A collection of mathematical shaders. Math shaders can work on color or vector inputs.

#### Abs

Return the absolute value of input.

Return input1 input2.

#### Atan

Return the arctangent of y/x. The resulting value is in the range [-π/2, π/2], using the signs of the two arguments to determine the quadrant of the result.

#### Compare

Compare input1 and input2 with the following operators and return true or false:

• Equal (==)
• Not Equal (!=)
• Greater Than (>)
• Less Than (<)
• Greater Than or Equal (>=)
• Less Than or Equal (<=) Example of a Compare shader used to create a toon shading effect

#### Complement

Return one's complement (1 − input). Also known as reverse video.

#### Cross

Compute the cross product between two vectors, defined as the vector perpendicular to both input vectors, with its direction defined by the right-hand rule.

$$\mathbf{a}\times\mathbf{b}=\left(a_{y}b_{z}-a_{z}b_{y}\,,\quad a_{z}b_{x}-a_{x}b_{z}\,,\quad a_{x}b_{y}-a_{y}b_{x}\right)$$

The length of the cross product can be interpreted geometrically as:

$$\left\Vert \mathbf{a}\times\mathbf{b} \right\Vert=\left\Vert \mathbf{a}\right\Vert \left\Vert \mathbf{b}\right\Vert \sin\theta$$

#### Divide

Return input1 ÷ input2.

#### Dot

Compute the dot product between two vectors as follows:

ab=a x b x +a y b y +a z b z

The result is a scalar value that can be interpreted geometrically as:

ab=abcosθ

where the length of vector a is denoted by

a

and the angle between a and b is θ.

#### Exp

Return the exponential of input, einput. This is the inverse of Ln, see also Pow.

#### Fraction

Returns the fractional part of input. For example, an input of 123.456 would return 0.456.

#### Is Finite

Return false if input is either infinity or NaN, and true otherwise.

#### Length

Return the length of the input vector, with three possible distance definitions:

###### Euclidian

The "ordinary" length of the vector:  $$\sqrt{x^2+y^2+z^2}$$

Euclidian distance squared, which is cheaper to compute:  $$x^2+y^2+z^2$$

###### Manhattan

Measures distance following only axis-aligned directions, which is even cheaper to compute:  $$\left|x\right|+\left|y\right|+\left|z\right|$$

#### Log

Return the logarithm of input to base. The argument must be greater than zero. This is the inverse of Pow.

#### Max

Return the per-component maximum of input1 and input2.

#### Min

Return the per-component minimum of input1 and input2.

#### Modulo

Return input modulo divisor. This is the remainder of the division of input by divisor.

#### Multiply

Return input1 × input2.

Return −input.

#### Normalize

Return a normalized input vector, ie. a unit vector pointing in the same direction.

#### Random

The Random shader outputs a random color from various types of inputs. It is useful to do variations of colors or shader properties for example.

#### Reciprocal

Return the multiplicative inverse of input, ie. 1/input or input−1.

#### Sign

• Return -1 if input < 0
• Return 0 if input == 0
• Return 1 if input > 0

#### Sqrt

Return the square root of input, ie.

$$\sqrt{input}$$

#### Subtract

Return input1 − input2.

#### Trigo

Perform various trigonometric functions on input. The frequency and phase parameters make the most sense for the sine, cosine and tangent functions, but are available on all functions for orthogonality. The units parameter lets you choose between radians and degrees for the argument of sine, cosine, and tangent and for the result of the inverse functions. It has no effect on the hyperbolic functions.

FunctionFormulaUnits AffectsOutput Range
Cosinecos(input × frequency + phase)

argument

[-1, 1]
Sinesin(input × frequency + phase)[-1, 1]
Tangenttan(input × frequency + phase)[-∞, ∞]
Arccosinearccos(input × frequency + phase)

result

[0, π] or [0°, 180°]
Arcsinearcsin(input × frequency + phase)[-π/2, π/2] or [-90°, 90°]
Arctangentarctan(input × frequency + phase)[-π/2, π/2] or [-90°, 90°]
Hyperbolic Cosinecosh(input × frequency + phase)

(nothing)

[1, ∞]
Hyperbolic Sinesinh(input × frequency + phase)[-∞, ∞]
Hyperbolic Tangenttanh(input × frequency + phase)[-1, 1]

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