Fluid Morph

In my previous post I spoke about how to make curl fields to quickly approximate the effects one would see during a fluid sim. The effect works good enough if you’re only looking to sim around a second or so into the future, but it quickly breaks down after that. In order to create something a bit more realistic, we have to take two important properties of a fluid sim into account: Viscosity and Diffusion.

Viscosity is actually really simple. You just have to blur the vector field that you’re warping your image by. In our case, it’s the curl field that we learned how to generate in the Curl Fields post. Diffusion is also a blur, but it’s applied to the areas of the warped texture based on the intensity of the vector field we’re using to warp the image. To achieve a good result, we run about 6 iterations, blurring the textures every step. The strength of the blur that is applied to the vector field is the Viscosity value, and it is multiplied by the “Warp” strength. Diffusion is the strength of the blur that is applied to the image we’re warping, which is also applied every step. In the GIF below, you can see how the portions of the texture that are being warped gets blurred out a bit - this is the Diffusion in practice. Later in the GIF you’ll see the curls and warping “relax” a bit - this is the effect of viscosity.

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Below is a break down of the node, which you can now download for free on substance share.

You can see here that the node graph is pretty basic - it’s just 5 iterations of the same node expressions which you can see below.

An example of one of the iterations. We run a vector morph with a blurred version of the curl map (The blur amount is Viscosity). Then we blur the result by the divergence mask (See below) - and that gives us our diffusion. Then we pass it along to the next iteration.

Inside the Pixel Processor node, i calculate absolute divergence. All this does is calculate the absolute slope of the x and y components of the normal map, then add them together and divide by the inverse of the texture size. This gives me a nice mask where the white values correspond with areas of high fluid movement, where areas of no fluid movement remain black. To be honest this might be overkill and there could be an easier way to approximate this, but whatever.

This mask is used to mask the diffusion blur - so the more intense the vector field is, the more diffusion happens!

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So yeah this node is cool for generating some organic swirly things which is just another tool in the tool belt. Enjoy a couple quick examples below.

Example of using curl noise to add interesting decorative patterns to a tiling floor texture.

Anisotropic Noise Fluid Warped by Gaussian Noise

Thanks for reading, and Happy Holidays!

Curl Fields in Substance Designer

I’m writing this blog-post because during my google research, I couldn’t find any hits that helped me achieve fluid like warping of textures - similar to what you’d get by running a Navier-Stokes fluid simulation.

Example fluid sim from Google Images.

If you’re unfamiliar with fluid simulation, Jamie Wong gives a pretty good rundown of it on his blog. You can open that page and see a fluid sim right away, and even use your mouse to influence it.

My goal here is to use Substance Designer to create an easy-to-use node that gives us those curly vortex shapes that happen naturally in these fluid simulations. Unfortunately, the current off-the shelf tools that come with Substance Designer don’t give you the ability to get those nice vortex shapes without some setup. You’re able to warp images, but they often end up pinching or stretching in ways that don’t look like fluid at all.

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Typical result of using Vector Morph derived from a Gaussian noise. Notice the pinching and stretching that happens due to divergence in the vector field.

At first, I tried recreating the Navier-Stokes equation directly inside Substance Designer and succeeded (sort of), but the node was just too cumbersome since there’s many calculations that need to be done on several components of the simulation’s equation in order for it to look correct. Each calculation of the equation is just one time step, and you’ll need several hundred steps to get a result that’s acceptable. This approach ended up being completely impractical, however it wasn’t a total failure because I came away with the knowledge to achieve what I needed to in a much simpler way.

Before i get into that, i want to spend a moment to talk about what makes a good fluid simulation. This is a long walk, so bear with me. The key is having a non-divergent vector field to advect your texture with. Divergence, in this context, is the measure of how much fluid enters or leaves a given area in a single time step. If more fluid enters than leaves, it has positive divergence, which will eventually lead to pinching. If more fluid leaves than enters, it has a negative divergence, which leads to nasty stretching. A field that has no divergence has the same amount of fluid entering and leaving any given area which leads to a beautiful warping effect with no pinching or stretching. Unfortunately, as I explored the solutions offered to me in Jamie Wong’s post, I realized that creating a divergent free field is easier said than done. Doing so requires calculating pressure from divergence and then using like, 40 - 80 Poisson blurs to generate a nice enough pressure gradient that is then used to create ANOTHER vector field which is subtracted by the previous time step’s velocity field after it has been advected by itself, etc. It gets pretty complicated, but the end goal is to create a non-divergent vector field so that we get those pretty swirly shapes.

In order to cut down on complexity, we can take a step back and think about what’s necessary for us to achieve our end goal. Lets assume that we don’t care about several fluid properties like viscosity or diffusion rate or density for the time being. We also don’t care about variable force, because at the end of the day, we’re not running a simulation, we’re creating a single node that gives us results SIMILAR to a simulation. With that being said, we can just make the assumption that we’ll be using a constant vector field which does not change over time to drive our warping effect. With that assumption, we can just precompute a single vector field, and as long as that vector field is as non-divergent, we’ll get acceptable results.

But… how can I generate a divergent free vector field in Substance Designer? The answer is simpler than you’d think. We use a grayscale height field and calculate it’s curl to create a “Curl Field”. We do this because a Curl Field has the property of being divergent free! Unfortunately, there are no prepackaged tools that creates a Curl Field from a Height Field, but making one is incredibly easy to do, especially if you’re working with a two dimensional vector field.

The set up is easy. Grab a smooth grayscale noise like Perlin noise or Gaussian noise. Convert that into a normal map using Height-To-Normal World Units. (this gives a normal map with a nice range). Then use the Normal Vector Rotation node to rotate your normals by -90 or 90 degrees. That’s it. This creates a vector field where, instead of the vectors moving along the slope, it curls AROUND the slope, hence the name “Curl”.

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The same Vector Warp as above, but this time it’s being advected by a Curl Field instead.

An advantage to this setup is that you can experiment with other weird noise patterns. You can essentially use an HQ Blur on any height field and use the results to generate something usable! Here’s some more examples of some cool shapes.

This should be all you need to get started playing around with creating and using Curl Fields! My next blog post will cover an expansion of this where we use Curl Fields to create a fast “Fluid Morph” node that takes viscosity and diffusion into account. Stay tuned.

Creating fBm Noise with the FX-Map Node

The FX-Map is the muscle behind many of the powerful nodes that come with Substance Designer. It's used in pretty much all of the nodes that take an input and scatter it around, like the Tile Sampler and Splatter nodes. Some people use it to create custom scatter behaviors, but I mostly use it for generating noise patterns, so that's what i'm going to talk about in this post. But first, lets look at what Allegorithmic says about the FX-Map so we can all get a baseline understanding of it.

From Allegorithmic's Substance Designer documentation on the FX-Map:

The most common uses of FX-Maps are creating repetitive patterns, such as stripes and bricks, and noises, such as Perlin, Brownian and Gaussian noises. Noises are particularly useful in creating organic, natural-looking textures like dirt, dust, concretes, stone surfaces, liquid spatters and so on.

An FX-Map graph can contain one or more of the three FX-Map node types: Quadrant, Iterate and Switch. Of these nodes, the one you will likely use most often is the Quadrant, with the Iterate node a close second.

The [Quadrant] node is the prime mover of FX-Maps. It creates the core region quad-tree graph FX-Maps rely on, but it is not displayed as one. Visually, the quad-tree graph is shown in the form of a Markov Chain.

When rendering the FX-Map, the simplified FX-Map graph is ‘unwrapped’ to look like the big tree-like graph. The engine “walks” the entire quad-tree, working top to bottom, then left to right.

FX-Map nodes don’t blindly copy and paste their images. When each image is rendered, any dynamic functions it has are run. The functions affect each image rendered by the node. You can therefore give each individual image a random rotation, or scale factor, or a number of other adjustments.

They then goes on to give a short description of the 3 nodes that you can use inside an FX-Map node:

Quadrant

This splits the image at this step in the graph into four quadrants. This is the most common node type. A chain of Quadrant nodes can create very complex-looking images, as well as intricate patterns.

In fact, Quadrant nodes represent a level—or octave—in a quad-tree graph. FX-Map graphs hide this tree structure by representing each level in the tree with a single Quadrant: every time you connect one Quadrant node to another, you are actually creating a complete tree level. The reason for this 'cheat' technique is to remove the need to represent each node at every level of a tree individually: after just four layers of depth, you would need to use 4 x 4 x 4 x 4 nodes, which is 256 individual nodes! Instead, each Quadrant node "knows" which level it's at in the tree and generates its imagery accordingly.

Iterate

Repeats the image passed into the right-hand connector over the image passed into the left-hand connector by the set number of iterations. This node is most often used with one or more Dynamic Functions graphs to move or rotate the input image in some way at each iteration.

Switch

This takes two inputs and simply switches between one or the other, as defined by its Selector setting. As with the Iterate node, the Selector setting is often chosen by a Dynamic Function.

The FX-Map sub-node that i want to focus on for this post is the Quadrant node. Specifically, i want to focus on it's ability to create Brownian noises. The quadrant lets us create a very similar form of Fractal Brownian Motion, or "fBm" for short. The difference between our noise and traditional fBM noise is that our noise will reuse the same noise map in all of its octaves, instead of resampling the noise with different parameters for each octave.

In my opinion, this technique is incredibly useful for creating realisitc textures. So lets dive into how to make it.

The above images shows the initial setup i'm using. The right image shows the properties of my FX-Map. I'm using two Gradient Linear 1  nodes at different rotations and a Uniform Color (set to grayscale) node set to black. I then plug those into the RGBA Merge which will act as the 3D Coordinates that the 3D Worley Noise needs to do its thing. The 3D Worley Noise's properties are all default other than the scale parameter, which is set to 16.0. I plug that into a Make It Tile Photo (with default settings) to help reduce any seam artifacts that might come about from the fBm generation, which then goes into the FX-Map's Input Image 0 slot. The only thing I've done in the FX-Map at this point is set its Color Mode to "Grayscale". If you plug in a Grayscale input and leave it as Color, nothing will show up. 

Now that the setup is complete, go ahead and double click the the FX-Map node to preview its output, then hit Ctrl+E to dive into the sub-graph. The first thing you'll see is a Quadrant node. Click on it, and go into the properties and set the Pattern mode to "Input Image". If you've done things correctly, you'll see the Input Image 0 as the output preview. Copy paste the Quadrant node and move it underneath the original one, then connect all four of the original nodes' outputs to the new node's input. Then go into the new node and set the Pattern rotation property to 90 Degrees. For each new Quadrant node we add, we'll increment the degrees by 90.  We'll do this 3 more times until we have a 5 node chain. In other words, we'll be creating 5 "Octaves". When you're done, double click the background of the FX-Map to display the global properties of the FX-Map. At the bottom, find the "Roughness" (no, it's not related to the roughness you're probably thinking about) property, and slide it back and forth to get an idea of what the property does. I usually set this value to around 0.5. When your done, your graph should look similar to below:

So, why should i use this method when i could just set up a chain of transform nodes to do pretty much the same thing? Well... for one, it's fast. at 2048 res, the FX-Map node is only taking about 0.47 ms on my machine to compute, which makes it a great candidate for packaging it up for use in Substance Painter. Also, that "Roughness" parameter is amazing for tweaking your noise to get different levels of frequency. Setting up that behavior on a custom chain would be really tedious.

I'm not done with this yet, however. I want to show you what you can do with this once the setup is complete. Go ahead and pop back into your main substance graph, and lets check out the 3D Worley Noise node. You might be wondering why I've chosen to use this node instead of one of the Cells nodes or a simple Perline Noise node. While those nodes would be useful and legitimate to use, i like the 3D Worley Noise node because it's packed with cool parameters to get a wide variety of shapes. There's a bunch of different noise "Modes" contained in the properties, all with several "Styles" to choose from. 

I'm going to go over the different Worley Noise modes. Euclidian will give you a bunch of cone shapes. Manhattan's gives you pyramids rotated at a 45 degree angle. Chebyshev gives you pyramids, but with the added feature of having them "sliced" to allow for flat sections of the noise. And then there's good ol' Minkowski (a bit of an over-achiever, if you ask me). Minkowski noise comes with a special property called the Minkowski Number. Depending on this number, you can get shapes that pretty much look identical all 3 of the previous noise modes, with the exception of Minkowski 1.0, which looks to have a greater range than Manhattan does.  

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Euclidian

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Minkowski - 2.0

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Manhattan

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Minkowski - 1.0

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Chebyshev

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Minkowski - 20

Go ahead and try changing some of the Worley Noise properties. Try setting the mode to Minkowski and playing with the Minkowski Number and diffrent Styles. You'll see that you can get some pretty interesting noises as a result. In the below gif, i'm using a simple preview  to see what my noise would do with some AO, Height, Curvature, and Normal information. 

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Doing some simple Levels adjustments to the output can yield some nice results as well.

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Not only does fBm noise serve well as height information - it also can act as a mask for many organic effects. In the below example i'm using Minkowski 2.0 with the F2-F1 Style and a Roughness of around 0.2 to generate an alpha decay mask.

When using this mask as the base to a paint peeling effect, you can get some really cool results.

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Tweaking the Minkowski number, inverting the output or changing the mode of the Worley noise will give you a completely different feel. I could make a few tweaks to go from a flaky, cracked paint to a blistering, corroding paint. 

Below are a few shots of the node chain i'm using to generate the mask and the peel effect. The rest of the stuff is just boiler plate material blending, nothing too special going on. 

The take away from all of this is fBm noise is extremely useful and pretty easy to make in Substance Designer. I encourage you to try experimenting by substituting Worley 3D Noise with some other things like Gaussian Noise, or use a combination of the Shape and Splatter nodes. You'll get very detailed noise maps that you should be able to use for many, many effects.