Implicit and Explicit Procedural
By Neil Blevins
Apr 3rd 2015
A quick little discussion on Implicit and Explicit Procedural Noise.
I've been playing around a bit using Allegorithmic's Substance
Designer, and they use "Explicit Noise". I know the difference
between Implicit and Explicit modeling and shading, but had never heard
of "Explicit Noise" before. Upon finding almost no literature on the
web on the subject, I did some digging and here's the result.
First, a very basic definition of Implicit and Explicit...
1) An Implicit thing in CG is where a mathematical equation
can represent something.
2) An Explicit thing in CG is where you have a good approximation of
So for example, in geometry, an implicit model is where it calculates
the sphere as an equation, a standard sphere equation would be x^2 +
y^2 + z^2 = 1. So if you want to get the xyz point anywhere on that
sphere, it can be calculated to an exact position.
A polygonal sphere is an explicit model, because you only have an
approximation of a true sphere. Even if you increase the number of
polygons, you're just getting a better and better approximation, you
will never actually reach a perfect sphere at any point.
In texturing, a standard procedural noise is implicit (for example,
because when you zoom in, it just calculates more of the image based on
the original algorithm, so you never reach a point where you can't zoom
in any more.
Something like a bitmap is an explicit image, since the result is
stored as a set of pixels, if you zoom in past the pixel resolution of
the image, you don't get more information, and it just looks all
pixelated. Its an approximation of the original implicit noise.
So what is "Explicit Noise" in Substance Designer? While they don't
give the exact formula, basically their noises are made up by taking an
image and repeatedly placing it on a 2d surface, each randomly rotated
and placed, then the image is subdivided and the process repeats. For
more info, read here: http://support.allegorithmic.com/documentation/display/SD5/FXMaps?src=contextnavpagetreemode
This can create patterns that are very similar to implicit procedural
noise, but with a few different advantages and disadvantages.
- One advantage is you can create a larger number of noise looks
because you're starting with any arbitrary image.
- The noises can also be seamless.
Another example of a procedural pattern that can be Explicit is Texture
Bombing, which involves dropping image particles on a surface with
random positions, rotations and scales.
- The main disadvantage is you lose functionality such as
scale/frequency and unlimited resolution.
For example the Photoshop plugin FilterForge has a "Bomber"
The result can look very noise like, but since you're using 2d images
as particles (in this case, stars), they are explicit, and will reveal
resolution issues when you get too close.
Another bombing example is Modo's Texture
Anyways, if I get more information on exactly how Substance Designer's
noises work, I'll update the tutorial, but this should at least give
you some general idea as to what counts as explicit and implicit.
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