120 lines
13 KiB
Markdown
120 lines
13 KiB
Markdown
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# Math nodes
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Perform a mathematical operations, from basic arithmetic to advanced functions like trigonometry, vectors, matrices, interpolation, and waves.
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## Advanced
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| **Topic** | **Description** |
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| [Absolute](Absolute-Node.md) | Returns the absolute value of input In. |
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| [Exponential](Exponential-Node.md) | Returns the exponential value of input In. |
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| [Length](Length-Node.md) | Returns the length of input In. |
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| [Log](Log-Node.md) | Returns the logarithm of input In. |
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| [Modulo](Modulo-Node.md) | Returns the remainder of input A divided by input B. |
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| [Negate](Negate-Node.md) | Returns the inverse value of input In. |
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| [Normalize](Normalize-Node.md) | Returns the normalized vector of input In. |
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| [Posterize](Posterize-Node.md) | Returns the input In converted into a number of values defined by input Steps. |
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| [Reciprocal](Reciprocal-Node.md) | Returns the result of 1 divided by input In. |
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| [Reciprocal Square Root](Reciprocal-Square-Root-Node.md) | Returns the result of 1 divided by the square root of input In. |
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## Basic
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| **Topic** | **Description** |
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|------------------------------------|--------------------------------------------------------|
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| [Add](Add-Node.md) | Returns the sum of the two input values. |
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| [Divide](Divide-Node.md) | Returns the result of input A divided by input B. |
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| [Multiply](Multiply-Node.md) | Returns the result of input A multiplied by input B. |
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| [Power](Power-Node.md) | Returns the result of input A to the power of input B. |
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| [Square Root](Square-Root-Node.md) | Returns the square root of input In. |
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| [Subtract](Subtract-Node.md) | Returns the result of input A minus input B. |
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## Derivative
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| **Topic** | **Description** |
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|----------------------|-------------------------------------------------------------------------------|
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| [DDX](DDX-Node.md) | Returns the partial derivative with respect to the screen-space x-coordinate. |
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| [DDXY](DDXY-Node.md) | Returns the sum of both partial derivatives. |
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| [DDY](DDY-Node.md) | Returns the partial derivative with respect to the screen-space y-coordinate. |
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## Interpolation
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| **Topic** | **Description** |
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|--------------------------------------|----------------------------------------------------------------------------------------------------------------------|
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| [Inverse Lerp](Inverse-Lerp-Node.md) | Returns the parameter that produces the interpolant specified by input T within the range of input A to input B. |
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| [Lerp](Lerp-Node.md) | Returns the result of linearly interpolating between input A and input B by input T. |
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| [Smoothstep](Smoothstep-Node.md) | Returns the result of a smooth Hermite interpolation between 0 and 1, if input In is between inputs Edge1 and Edge2. |
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## Matrix
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| **Topic** | **Description** |
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|----------------------------------------------------|---------------------------------------------------------------------------|
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| [Matrix Construction](Matrix-Construction-Node.md) | Constructs square matrices from the four input vectors M0, M1, M2 and M3. |
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| [Matrix Determinant](Matrix-Determinant-Node.md) | Returns the determinant of the matrix defined by input In. |
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| [Matrix Split](Matrix-Split-Node.md) | Splits a square matrix defined by input In into vectors. |
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| [Matrix Transpose](Matrix-Transpose-Node.md) | Returns the transposed value of the matrix defined by input In. |
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## Range
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| **Topic** | **Description** |
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|--------------------------------------|----------------------------------------------------------------------------------------------------------------------|
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| [Clamp](Clamp-Node.md) | Returns the input In clamped between the minimum and maximum values defined by inputs Min and Max respectively. |
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| [Fraction](Fraction-Node.md) | Returns the fractional (or decimal) part of input In; which is greater than or equal to 0 and less than 1. |
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| [Maximum](Maximum-Node.md) | Returns the largest of the two inputs values A and B. |
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| [Minimum](Minimum-Node.md) | Returns the smallest of the two inputs values A and B. |
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| [One Minus](One-Minus-Node.md) | Returns the result of input In subtracted from 1. |
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| [Random Range](Random-Range-Node.md) | Returns a pseudo-random number that is between the minimum and maximum values defined by inputs Min and Max. |
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| [Remap](Remap-Node.md) | Remaps the value of input In from between the values of input Out Min Max to between the values of input In Min Max. |
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| [Saturate](Saturate-Node.md) | Returns the value of input In clamped between 0 and 1. |
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## Round
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| **Topic** | **Description** |
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|------------------------------|--------------------------------------------------------------------------------------------------------------|
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| [Ceiling](Ceiling-Node.md) | Returns the smallest integer value, or whole number, that is greater than or equal to the value of input In. |
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| [Floor](Floor-Node.md) | Returns the largest integer value, or whole number, that is less than or equal to the value of input In. |
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| [Round](Round-Node.md) | Returns the value of input In rounded to the nearest integer, or whole number. |
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| [Sign](Sign-Node.md) | Returns -1 if the value of input In is less than zero, 0 if equal to zero and 1 if greater than zero. |
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| [Step](Step-Node.md) | Returns 1 if the value of input In is greater than or equal to the value of input Edge, otherwise returns 0. |
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| [Truncate](Truncate-Node.md) | Returns the integer, or whole number, component of the value of input In. |
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## Trigonometry
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| **Topic** | **Description** |
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|--------------------------------------------------|--------------------------------------------------------------------------------------------------------------|
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| [Arccosine](Arccosine-Node.md) | Returns the arccosine of each component the input In as a vector of equal length. |
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| [Arcsine](Arcsine-Node.md) | Returns the arcsine of each component the input In as a vector of equal length. |
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| [Arctangent](Arctangent-Node.md) | Returns the arctangent of the value of input In. Each component should be within the range of -Pi/2 to Pi/2. |
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| [Arctangent2](Arctangent2-Node.md) | Returns the arctangent of the values of both input A and input B. |
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| [Cosine](Cosine-Node.md) | Returns the cosine of the value of input In. |
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| [Degrees to Radians](Degrees-To-Radians-Node.md) | Returns the value of input In converted from degrees to radians. |
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| [Hyperbolic Cosine](Hyperbolic-Cosine-Node.md) | Returns the hyperbolic cosine of input In. |
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| [Hyperbolic Sine](Hyperbolic-Sine-Node.md) | Returns the hyperbolic sine of input In. |
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| [Hyperbolic Tangent](Hyperbolic-Tangent-Node.md) | Returns the hyperbolic tangent of input In. |
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| [Radians to Degrees](Radians-To-Degrees-Node.md) | Returns the value of input In converted from radians to degrees. |
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| [Sine](Sine-Node.md) | Returns the sine of the value of input In. |
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| [Tangent](Tangent-Node.md) | Returns the tangent of the value of input In. |
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## Vector
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| **Topic** | **Description** |
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| [Cross Product](Cross-Product-Node.md) | Returns the cross product of the values of the inputs A and B. |
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| [Distance](Distance-Node.md) | Returns the Euclidean distance between the values of the inputs A and B. |
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| [Dot Product](Dot-Product-Node.md) | Returns the dot product, or scalar product, of the values of the inputs A and B. |
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| [Fresnel Effect](Fresnel-Effect-Node.md) | Fresnel Effect is the effect of differing reflectance on a surface depending on viewing angle, where as you approach the grazing angle more light is reflected. |
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| [Projection](Projection-Node.md) | Returns the result of projecting the value of input A onto a straight line parallel to the value of input B. |
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| [Reflection](Reflection-Node.md) | Returns a reflection vector using input In and a surface normal Normal. |
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| [Rejection](Rejection-Node.md) | Returns the result of the projection of the value of input A onto the plane orthogonal, or perpendicular, to the value of input B. |
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| [Rotate About Axis](Rotate-About-Axis-Node.md) | Rotates the input vector In around the axis Axis by the value of Rotation. |
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| [Sphere Mask](Sphere-Mask-Node.md) | Creates a sphere mask originating from input Center. |
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| [Transform](Transform-Node.md) | Returns the result of transforming the value of input In from one coordinate space to another. |
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## Wave
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| **Topic** | **Description** |
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|----------------------------------------------|-------------------------------------------------------------------------------------------------------------------|
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| [Noise Sine Wave](Noise-Sine-Wave-Node.md) | Returns the sine of the value of input In. For variance, random noise is added to the amplitude of the sine wave. |
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| [Sawtooth Wave](Sawtooth-Wave-Node.md) | Returns a sawtooth wave from the value of input In. |
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| [Matrix Split](Matrix-Split-Node.md) | Splits a square matrix defined by input In into vectors. |
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| [Matrix Transpose](Matrix-Transpose-Node.md) | Returns the transposed value of the matrix defined by input In. |
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