10

There is a great paper from 2006 on this topic, Filter Importance Sampling. They propose your method 2, study the properties, and come out generally in favor of it. They claim that this method gives smoother rendering results because it weights all samples that contribute to a pixel equally, thereby reducing variance in the final pixel values. This makes ...


9

From a signal processing point of view, you're sampling a continuous-domain signal, and you need to filter it to get rid of frequencies beyond the Nyquist limit. It's that filtering that leads to integrating over the pixel area—or more generally, integrating over the support of your antialiasing kernel (which need not be a box). Consider your rendering ...


7

Super-sampling for ray-tracing doesn't just mean rendering an area at higher resolution and then downscaling the finished image: in fact, this simplest super-sampling technique is really not effective enough for high-quality production rendering. In a production ray-tracer, super-sampling means sending more than one primary ray per pixel (16 primary rays ...


4

You are in fact doing both things. You are integrating the area and because your result is still discrete samples you are reconstructing the signal to make it continious function. Therefore the higher order filtering. (Also human eye is a discrete sampler so it also reconstructs the signal) It took me a considerable amount of time to come into terms with ...


1

In signal processing, it is well-understood that you cannot accurately reproduce an analog signal of higher frequency than half the frequency of your digital sampling rate. That's just how the math works. Various aspects of rendering are just forms of signal processing, so this applies here too. So you're going to get some kind of artifact. You have a ...


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