Band limited repeatable `random' function
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Noise appears random, but isn't really.
If it were really random, then you'd get a
different result every time you call it.
Instead, it's "pseudo-random" - it gives
the appearance of randomness.
Noise is a mapping from Rn to R - you input an n-dimensional point with real coordinates, and it returns a real value. Currently the most common uses are for n=1, n=2, and n=3. The first is used for animation, the second for cheap texture hacks, and the third for less-cheap texture hacks. Noise over R4 is also very useful for time-varying solid textures, as I'll show later. Noise is band-limited - almost all of its energy (when looked at as a signal) is concentrated in a small part of the frequency spectrum. High frequencies (visually small details) and low frequencies (large shapes) contribute very little energy. Its appearance is similar to what you'd get if you took a big block of random values and blurred it (ie: convolved with a gaussian kernel). Although that would be quite expensive to compute. To make noise run fast, I implement it as a pseudo-random spline on a regular grid. Now we'll examine this fast implementation in some detail. |