A Pixel is Not a Little Square
by Alvy R Smith
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| url: | http://www.cs.cmu.edu/afs/cs/academic/class/15869-f11/www/readings/smith95_pixelsquare.pdf | | abstract: | My purpose here is to, once and for all, rid the world of the misconception that a pixel is a little geometric square. This is not a religious issue. This is an is- sue that strikes right at the root of correct image (sprite) computing and the abil- ity to correctly integrate (converge) the discrete and the continuous. The little square model is simply incorrect. It harms. It gets in the way. If you find yourself thinking that a pixel is a little square, please read this paper. I will have suc- ceeded if you at least understand that you are using the model and why it is permissible in your case to do so (is it?).
Everything I say about little squares and pixels in the 2D case applies equally well to little cubes and voxels in 3D. The generalization is straightforward, so I won’t mention it from hereon1.
I discuss why the little square model continues to dominate our collective minds. I show why it is wrong in general. I show when it is appropriate to use a little square in the context of a pixel. I propose a discrete to continuous map- ping—because this is where the problem arises—that always works and does not assume too much.
I presented some of this argument in Tech Memo 5 ([Smith95]) but have en- countered a serious enough misuse of the little square model since I wrote that paper to make me believe a full frontal attack is necessary. |
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