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The problem is that "figuring out the coverage" already assumes you're modeling the pixels as little squares, and that is not the optimal model for pixels.
by mark-r 7y ago
The problem is that "figuring out the coverage" already assumes you're modeling the pixels as little squares, and that is not the optimal model for pixels.
- jacobolus 7y agoYou are misunderstanding me. Imagine we have infinite samples (i.e. a continuous brightness function), and we are using some radially symmetric reconstruction filter. Then the value of each output pixel is the sum (2d integral) of the brightness at the sample points multiplied by our function evaluated at the distance to the sample. If our continuous brightness data consists of one color on one side of a line and a different color on the other side of the line, then if we take the contribution of every point in the plane and integrate them, the output value at our pixel is going to be a combination of the two colors lerp(color1, color2, x(d)), where x is some monotonic function of the minimum distance between the pixel center and the line, which will depend on the specific reconstruction filter we are using. But as for the little square model: the linked article proposed that because it is being used right now, today, in many shipping vector graphics rasterizers, e.g. for fonts. I agree with you that it yields suboptimal results, so I am proposing an alternative.