Path: utzoo!censor!geac!torsqnt!news-server.csri.toronto.edu!cs.utexas.edu!sdd.hp.com!usc!ucsd!ucbvax!pasteur!miro.Berkeley.EDU!ph From: ph@miro.Berkeley.EDU (Paul Heckbert) Newsgroups: comp.graphics Subject: Re: Lunar Distortions Keywords: projection, perspective, distortion Message-ID: <9236@pasteur.Berkeley.EDU> Date: 27 Nov 90 05:42:12 GMT References: <27332@cs.yale.edu> <1097@shakti.ncst.ernet.in> Sender: news@pasteur.Berkeley.EDU Reply-To: ph@miro.Berkeley.EDU (Paul Heckbert) Organization: University of California at Berkeley Lines: 62 musgrave-forest@CS.YALE.EDU (F. Ken Musgrave) writes: > A very wide-angle view of a scene with a sphere in an extreme corner of > the image yields a very distorted sphere in the image... dilip@ncst.ernet.in (Dilip Khandekar) responds: > I also encountered the same problem and would be interested in any method >or projection-model which circumvents this problem. If the pin-hole camera >model is not a good model for the human eye-brain system then is there any >other model which is more accurate? Pictures generated with a standard perspective camera model only look "normal" if the viewing angle used during rendering matches the angle at which you view the picture. If you use a horizontal view angle of theta during perspective rendering, and view the pictures on a monitor of width w, then if you view the screen at a distance of d = w/2*cot(theta/2), the picture will not look distorted. Here's a little table for a w=14" screen: telephoto about normal wide angle view angle (degrees), theta : 10 50 90 recommended viewing distance, d : 80" 15" 7" The same argument applies in photography: shoot a photograph with a standard (50mm focal length) lens, print it at 8x10" size, say, and it will look pretty normal when viewed at a distance of about one foot. If you shoot a picture with a wide angle lens (24mm, say) and print it at 8x10, you will perceive "perspective distortion" if you view it at a distance of a foot, but it will look much less distorted if you hold it close to your face, so that your viewing angle matches the view angle captured by the lens. The argument also applies in projection of movies and slides: there is only one point in a movie theater from which a viewer will see the same image as that seen by the camera (i.e. same angle of view). Theater geometry and the lenses used for shooting and projection are usually chosen to put that "ideal viewer position" near the middle of the theater, I imagine. Assuming perfect filming and projection and one eye closed, viewers at this ideal position will not see any distortion artifacts of the projection -- that is, they will not be able to tell the difference between a projected film and a window into a 3-D scene. Viewers not at the ideal viewing position, such as those in the first row, will see the familiar artifacts of perspective "distortion" that will easily allow them to distinguish between a projected image and a real 3-D scene. Another interesting observation about projections is that you can project onto ANY shape screen you like (planar, spherical, cube corner, curtain, human torso, ...) and there will be no artifacts of the projection if the projection lens matches the shooting lens, the viewer is right at the projector, and the surfaces are properly finished. --- Related question: is there a formula relating camera lens focal length and angle of view? (I would guess that such a relationship would not be theoretical, but would be based on praticalities, and would vary from manufacturer to manufacturer) Paul Heckbert, Computer Science Dept. 570 Evans Hall, UC Berkeley INTERNET: ph@miro.berkeley.edu Berkeley, CA 94720 UUCP: ucbvax!miro.berkeley.edu!ph