Kenneth wrote:
> Tek's recent beautiful and complex ocean wave images got me to thinking
> about adding noise blobs to the tops of isosurface wave crests, to see if
> the look of foam and spray could be better simulated there, to some degree.
>  Certainly not a new concept. ;-) The essence of the idea involves the noise
> being constrained, more or less, to only the tips of the waves, "fading in"
> in intensity there. I vaguely remember seeing some POV-Ray images that may
> have used this trick, but can't remember where.
> 
> An interesting question was raised, about whether the noise blobs--being
> smooth by nature--would assume a "sharper" look due to the underlying sharp
> wave crests. I made some tests to see what might happen; the isosurface code
> is posted below.
> 
> My *quick and dirty* water waves are just triangles (from a pigment
> function) bent with a cosine wave to curl over, plus noise. Good enough to
> test the idea. The wave crests curl in the +z direction.  BTW, the triangle
> waves aren't actually "bent"--they're SHEARED in the z direction. Every
> point on the isosurface stays at the same height it began at (a limitation
> of my own current understanding of function-bending.)
> 
> Just to keep things as simple as possible, the noise "appears" at a set
> height, rather than being made to follow any vertical undulations (though
> it does follow the wave curls, in z, to impart a wind-blown look.)
> 
> Image #1 is just a "proof of concept."
> #2 is a close-up, to see what the noise blobs look like--whether they're
> still blobby, or look like sharp, flattened spikes due to the triangle
> waves. Looks like a cross between the two. But even seen edge-on, they
> still look reasonably rounded. The noise intensity is fading in so quickly
> that it seems to overwhelm the sharp triangle edge. Part of the blobbiness
> appears to be out beyond the edge anyway.
> #3 is with some choppy distortion laid onto the isosurface. Since both the
> noise position and the gradient y texture don't move, the white "foamy"
> areas happen to correspond to the noise blobs. Interesting!
> 
> Unfortuntely, every value in my noise_compressor function is critical, due
> to the exponent behavior. The values have to be finessed, to constrain and
> position the noise *just so.* I'm still not satisfied with the final look;
> needs more tweaking.
> 
> The contained_by box's upper y dimension is also critical, to keep the noise
> from quickly fading back in above the waves (a result of the way the
> noise_compressor function is currently built.) That might(?) be a problem
> for more complex water waves. But there are methods of using the underlying
> water-wave function(s) to make the noise follow any changes in wave
> height...so the contained-by box size may not be a problem. But right now,
> there IS an abrupt (and probably apparent) cut-off of the noise right above
> the wave tips. I'm still experimenting to find a way around that.
> 
> What I see a need for--just from this basic experiment--is to scale the SIZE
> of the noise blobs in the +y direction, larger to smaller. The result would
> be a two-fold improvement, I believe: to make the noise larger and smoother
> as it *approaches* the wave tips; but then tiny and more pronounced AT the
> tips. Given a set noise intensity in the noise_compressor function.  But I
> don't yet know how to variably scale a function's "size" across space. :-(
> 
> Does the blobby effect add realism?  That's...a good question.  I kind of
> like it. With some good water waves and textures...?
> 
> Here's the isosurface code, for image #1. If anyone is interested, I'd be
> glad to "deconstruct" the various functions, as to what they do (though I'm
> still learning the finer points of functions myself.) I'm sure they could be
> improved.
> 
> Comments, critiques, suggestions--all welcome. This is definitely a learning
> experience!
> 
> Ken Walker
> 
> -----------
> #include "functions.inc"
> 
> #local triangle_waves =
> function{
> pigment{
> gradient z
> triangle_wave
> color_map{
> [0.0 rgb 0]
> [1.0 rgb 1]
> }
> scale .35
> }
> }
> 
> #local wave_bender =
> function(y){.13*cos(11*y - 1.9) + .6};
> 
> #local noise_compressor =
> function(y){775*pow(y + .390,30)};
> 
> isosurface{
> function{
> y - .3
> + triangle_waves(x,y,z + wave_bender(y)).gray*.13
> - f_noise3d(150*x,100*y,100*(z + wave_bender(y)))*noise_compressor(y)
> }
> threshold 0
> max_gradient 6.3
> accuracy .00001
> contained_by{box{<0,0,-.6>,<1.2,.328,3>}}
> }
> 
> 
> 
> 
> 
> ------------------------------------------------------------------------
> 
Looks like it would have great potential to show waves curling and 
crashing against a beach.

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