# Page History

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The functions here all have green Scalar inputs and outputs.

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This can be very useful for extracting stepped data from smooth gradations among many other things. See the I/O graph below to get an idea of what is going on under the hood:

 Input: Result: 0.2 0.6 1 1.4 1.8 2.2 2.6 3 1 1 1 2 2 3 3 3

## Clamp

This node will clamp incoming values to a user specified cap or limiter value. There is a cap for the high limit (or top of the range) and one for the low. Values that are greater than the specified high limit will be set to the high limit value. Values that are lower than the low limit will be set to the low limit. Incoming values that are between the specified high and low limits will not be modified or scaled.

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The Floor node finds the largest integer less than or equal to the In input. A few examples:

 In: Out: -2.9 -2 -1.5 0 0.5 1.5 2 2.9 -3 -2 -2 0 0 1 2 2

The floor function can be considered as a round function much like Ceil, with the exception that it is derived from the lowest integer (the floor) rather than the highest integer (the ceiling).

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The Max node simply takes the A and B inputs and outputs the largest. A and B may be connected to other nodes or controlled manually. This means that the node can be used to clamp the maximum minimum value of a scalar.

## Min

The Min node simply takes the A and B inputs and outputs the smallest. A and B may be connected to other nodes or controlled manually. This means that the node can be used to clamp the minimum maximum value of a scalar.

## Mod

The Mod node derives the modulus of the A input in the form Result=A mod B. The modulus is effectively the remainder leftover when A is divided by B, as in 7 divided by 2 is 3 with a remainder 1. So a few examples would be:

 Input A: Input B: Result: 0 1 2 3 4 5 6 2 2 2 2 2 2 2 0 1 0 1 0 1 0

This function is useful because it can be used to repeat a regular function over a shorter period. Take, for example, a linear gradient that varies from 0.0 at the top of an object to 6.0 at the bottom. By using this gradient as the A input and making B 2.0, you can see from the above table that the gradient would ramp from 0.0 to 1.0 three times.

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The Sign node simply changes the sign of the input so that positive scalars become negative and negative scalars positive.

 In: Out: -2 -1 -0.5 0 0.5 1 2 2 1 0.5 0 -0.5 -1 -2

## Smooth Step

A smooth step is a rounded, ramped step function. Two limits are set by the Begin and End inputs. If the In input is less than the Begin input, then the output will be 0.0. Conversely, if the In input is greater than the End input, then the output will be 1.0. If the input is between Begin and End, then the output will vary between 0.0 and 1.0 proportionally as a smoothed ramp. Effectively the Smooth Step clamps between the begin and end values and normalizes the output between 0.0 and 1.0 with a smoothed transition.

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