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With a Math node, we can do several different
operations.
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Let's take a look at some of the basic math
operations.
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These are mostly self explanatory, but there
are some things to look out for.
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The Math node takes one to three inputs, depending
on the selected operation, and always has
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a single output.
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Perhaps the simplest of all operations is
addition.
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We all know what it is, but let's take a look
at it in context.
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Here we have a constant value of zero being
fed into the first and second inputs.
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On the top we can see the color representation
of the value, and on the bottom we have a
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plot of the value over the X axis.
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If we start changing one of the inputs, we
see the output value changing accordingly.
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Now, looking at an example where we have a
Noise Texture fed into one of the inputs,
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we basically see the same thing, the output
moves up and down based on the value we're
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adding.
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But something interesting happens when we
feed it a linear gradient, such as the X channel
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from a texture coordinate.
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Here, the output seems to move side to side.
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However, we know that we cannot shift values
through space, as we cannot access values
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from other points.
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And if we highlight a point on the line, we
can see that it is indeed moving up and down
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according to the value being added.
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This effect happens because with a linear
gradient, there is no difference between shifting
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up and down, and shifting left to right.
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This is significant as it is the foundation
of what allows us to move coordinate spaces
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around.
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We are calculating the values of a shifted
gradient, from the original values themselves.
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Note that this only works because we have
an infinite gradient.
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If we use a clamped gradient, such as the
one output by the gradient node, initially
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it looks the same, as we cannot see the values
below zero or above one as colors, but if
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we change the addition now, the horizontal
shift only happens within the small region
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where the values are not clamped.
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So far we've only added a constant value to
different inputs, which just offsets everything
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up and down.
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But nothing stops us from plugging varying
values, like a noise and a gradient, into
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both sockets to add them together.
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Moving on to the other operations, subtraction
is identical to addition, except that the
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sign gets flipped.
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So let's move on to multiplication.
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Multiplication allows us to change the amplitude
of a texture.
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It's also interesting to note that on a linear
gradient, we change the slope, which is equivalent
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to a scaling operation, squashing the values
together in space.
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Division is the reciprocal of multiplication,
meaning that it's the same as multiplying
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by one over the value.
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Moving on to the Power operation, applying
this to a gradient, we get the typical power
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curve.
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Keep in mind that only the real part of the
output is given, and the power of negative
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values is set to zero except when the exponent
is an integer.
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Power is useful for smoothing, and for changing
the distribution of things.
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We'll explore some uses of the Power operation
throughout the course.
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Lastly, the Absolute operation, which takes
a single input, simply flips the sign of any
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negative values.
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When applied to a linear gradient, this is
especially useful for creating symmetry.
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