Quote - > Quote - So far all I did was black cloth. To support colors, turn on the Diffuse_Value and hook it up to the Anisotropic node with a subtract node, to maintain the principle of Conservation of Energy.

Dumb question:
Anisotropic out -> Subtract(1,1) -> Diffuse_Color is CoE, right?
[Q] Why Math_Function Subtract() and not Color_Math Subtract? Is Specular info numeric only?

You've found one of my cheats.

I really am not interested in the specular color - just its luminance. And truthfully, this is not a perfect implementation of CoE. What I really need is the raw specular reflectance calculated inside that node, not its final color that comes out. But there's no node that will do that. So I make the best of a bad situation.

As has been brought up many times before, if I could get at the Poser source code, I could fix the material system quite a bit.

Thank you, Bill... have a good sleep.

More rockin' Billstuff. Watching with interest.

Quote - As has been brought up many times before, if I could get at the Poser source code, I could fix the material system quite a bit.

Next time Smith Micro issue one of their questionnaires, I must remember to make that suggestion. If we all do it, maybe it will happen...

fantastic BB.

but the question is to the poster who opened the thread. are you sure you want to render IDL,raytraced shadows with transparency?

if we would have rendermans deep shadows this wouldnt be such a problem. but here? uhhhhhh this will get interesting ;)

Quote - So what is the math of these gaps? 

It's pretty simple. I'll just say what it is, but if somebody asks, I can make a trigonometry diagram to show how I derived this formula.

Let's let D represent the "density" of the tubes, expressed as a fraction...

Now we also need to consider the angle between the normal of the "surface" comprising these tiny tubes and the observer. Let's call that angle alpha.

Ready?

The opacity of the surface is

D / cos(alpha)
...

BB, I would like to see the trigonometry diagram showing how you derived the formula.
 

Quote -   ...

In Poser, the Edge_Blend node internally calculates and uses the cosine of the angle of incidence. If you set the parameters to white, black, and 1, then the cos(alpha) is actually what it generates as its output. How nice!

... 

BB, I'm a little lost.  How do white, black, and 1 end up generating the cosine of alpha in the Edge_Blend node?

Quote - > Quote -   ...

In Poser, the Edge_Blend node internally calculates and uses the cosine of the angle of incidence. If you set the parameters to white, black, and 1, then the cos(alpha) is actually what it generates as its output. How nice!

... 

BB, I'm a little lost.  How do white, black, and 1 end up generating the cosine of alpha in the Edge_Blend node?

I'll need a little time to produce the diagram, but meanwhile I'll answer this question.

The answer is I formed several hypotheses about how Edge_Blend works, designed some tests to distinguish between the possibilities, and thereby discovered exactly what it does.

We know from the start that the EB node interpolates between two colors; Inner_Color and Outer_Color. Interpolation (or Blending) can be done a number of ways, but the most obvious is linear interpolation. In fact, this is what the Blender node does.

Blender(a, b, f) is:

(1-f) * a + f * b

As I said in a previous post, this is also called a weighted sum. The weight given to "a" versus "b" is determined by f. When f is 0, all you get is "a". When f is 1, all you get is "b". When f is .5, we expect the result to be an average of a and b. This is easily verified by examining the formula for those cases.

f = 0: (1-0) * a + 0 * b = 1 * a + 0 = a
f = 1: (1-1) * a + 1 * b = 0  + b = b
f = .5: (1 - .5) * a + .5 * b = .5 * a + .5 * b = .5 * (a + b) = (a + b) / 2

An interesting special case of the Blender node, one we'll get to at the end, is when a = 0 and b = 1.
If a = 0 and b = 1, then we get:

(1-f) * a + f * b
= (1-f) * 0 + f * 1
= f

The relevance of this is about to be revealed, because I'm going to show how, hidden inside, the value of f is cos(alpha).

Now the Edge_Blend node is actually a Blender node with the factor, f, generated internally. The question is, how is it generated?

There are only two reasonable guesses. The angle of incidence, alpha, could be used, or the cosine of the angle, cos(alpha).

The angle itself is the obvious one, and we could assume that if the angle is expressed from 0 to 90, that f is simply alpha/90. Thus when alpha is 0, f = 0. When alpha is 90, f = 1. This would be a reasonable way to go, except that Poser doesn't actually know the angle, at least not easily.

Far easier for Poser is to calculate the cosine of the angle. I don't know if you are familiar with vector math, but it turns out that given two vectors, P and Q, the cosine of the angle between them is trivially given by computing the dot product of P and Q, as long as the vectors are unit length. In math notation, you actually write a dot between them, but I don't know how to type such a thing, so I'll just say P dot Q.

So - why is P dot Q so cheap? Because it is simply:

P.x * Q.x + P.y * Q.y + P.z * Q.z

That's three multiplies and two adds - pretty much free in the world of 3D math.

Given the surface normal, N, which is needed to do any kind of lighting, and the normalized vector towards the camera or viewer, V, the cosine of the angle of incidence, alpha, is just N dot V!! Since N and V are already needed for lots of other things, they don't cost anything when an Edge_Blend node is used. .They're already there. And they're normalized, too, because dot products and cosines of angles are used in lots of lighting calculations.

So Poser has a super trivial way to compute cos(alpha) without doing any transcendental math at all. And this very neatly gives a value of 1 when the surface points straight at the camera, and 0 when it points away to the side. Values in between decrease monotonically from 1 to 0.

So I guessed that Poser was somehow using N dot V, or cos(alpha) to blend Inner_Color and Outer_Color.

There is a third parameter, however, called Attenuation. What is this for?

Since I knew something about how angles are used in shaders, particularly in RSL shaders, I knew that many effects are commonly controlled with respect to a cone of influence by taking the cos(alpha) and raise it to some power, i.e.

cos(alpha) ** P

This has the effect of making any modulation based on cos(alpha) become more weighted towards or away from the center, depending on whether P is more or less than 1.

I then hypothesized, tested for, and verified that the full equation of Edge_Blend is:

Blender(Outer_Color, Inner_Color, cos(alpha) ** Attenuation)

Expanding that out we get this for Edge_Blend:

(1 - cos(alpha) ** Attenuation) * Outer_Color + (cos(alpha) ** Attenuation) * Inner_Color

Now: plug in the values I said: Inner_Color =1 (white), Outer_Color = 0 (black) and Attenuation = 1.

(1 - cos(alpha) ** 1) * 0 + (cos(alpha) ** 1) * 1

Reduce all that, and you're left with:

cos(alpha)

So let's consider the case when the tubes or fibers are not opaque, but partially transparent.

The attached diagram shows how light has to pass through the cloth at various angles.

When the angle of incidence is 0, the distance that the light must travel is shortest. In fact, it is precisely the thickness of the cloth. This is the first case.

When the angle increases, the distance increases. You can see that in the second case, where the angle is 45 degrees, the distance that the light must pass through is 1.414 (sqrt of 2) times the original distance.

In the third case, at 60 degrees, the distance is twice the original distance.

Now the question is, what effect does this have?

Each plane removes some of the light passing through. Let's let T represent the transparency, or the fraction of light that can pass through.

The luminance through one layer is T times the object behind the layer, my checkerboard.

The second does the same, taking what comes in and letting T of that through. So the 2nd layer passes T * T of the light.

The third layer passes T * T * T.

It should be apparent that the Nth layer passes T ** N of the light through.

Now when we model a volume of translucent material with sheets like this, we're letting each sheet represent a slice of the volume. The more of these we use to model the volume, the more transparent each sheet needs to be. Using calculus, if we take the limit as the number of sheets approaches infinity, and the thickness of each slice approaches 0, it exactly models a volume. And in that limit, the effective transparency is T ** D, where D is the distance that the light has to pass through.

If the distance is infinitely long then the amount of light passing through is T to the infinite power, which is 0. But for any distance that is not infinite, then the transparency is greater than 0. So this is interesting. A translucent material of finite thickness cannot block all the light. There is always some non-zero amount that can get through. 

We're building shaders around opacity, but the distance-based transparency attenuation I explained in the previous post needs transparency, T, not opacity, O.

Remember that I said opacity and transparency are complements of each other.

So: O = 1 - T and T = 1 - O

Remember that the transparency is T ** D, where D is the distance.

T ** D
= (1 - O) ** D

This gives the effective transparency.  We need to convert that to opacity to plug into the Poser Surface.

1 - (1 - O) ** D

This is the heart of the shader above. But what is D?

Guess what ... it is 1 / cos(alpha) again.

In the shader, the bottom right node is the desired cloth opacity, O. The rest is the equation:

1 - (1 - O) ** (1 / cos(alpha))

Now, that shader works fine for the horizontal transparent fibers. As they bend around the curve, we look through more of each fiber, so that the distance we're looking through increases, just as the math above describes.

But what about the vertical fibers?

Now begins part 4.

In the center we see through only one layer, and there are gaps.

As we approach the edge, the gaps are eliminated, and they start to overlap. We didn't care about this when they were opaque. But now we have to care.

At first, they only overlap a little, but getting closer to the edge, they overlap more. At some point, we start to have double overlap, where there are places we're looking through three or four tubes. Then four or five, and so on. Eventually, at the very edge, we're looking through many tubes, and they get very dark again, almost opaque. But not quite opaque.

The math for this is ... intense. So I won't show it. The interesting thing about it is that in the statistical sense of a lot of fibers, there are some simplifications we can make. I have made these simplifications in my shader and I'll just demonstrate what it looks like.

I still have a few more tweaks to do to it. When it's ready, I'll publish it.

Now I'll make some demo renders.

(Note: There's a little more to this - I have a weave set up as a bump to give it some texture.)

I really don't know how nylon actually is woven and what the real density is, but it sure looks more like nylon this way. So I'm guessing that nylon is pretty tightly woven and the fibers are far from opaque.

:woot: This is beyond exciting!!! :woot: Oh, the materials that I'm going to play with! :tt1: I just love this, Bill! Thank-you thank-you THANK-YOU!!!

grin

Here's a light brown - the typical color of ordinary hosiery.

In the above examples (excluding the white) there seems to be a seam and tint change under the left arm to the hip. What causes that, is it supposed to be there?

This is part 5. Lace.

Quote - In the above examples (excluding the white) there seems to be a seam and tint change under the left arm to the hip. What causes that, is it supposed to be there?

Isn't that in the mesh itself?

Quote - In the above examples (excluding the white) there seems to be a seam and tint change under the left arm to the hip. What causes that, is it supposed to be there?

Yes the blouse has a seam there, literally it's modeled in. And there are cuffs, too.

Quote - I have to get to bed soon, but I'll leave you with the teaser.

This is part 5. Lace.

I'll be back for the lace - definitely! You should charge admission, Bill :lol: This is incredible...

Looking forward to the lace too.

White lace.

With each image the imagination spins into overdrive. This is going to be one FANTASTIC weekend. I hope it's as rewarding for you, Bill...

These examples are what I was looking for!

You can see why I held off, Latex... when BB is on it, one learns to shut up and wait for it... it's going to exceed the wildest expectations.
This is phenomenally unique... you're not going to find materials designed with the same profound understanding of what the nodes do in the rest of the community.

This isn't just about nylon: it's about how EdgeBlend and Blender and the Opacity channel (misnamed Transparency) work.

That's where the real gold lies. I'm incredibly grateful to BB for sharing this information!

Not to minimise the material shader itself... it's mind-blowing in its simplicity and incredible versatility. The imagination positively reels...

Quote - I'll leave you with the teaser. This is part 5. Lace.

:jawdrop:

pardon, but why would lace be hard once the general shader is in place?  if you have an opacity setting, that means you can make the opacity anything you want, right?  0.7, image node, fractal cloud, whatever?  or am i missing a complexity?

Maybe I'm missing a simplicity. Do please post your own procedural lace shader if you have one. 

oh, i think we're at cross purposes.  so, someone, i can't remember who now, posted that they wanted to know how this might work with an image of lace.  but it was after discussing the notion of opacity or transparency as a variable (but before the full explanation). so my point was that once bagginsbill said opacity was a variable, to me there was no need to show it as lace at all.  if you give me an equation with O opacity, i'm perfectly content with understanding that O can be anything you want to put there.

that said, maybe there's an aspect to opacity i'm missing, and you'd need to do something more than just define O.  maybe you'd want density to vary too, or some other aspect i'm not seeing.

personally, i'm not that into procedural lace, or most generated geometric patterns.  i've seen way, way, way too much of it over the years to really appreciate it.  there's even tons of it in the marketplace.  not built with Poser, but the effect is the same.  for me, it's up there with lens flare, heavy drop shadows and other common 2d stuff.  it just didn't occur me that's what you meant.

Sorry, yes, we probably are at cross purposes. My jaw was dropping at the procedural lace - I assume that it is procedural, knowing BB - and I also assume that was what everyone else was raving about. If it's commonplace stuff then I'm only slightly deflated.

The way that opacity varies with angle should be more complex with lace, because of its construction. I expect the "thick bits" to interact with lighting in a different way to the "thin bits" (don't know the proper lace terminology, I' m sure there is one), and I'm anticipating that BB will have addressed that aspect too.

We'll just have to wait and see. I'm sure the wait will be worthwhile.

Excellent. I was hoping for this... lots of questions but,,, I'll wait.

Whoops - I may have inadvertantly misled. The lace pattern is not procedural. I'm using a lace transparency map, as Latexluv suggested:

Quote - But others may like the idea of being able to add lacy trancparencies to the shader for items like frilly underwear.

I think I could come up with some sort of procedural lace, but it wouldn't be easy and it wouldn't be as good as real lace. In fact, the lace map I'm using looks to have been made with a procedure and could be improved upon. I'm just doing a demo and I don't have much in the way of lace maps to work with, as I'm not about to buy some just to show how to use it and I can't draw to save my life.

Still - how to connect the lace map to the nylon shader isn't obvious, at least to most people. So part 5 is about how to do that sort of thing.

KK is not missing anything, really. The basic idea is to modulate the density and opacity and shine and bump with the lace map. But how to modulate it, how to make one map work for bump and all those other things, which actually require a slightly different map but can be done with one map and some math, is what part 5 will be about.

Amazing stuff, jumping on board this thread..

But I want you guys to have something to play with in case I don't get to finishing this shortly.

So here is a prelim version of my BBNylon material file. Save it as BBNylon.mt5 somewhere in your materials folder. It is 68 nodes. Don't be scared. Just use the ones on the left for controlling it.

There are many parameters. We've talked about density and opacity, so that should be clear enough.

To use a lace map, load it into the Lace Map node, and set Enable Lace to 1.

To use a different color on the lace, set Enable Lace Color to 1.

Quote - Whoops - I may have inadvertantly misled. The lace pattern is not procedural. I'm using a lace transparency map, as Latexluv suggested

That's cool - there's more than enough here already. It's just that we tend to have high expectations of your appearances on the forum. :)

Thanks for the material. It's nearly time to go home, then I can play...

Here it is on some stockings at the default settings.

Sorry about no shadows - I'm in a hurry.

BB thank you so very much! I will gladly play with the preliminary version of this shader!

Endless possibilities.  Thank you.