3D Modeling & Texturing: [UE4 Material] Graphing Functions

Being interested in math and shaders I recently got into shadertoy and made a shader to draw some interesting looking implicit functions. This was fun but it was also just a matter of time until I'd do something similar using Unreal Engine.
So here we go, a tutorial about graphing a mathematical function with the UE3/4 material editor alone. There are no textures involved, everything is just done in the pixel shader.

In order to actually draw the graphs I'm using a method suggested by Iñigo Quílez:
http://www.iquilezles.org/www/articles/distance/distance.htm

The shader code described isn't very complex but requires the derivatives to be computed.
So in total there are 4 things required for graphing a function in the material editor:
A function.
Any kind of function will work but the elements need to be reordered so one
side of the equation is zero. E.g. y=x² will become 0=x²-y.
Derivatives of the function.
It's recommended to to manually do the differentiation. However if the math
is out of reach you can use finite differences instead.
A coordinate system.
Usually this will be the UVs, screen coordinates or the worldposition.
A grid.
This is optionally but helps to read the graph. I'd suggest to draw the x/y-axis at the very least.
Material Setup

I'm starting off with a rather simple function:
0 = x³-y²

The derivatives of this function are as follows:
d/dx = 3*x²
d/dy = -2*y

The coordinate system is based on the UVs. Since these range from 0-1 for the preview meshes a negative offset of -0.5 is added to the texture coordinates.
If you prefer an automated process over manual differentiation you can use forward differencing to calculate the derivatives. This will calculate the function 2 additional times with a slight offset on the x- and y-axis.
Keep in mind that this might increase the instruction count a lot, depending on the functions complexity.
With the function and its derivatives available we can now draw the graph:
Visalizing the x/y-axis is pretty similar to drawing the graph but much easier at the same time since it's directly based on the absolutes of the coordinates.
For a real grid with multiple sub-lines use this setup instead:
Putting it all together
To replicate this network of nodes just copy and paste the code below to your own material:

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      SizeY=432
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      MaterialExpressionEditorY=-3088
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   NodeHeight=448
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1 comment:

WerwackSeptember 17, 2015 at 3:24 PM
Hi Oliver,

Thank you for sharing this. The approach is really interesting.
I have not implemented it but I took several ideas to develop my own function shader. I needed something like that to check the values of variables in a shader. My shader is limited to bijective functions though.
http://werwackfx.com/index.php/graphictools/ue4-main/ue4-articles/35-shaderwkfunctiondrawer

Best regards
3D Modeling & Texturing

Pages

Friday, December 5, 2014

[UE4 Material] Graphing Functions

1 comment:
