Now that stb_perlin.h is back (yes!) it would be nice to have analytical derivatives of Perlin noise available available out-of-the-box (I assume a bunch of people would appreciate it, not just me). They are expected to be both more accurate and faster then numerical approximations (and just more convenient). The computation is not complicated.
I (presently?) only care about the first-order derivatives. Not sure how much demand is there for higher-order (note: there are only so many interesting derivatives of Perlin noise, at high enough order they are all 0/discontinuity).
I don't much care whether stb_perlin_fbm_noise3, etc., get derivatives (maybe someone else does?).
I have a draft implementation, and can make a pull request if need be.
Regarding accuracy: according to my tests (to be taken with a grain of salt) symmetric difference approximation (with step size2e-3 which seems to minimize the error) introduces an RMS absolute error of about 3e-5 (8e-6 with -mfpmath=387) compared to analytical derivatives (max. error is 2.5e-4 and 1e-4 respectively).
Regarding speed: my implementation always produces the value of the Perlin noise function itself, and optionally some of the x/y/z partial derivatives. The speed looks like this (benchmarked straight on godbolt, reported CPU is Intel(R) Xeon(R) Platinum 8275CL CPU @ 3.00GHz, compiled with -O3 on x64 GCC 12.2):
This roughly corresponds to 20+8*n (where n is the number requested components) nanoseconds per call. No-derivatives case ([_,_,_]) should be essentially the same speed as the current stb_perlin_noise3_internal.
Compared to that, with a numerical approximation, to compute Perlin noise and 3 derivatives, one would need 7 (if using symmetric differences) or 4 (if using forward differences) taps (i.e. calls to stb_perlin_noise3). Note: if using a function specifically to fill an evenly-spaced grid (e.g. a texture), one can get derivatives almost for free (assuming step size equal to grid spacing is acceptable).
Aside (unrelated): stb_perlin_noise3_wrap_nonpow2 exists but is not mentioned in the documentation block. Any reason for that?
Now that
stb_perlin.his back (yes!) it would be nice to have analytical derivatives of Perlin noise available available out-of-the-box (I assume a bunch of people would appreciate it, not just me). They are expected to be both more accurate and faster then numerical approximations (and just more convenient). The computation is not complicated.I (presently?) only care about the first-order derivatives. Not sure how much demand is there for higher-order (note: there are only so many interesting derivatives of Perlin noise, at high enough order they are all 0/discontinuity).
I don't much care whether
stb_perlin_fbm_noise3, etc., get derivatives (maybe someone else does?).I have a draft implementation, and can make a pull request if need be.
Regarding accuracy: according to my tests (to be taken with a grain of salt) symmetric difference approximation (with step size
2e-3which seems to minimize the error) introduces an RMS absolute error of about3e-5(8e-6with-mfpmath=387) compared to analytical derivatives (max. error is2.5e-4and1e-4respectively).Regarding speed: my implementation always produces the value of the Perlin noise function itself, and optionally some of the x/y/z partial derivatives. The speed looks like this (benchmarked straight on godbolt, reported CPU is
Intel(R) Xeon(R) Platinum 8275CL CPU @ 3.00GHz, compiled with-O3on x64 GCC 12.2):This roughly corresponds to 20+8*n (where n is the number requested components) nanoseconds per call. No-derivatives case (
[_,_,_]) should be essentially the same speed as the currentstb_perlin_noise3_internal.Compared to that, with a numerical approximation, to compute Perlin noise and 3 derivatives, one would need 7 (if using symmetric differences) or 4 (if using forward differences) taps (i.e. calls to
stb_perlin_noise3). Note: if using a function specifically to fill an evenly-spaced grid (e.g. a texture), one can get derivatives almost for free (assuming step size equal to grid spacing is acceptable).Aside (unrelated):
stb_perlin_noise3_wrap_nonpow2exists but is not mentioned in the documentation block. Any reason for that?