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What are some practical applications of these different decomposed frequencies in modern graphics/haptics?


What is the difference between a "Fourier decomposition" and a "Fourier transform"?


By frequency decomposition using Fourier Transform, we can represent the original function with the strength of various frequency basis. While this can help compress the data, what techniques is usually applied to minimize information loss, since the basis that we can take into consideration is limited, and many frequency can not be included?


Are convolutions useful in graphics? (Fourier transforms can be used to calculate convolutions using the convolution theorem)


Can using frequency decomposition of signals be used to reduce the complexity of a mesh? Or "predict" more detail?


How close do rendering engines stick to general ideas when implementing their versions of freq decomp for example - are there lots of innovations/customizations hidden in the source?

I suppose this question could also apply to other math-y parts of rendering beyond just F.D.


What exactly is the frequency decomposition of signals meant to look like on a 2d or 3d function? As in, what would a basis image/mesh give you?


Not quite understand the Fourier Decomposition with the examples. Can you explain a little bit?