association 2010. DOI: 10.2312/COMPAESTH/COMPAESTH10/009-016