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# Math

## All node variations

All Math operations have the ability to blend (Mix) between value 1 and the result of the operation

## Math Italicized words are the names of the inputs

### Mix

• Blend the value inputs via the Fac(tor) input

• The sum of the two values.
• Value 1 + Value 2
-
Ex: 1 + 2 = 3

### Subtract

• The difference between the two values
• Value 1 - Value 2
-
Ex: 1 - 2 = -1

### Multiply

• The product of the two values
• Value 1 * Value 2
-
Ex: 3 * 2 = 6

### Divide

• The division of the first value by the second value.
• Value 1 / Value 2
-
Ex: 6 / 2 = 3

• The sum of the product of the two values with Addend.
• Value * Multiplier + Addend

### Power

• The Base raised to the power of Exponent.
• BaseExponent
- Ex: 32 = 9

### Logarithm

• The log of the value with a Base as its base.
• logBase(Value)
- Ex: log(3) = 1.0986122886681098

### Square Root

• The square root of the value.
• √Value
-
Ex: √4 = 2

### Inverse Square Root

• One divided by the square root of the value.
• 1 / √Value
-
Ex: 1 / √4 = 0.5

### Absolute

• The input value is read with without regard to its sign. This turns negative values into positive values.
• | Value |
- Ex: | -2 | = 2
- Ex: | 5 | = 5

### Exponent

• Raises Euler’s number to the power of the value.
• eValue
• e5 = 148.41315910257657

### Minimum

• Outputs the smallest of the input values.
• Returns the smallest value min(Value 1, Value 2)
• min(3,7) = 3
• min(10,-8) = -8

Maximum

• Outputs the largest of two input values.
• Returns the largest value max(Value 1, Value 2)
-
max(3,7) = 7
- max(10,-8) = 10

### Less Than

• Outputs 1.0 if the first value is smaller than the second value. Otherwise the output is 0.0.
• Returns 1 if True, 0 if False Value < Threshold
-
3 < 7 = 1 (True)
- 10 < -8 = 0 (False)

### Greater Than

• Outputs 1.0 if the first value is larger than the second value. Otherwise the output is 0.0.
• Returns 1 if True, 0 if False Value > Threshold
-
3 > 7 = 0 (False)
- 10 > -8 = 1 (True)

### Sign

• Extracts the sign of Value. All positive numbers will output 1.0. All negative numbers will output -1.0. And 0.0 will output 0.0.
- sign(3) = 1.0
- sign(-50.758) = -1.0
- sign(0) = 0.0

### Compare

• Outputs 1.0 if the difference between Value 1 and Value 2 is less than or equal to Epsilon.
- Value 1 = 0.5
- Value 2 = 0.7
- Epsilon = 0.0
- Returns 0.0
- Epsilon = 0.2
- Returns 1.0

### Smooth Minimum

• Like the Minimum function but rounded instead of pointed (linear)
• Smooth Minimum

### Smooth Maximum

• Like the Maximum function but rounded instead of pointed (linear)
• Smooth Maximum

### Round

• Round Value to nearest whole number
- 0.5 = 0.0
- 0.51 = 1.0
- 5.25 = 5.0
- 5.75 = 6.0

### Floor

• Round Value down to a whole number
- 0.5 = 0.0
- 0.51 = 0.0
- 5.25 = 5.0
- 5.75 = 5.0

### Ceil

• Round Value up to a whole number
- 0.5 = 1.0
- 0.51 = 1.0
- 5.25 = 1.0
- 5.75 = 1.0

### Fraction

• Returns everything after the decimal point of Value
-
0.5 = 0.5
- 0.51 = 0.51
- 5.25 = 0.25
- 5.75 = 0.75

### Truncate

• Outputs the integer part of the Value
-
0.5 = 0.5
- 0.51 = 0.51
- 5.25 = 0.25
- 5.75 = 0.75

### Modulo

• Outputs the remainder once Value 1 is divided by Value 2.
- 5 % 3 = 2
- 5 % 2 = 1

### Wrap

• Outputs a value between Min and Max based on the absolute difference between Value and the nearest integer multiple of Max less than the Value.
• Assume Min is 0.0 and Max is 0.1. The result of wrap increase as Value increase. BUT once Value = Max the result goes back to 0.0 and starts over.
- Min = 0.0
- Max = 0.2
- wrap(0.05) = 0.05
- wrap(0.175) = 0.175
- wrap(0.2) = 0.0
- wrap(0.2 + 0.05) = 0.05
- wrap(0.2 + 3.175) = 0.175

### Snap

• Round Value down to the nearest integer multiple of Increment.
• floor( Value 1 / Increment ) * Increment

### Ping-Pong

• The output value is moved between 0.0 and the Scale based on the input value.
• Like Wrap but with a linear progression back down to 0 instead of instantly at 0
- Scale = 0.2
- ping-pong(0.05) = 0.05
- ping-pong(0.175) = 0.175
- ping-pong(0.2) = 0.2
- ping-pong(0.2 + 0.05) = 0.195
- ping-pong(0.2 + 0.175) = 0.025

### Sine

• The Sine of Value
• sin(Value)

### Arctan2

• Outputs the Inverse Tangent of the first value divided by the second value measured in radians.
• atan2(Value)

### Hyperbolic Sine

• The Hyperbolic Sine of Value

### Hyperbolic Cosine

• The Hyperbolic Cosine of Value

### Hyperbolic Tangent

• The Hyperbolic Tangent of Value

### Clamp

• Limits the output to be between the Min and Max
- Value
: -1, Min: 0, Max: 1 = 0
- Value: 2 Min: 0 Max: 1 = 1
- Value: 0.56 Min: 0 Max: 1 = 0.56 Italicized words are the names of the inputs

### Mix

• Blend the value inputs via the Fac(tor) input

• The sum of the two values.
• Value 1 + Value 2
-
Ex: 1 + 2 = 3

### Subtract

• The difference between the two values
• Value 1 - Value 2
-
Ex: 1 - 2 = -1

### Multiply

• The product of the two values
• Value 1 * Value 2
-
Ex: 3 * 2 = 6

### Divide

• The division of the first value by the second value.
• Value 1 / Value 2
-
Ex: 6 / 2 = 3

• The sum of the product of the two values with Addend.
• Value * Multiplier + Addend

### Power

• The Base raised to the power of Exponent.
• BaseExponent
- Ex: 32 = 9

### Logarithm

• The log of the value with a Base as its base.
• logBase(Value)
- Ex: log(3) = 1.0986122886681098

### Square Root

• The square root of the value.
• √Value
-
Ex: √4 = 2

### Inverse Square Root

• One divided by the square root of the value.
• 1 / √Value
-
Ex: 1 / √4 = 0.5

### Absolute

• The input value is read with without regard to its sign. This turns negative values into positive values.
• | Value |
- Ex: | -2 | = 2
- Ex: | 5 | = 5

### Exponent

• Raises Euler’s number to the power of the value.
• eValue
• e5 = 148.41315910257657

### Minimum

• Outputs the smallest of the input values.
• Returns the smallest value min(Value 1, Value 2)
• min(3,7) = 3
• min(10,-8) = -8

Maximum

• Outputs the largest of two input values.
• Returns the largest value max(Value 1, Value 2)
-
max(3,7) = 7
- max(10,-8) = 10

### Less Than

• Outputs 1.0 if the first value is smaller than the second value. Otherwise the output is 0.0.
• Returns 1 if True, 0 if False Value < Threshold
-
3 < 7 = 1 (True)
- 10 < -8 = 0 (False)

### Greater Than

• Outputs 1.0 if the first value is larger than the second value. Otherwise the output is 0.0.
• Returns 1 if True, 0 if False Value > Threshold
-
3 > 7 = 0 (False)
- 10 > -8 = 1 (True)

### Sign

• Extracts the sign of Value. All positive numbers will output 1.0. All negative numbers will output -1.0. And 0.0 will output 0.0.
- sign(3) = 1.0
- sign(-50.758) = -1.0
- sign(0) = 0.0

### Compare

• Outputs 1.0 if the difference between Value 1 and Value 2 is less than or equal to Epsilon.
- Value 1 = 0.5
- Value 2 = 0.7
- Epsilon = 0.0
- Returns 0.0
- Epsilon = 0.2
- Returns 1.0

### Smooth Minimum

• Like the Minimum function but rounded instead of pointed (linear)
• Smooth Minimum

### Smooth Maximum

• Like the Maximum function but rounded instead of pointed (linear)
• Smooth Maximum

### Round

• Round Value to nearest whole number
- 0.5 = 0.0
- 0.51 = 1.0
- 5.25 = 5.0
- 5.75 = 6.0

### Floor

• Round Value down to a whole number
- 0.5 = 0.0
- 0.51 = 0.0
- 5.25 = 5.0
- 5.75 = 5.0

### Ceil

• Round Value up to a whole number
- 0.5 = 1.0
- 0.51 = 1.0
- 5.25 = 1.0
- 5.75 = 1.0

### Fraction

• Returns everything after the decimal point of Value
-
0.5 = 0.5
- 0.51 = 0.51
- 5.25 = 0.25
- 5.75 = 0.75

### Truncate

• Outputs the integer part of the Value
-
0.5 = 0.5
- 0.51 = 0.51
- 5.25 = 0.25
- 5.75 = 0.75

### Modulo

• Outputs the remainder once Value 1 is divided by Value 2.
- 5 % 3 = 2
- 5 % 2 = 1

### Wrap

• Outputs a value between Min and Max based on the absolute difference between Value and the nearest integer multiple of Max less than the Value.
• Assume Min is 0.0 and Max is 0.1. The result of wrap increase as Value increase. BUT once Value = Max the result goes back to 0.0 and starts over.
- Min = 0.0
- Max = 0.2
- wrap(0.05) = 0.05
- wrap(0.175) = 0.175
- wrap(0.2) = 0.0
- wrap(0.2 + 0.05) = 0.05
- wrap(0.2 + 3.175) = 0.175

### Snap

• Round Value down to the nearest integer multiple of Increment.
• floor( Value 1 / Increment ) * Increment

### Ping-Pong

• The output value is moved between 0.0 and the Scale based on the input value.
• Like Wrap but with a linear progression back down to 0 instead of instantly at 0
- Scale = 0.2
- ping-pong(0.05) = 0.05
- ping-pong(0.175) = 0.175
- ping-pong(0.2) = 0.2
- ping-pong(0.2 + 0.05) = 0.195
- ping-pong(0.2 + 0.175) = 0.025

### Sine

• The Sine of Value
• sin(Value)

### Arctan2

• Outputs the Inverse Tangent of the first value divided by the second value measured in radians.
• atan2(Value)

### Hyperbolic Sine

• The Hyperbolic Sine of Value

### Hyperbolic Cosine

• The Hyperbolic Cosine of Value

### Hyperbolic Tangent

• The Hyperbolic Tangent of Value

### Clamp

• Limits the output to be between the Min and Max
- Value
: -1, Min: 0, Max: 1 = 0
- Value: 2 Min: 0 Max: 1 = 1
- Value: 0.56 Min: 0 Max: 1 = 0.56
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Created:
Sunday, August 6, 2023
updated:
Wednesday, August 9, 2023

#### True-VFX

Author |
Heather @ True-VFX