Original subtitles

The Voronoi node generates random tiles.

To understand the outputs of the Voronoi node, we need to look at how the Voronoi pattern

is generated.

Let's start by looking at the 1D case.

Here, if we feed it horizontally varying coordinates, we see some random vertical bars.

These bars are represented in different ways in each of the three outputs.

So let's take a look at how we arrived at this pattern.

It's easiest if we look at the input on a number line.

Firstly, throughout space, points are placed at regular intervals, let's call them origins.

The distance between the origins is determined by the Scale parameter.

Just like with the Noise node, the input value gets multiplied by the scale parameter before

anything else happens, so the higher the value, the smaller the distance between the points.

For the purpose of this explanation, let's just ignore the scale, by setting it to one,

so that it doesn't change the input, and the origins are all one unit apart.

Now, for each origin, a color formed by three random channels between zero and one is computed,

similarly to the White Noise node.

Then the first color channel, which is just a random value between zero and one, gets

scaled by the Randomness parameter, and added to the origin's position.

So with a randomness of zero, the origins stay exactly where they are, and as we increase

the randomness, they start shifting by different amounts.

Note that the origins never cross over each other, as the random value's range is between

zero and one, which is the distance between the origins, so an origin can never cross

over another origin's initial location.

Now, from each origin, the color expands, flooding the surrounding area, until it meets

the neighboring colors.

These resulting colored sections are called cells.

The cells have the neat property that any point within a cell is closer to that cell's

own origin than to any other origin.

From this, we get the three outputs.

The Color output is the random color that was assigned to each cell.

The Distance output is the distance to the cell's origin.

And the W output is the location of the cell's origin.

When we move to 2D, basically the same thing happens.

This time the origins are placed in a 2D grid, and shifted with a random 2D vector, which

is formed by the two first channels of the random color.

Then the colors flood the space until reaching the neighboring colors, thus forming the cells.

This is the Color output, now if we look at the Distance output, we see a black dot at

each origin, as the distance there is zero, and as we move away from the origin, the value

gets higher.

And now, instead of the W value output, we get a Position vector output, which encodes

the 2D coordinates of each cell's origin.

If we apply this to a 3D object, we see that the texture is constant along the coordinate

space's Z axis, just like with the Noise node.

Switching to 3D, now the origins are arranged in 3D space, and randomized with 3D vectors,

using all three channels of the random colors.

And this time, the cells are 3D volumes.

It is interesting to highlight, that the cell colors that we see in the Color output, are

the very same that get used as vectors when randomizing the origin locations.

This is undocumented in the Blender manual, but is useful to know when doing certain things

with the cell positions.

When looking at the Distance output, notice how there isn't a black dot in the middle

of every cell anymore.

That's because with the origins distributed in 3D space, they are not necessarily on the

mesh surface, in which case, the point where the distance is zero, is also off the surface.

Finally, there is a 4D mode, where we have an additional W parameter, which enables us

to animate the texture, just like with the 4D Noise Texture.

All of this functionality is given by the Voronoi node just in F1 mode, however, the

Voronoi node has several other modes.

So let's look at a couple of the other main ones.

The smooth F1 mode, works exactly like the regular F1 mode we looked at, but additionally

exposes a Smoothness parameter, which enables us to blend neighboring cells, creating a

smooth texture.

And lastly, the distance to edge mode, works kinda like the usual distance parameter, except

that instead of outputting the distance to the origin, it outputs the distance to the

cell boundaries.

Note that here we are looking at the 2D version.

If we switch to 3D, the distances get a lot less even, and there are some very dark cells.

This is again because in 3D mode, the cells exist in 3D space, as volumes, so the boundaries

of a cell can be near the surface of the mesh, in which case we get darker values.