Functions, Variables and Expressions

All of the math functions can be found in the include/nreal.h file. You can easily declare your own functionsin your own .h file.

Arithmetic Operators  
* Multiply
/ Divide
+ Plus
- Subtract
Relational Operators  
< Less than
> Greater than
<= Less than or equal to
>= Greater than or equal to
== Equal to
!= Not equal to
Logical Operators  
&& And
|| Or
! Not
Conditional Expression  
expr1?expr2:expr3 If expr1 is true (non-zero), then to expr2, else do expr3
Global Variables  
time the current frame number.
Image Variables These are variables carried by each node.
parameterName the value of parameterName from inside that node.
nodeName.parameterName the value of parameterName in nodeName from outside of that node.
parameterName@@time

This allows you to access a value at a different frame. For example:

Blur1.xPixel@@(time-3) will look at the value from 3 frames earler.

bytes The number of bytes in that image. This takes the input bit-depth when called from inside of the node, and the output bit-depth when called from outside of the node.
width width of the image. This takes the input width when called from inside of the node, and the output width when called from outside of the node.
height height of the image. This takes the input height when called from inside of the node, and the output height when called from outside of the node.
dod[0], dod[1], dod[2], dod[3] The variable for the Domain of Definition xMin, yMin, xMax, yMax, respectively.
In-Node Variables These are channel variables used in some nodes like ColorX, LayerX, Reorder, etc. Check the documentation for specific support of any variable.
nr, ng, nb, na, nz New red, green, blue, alpha, Z channel
r, g, b, a, z Original red, green, blue, alpha, Z channels
l Luminance channel for Reorder
n Null channel. Strips out the alpha in Reorder when used like this: rgbn
r2, g2, b2, a2, z2 Second image's channel for LayerX
Math Functions  
abs(x) integer absolute value. abs(-4) = 4. Be careful, as this will return an integer, not a float. Use fabs for float.
cbrt(x) cubic root. cbrt(8) = 2
ceil(x) truncates to next integer. ceil(5.3) = 6
clamp(x, lo, hi) clamps x to between lo and hi.
clamp(1.5,0,1) = 1
exp(x) natural exponent. exp(0) = 1
fabs(x) float absolute value. fabs(-4.1) = 4.1
floor(x) truncates to next lowest integer. floor(5.8) = 5
fmod(x,y) float modulus. Returns the remainder in float.
fmod(11.45,3) = 2 , ie, (3x3+2.45 = 11.45)
log(x) natural log. log(1) = 0
log10(x) returns base 10 log. log10(10) = 1
M_PI A variable set to pi at 20 decimal places.
max(a,b) returns maximum between a and b.
max(5,10) = 10
max3(a,b,c) returns maximum between a, b, and c.
max3(5,2,4) = 5
min(a,b) returns minumum between a and b.
min(5,10) = 10
min3(a,b,c) returns minumum between a, b, and c.
min3(5,2,4) = 2
a%b modulus. 27%20 = 7
pow(x,y) returns x to the y power. pow(2,4) = 16
round(x) rounds number off. Values below x.5 are rounded to x, values equal to or above x.5 are rounded to x+1. round(4.3) = 4
sqrt(x) square root. sqrt(9) = 3
Noise Functions These are ideal for WarpX and ColorX.
noise(x) 1 dimensional cubic spline interpolation of noise
noise2d(x,y) 2d noise
noise3d(x,y,z) 3d noise
noise4d(x,y,z,time) 4d noise, with time as the last value
lnoise(x) 1d linear interpolation of noise
lnoise2d(x,y) 2d noise
lnoise3d(x,y,z) 3d noise
lnoise4d(x,y,z,time) 4d noise
fnoise(x,xScale) 1d fractal noise based on noise()
fnoise2d(x,y,xScale,yScale)  
fnoise3d(x, y, z, xScale, yScale, zScale)  
turbulence(x, xScale) A cheaper, rougher version of fnoise().
turbulence2d(x, y, xScale, yScale ) continuous 2d noise
turbulence3d(x, y, z, xScale, yScale, zScale) continuous 3d noise
rnd(seed) hash-based pseudo-random numbers. Non-hash based RNG (like rand() or drand48()) should not be used in Shake because they can't be reproduced from one machine to another, and even on the same machine, repeated evaluations of the same node at the same time would produce different results.
rnd1d(seed, x) 1d random value
rnd2d(seed,x,y) 2d random value
rnd3d(seed,x,y,z) 3d random value
rnd4d(seed,x,y,z,w) 4d random value
Trig Functions (in radians)  
M_PI A variable set to pi at 20 decimal places.
acos(A) arc cosine in radians
asin(A) arc sine
atan(A) arc tangent
atan2(y,x) returns the radian verifying sin(a) = y and cos(a) = x.
cos(A) cosine
sin(A) sin
Trig Functions (in degrees)  
Hmmm, yummy trigonometry! Welcome back. For those of you who may have forgotten, here is a helpful chart for some commonly used equations.
acosd(A) arc cosine in degrees
asind(A) arc sine in degrees
atand(A) arc tangent in degrees
atan2d(y,x) returns the angle verifying sin(a) = y and cos(a) = x.
cosd(A) cosine in degrees
distance(x1,y1,x2,y2) calculates the distance between two points, (x1,y1) and (x2, y2)
sind(A) sin in degrees
tand(A) tangent in degrees
String Functions  
stringf( "xyz", ...)

Since you basically can write books on this, here is an example. Otherwise, we recommend purchasing a book on C. There are also several examples under the Scripts documentation. This example takes the scriptName parameter and uses the system function echo to print it:

extern "C" int system(const char*); 
const char *z= stringf("echo %s",scriptName); 
system(z);
printf( "xyz", ...)  
strsub(
  const char *string,
  int offset,
  int length
)
extracts a string from another string.
Curve Functions

The curve functions with implicit time (Linear, CSpline, etc) all imply that time is the first argument, ie, these following statements are identical:

LinearV(time,0,1@1,20@20)
Linear(0,1@1,20@20)

You can, however, adjust the time value explictly with the V version of each curve type. For more infomation on spline types, jump to About Splines.

These are the codes for the cycle type:

0 = KeepValue
1 = KeepSlope
2 = RepeatValue
3 = MirrorValue
4 = OffsetValue

biasedGain(x,gain,bias) Gives a smoothly ramped interpolation between 0 and 1, similar to Shake's contrast curve. gain increase the contrast, and bias offsets the center.
Linear(cycle,
value@key1,
value@key2,
...)
Linear interpolation from value at key1 to value at key2, etc.
LinearV(time_value, cycle, value@key1,
value@key2,
...)
Linear interpolation from value at key1 to value at key2, etc.
CSpline(cycle,
value@key1,
value@key2,
...)
Cardinal-spline interpolation, a.k.a. Catmull-Rom splines
CSplineV(time_value, cycle, value@key1,
value@key2,
...)
Cardinal-spline interpolation, a.k.a. Catmull-Rom splines
JSpline(cycle,
value@key1,
value@key2,
...)
Jeffress-spline interpolation

JSplineV(time_value, cycle, value@key1,
value@key2,
...)

Jeffress-spline interpolation
NSpline(cycle,
value@key1,
value@key2,
...)
Natural-spline interpolation
NSplineV(time_value, cycle, value@key1, value@key2,...) Natural-spline interpolation

Hermite(cycle,
[value,tangent1,tangent2]@key1,
[value,tangent1,tangent2]@key2,
...)

Hermite-spline interpolation
HermiteV(time_value, cycle,
[value,tangent1,tangent2]@key1,
[value,tangent1,tangent2]@key2,
...)
Hermite-spline interpolation