Formulas

This article describes the examples of formulas you can use in Animation mode to set up custom behaviors.

Functions

Syntax	Description	Use Examples
random(YOUR_MAX_VALUE)	Random integer in the range from 0 to YOUR_MAX_VALUE	random(234)
random(YOUR_MIN_VALUE, YOUR_MAX_VALUE)	Random integer in the range from YOUR_MIN_VALUE to YOUR_MAX_VALUE	random(1, 100)
getLocalPositionX('YOUR OBJECT NAME')	Local X-coordinate of the first object that comes across in the scene with the name YOUR OBJECT NAME	getLocalPositionX('car') + 1
getGlobalPositionX('YOUR OBJECT NAME')	Global X-coordinate of the first object that comes across in the scene with the name YOUR OBJECT NAME	getGlobalPositionX('car') + 1
getLocalPositionY('YOUR OBJECT NAME')	Local Y-coordinate of the first object that comes across in the scene with the name YOUR OBJECT NAME	a + getLocalPositionY('airplane') * 2
getGlobalPositionY('YOUR OBJECT NAME')	Global Y-coordinate of the first object that comes across in the scene with the name YOUR OBJECT NAME	a + getGlobalPositionY('airplane') * 2
getLocalPositionZ('YOUR OBJECT NAME')	Local Z-coordinate of the first object that comes across in the scene with the name YOUR OBJECT NAME	getLocalPositionZ('My Object') - 5
getGlobalPositionZ('YOUR OBJECT NAME')	Global Z-coordinate of the first object that comes across in the scene with the name YOUR OBJECT NAME	getGlobalPositionZ('My Object') - 5
getLocalRotationX('YOUR OBJECT NAME')	Local X-angle in degrees of the first object on the scene named YOUR OBJECT NAME	getLocalRotationX('Plane')
getGlobalRotationX('YOUR OBJECT NAME')	Global X-angle in degrees of the first object on the scene named YOUR OBJECT NAME	getGlobalRotationX('Plane')
getLocalRotationY('YOUR OBJECT NAME')	Local Y-angle in degrees of the first object on the scene named YOUR OBJECT NAME	getLocalRotationY('Plane')
getGlobalRotationY('YOUR OBJECT NAME')	Global Y-angle in degrees of the first object on the scene named YOUR OBJECT NAME	getGlobalRotationY('Plane')
getLocalRotationZ('YOUR OBJECT NAME')	Local Z-angle in degrees of the first object on the scene named YOUR OBJECT NAME	getLocalRotationZ('Plane')
getGlobalRotationZ('YOUR OBJECT NAME')	Global Z-angle in degrees of the first object on the scene named YOUR OBJECT NAME	getGlobalRotationZ('Plane')
getGlobalSizeInMetersX('YOUR OBJECT NAME')	Returns the X-size of a physical body in meters. The global AABB (axis aligned bounding box) is used	getGlobalSizeInMetersX('Phys Mesh')
getGlobalSizeInMetersY('YOUR OBJECT NAME')	Returns the Y-size of a physical body in meters. The global AABB (axis aligned bounding box) is used	getGlobalSizeInMetersY('Phys Mesh')
getGlobalSizeInMetersZ('YOUR OBJECT NAME')	Returns the Z-size of a physical body in meters. The global AABB (axis aligned bounding box) is used	getGlobalSizeInMetersZ('Phys Mesh')
getViewportWidth()	Returns width of viewport in pixels	getViewportWidth()
getViewportHeight()	Returns height of viewport in pixels	getViewportHeight()

System Variables

Name	Description	Use Examples
origin	The value assigned to the previous keyframe. In the first keyframe, it is equal to the value from the scene.	origin+10
iterator	The number in the order of the keyframe in the clip to which this keyframe belongs. The countdown starts from 0.	cos(2*pi*iterator/(amount-1))*10
amount	The number of keyframes in the animation track that this keyframe belongs to.	sin(2*pi*iterator/(amount-1))*10
pi	Pi number	2piR

Object Variables

Syntax	Description	Use Examples
${object name}.variableName	User's custom variable	${My character}.countOfCollectedCoins
Letters, numbers, symbols _ -	Variables created within a certain animation timeline that are applied to it only.	Var2*25 , SomeUsersVar-5 , randomDistance

Operations and Functions

Arithmetic and Assignment Operators

Operator	Definition	Use Examples
+	Addition between x and y.	x + y
-	Subtraction between x and y.	x - y
*	Multiplication between x and y.	x * y
/	Division between x and y.	x / y
%	Modulus of x with respect to y.	x % y
^	x to the power of y.	x ^ y
:=	Assign the value of x to y. Where y is either a variable or vector type.	y := x
+=	Increment x by the value of the expression on the right-hand side. Where x is either a variable or vector type.	x += abs(y - z)
-=	Decrement x by the value of the expression on the right-hand side. Where x is either a variable or vector type.	x[i] -= abs(y + z)
*=	Assign the multiplication of x by the value of the expression on the righthand side to x. Where x is either a variable or vector type.	x *= abs(y / z)
/=	Assign the division of x by the value of the expression on the right-hand side to x. Where x is either a variable or vector type.	x[i + j] /= abs(y * z)
%=	Assign x modulo the value of the expression on the right| | | hand side to x. Where x is either a variable or vector type.	x[2] %= y ^ 2

Equalities and Inequalities

Operator	Definition	Use Examples
== or =	True only if x is strictly equal to y.	x == y
<> or !=	True only if x does not equal y.	x <> y or x != y
<	True only if x is less than y.	x < y
<=	True only if x is less than or equal to y.	x <= y
>	True only if x is greater than y.	x > y
>=	True only if x greater than or equal to y.	x >= y

Boolean Operations

Operator	Definition	Use Examples
true	True state or any value other than zero (typically 1).
false	False state, value of exactly zero.
and	Logical AND, True only if x and y are both true.	x and y
mand	Multi-input logical AND, True only if all inputs are true. Left to right short-circuiting of expressions.	mand(x > y, z < w, u or v, w and x)
mor	Multi-input logical OR, True if at least one of the inputs are true. Left to right short-circuiting of expressions.	mor(x > y, z < w, u or v, w and x)
nand	Logical NAND, True only if either x or y is false.	x nand y
nor	Logical NOR, True only if the result of x or y is false.	x nor y
not	Logical NOT, Negate the logical sense of the input.	not(x and y) == x nand y
or	Logical OR, True if either x or y is true.	x or y
xor	Logical XOR, True only if the logical states of x and y differ.	x xor y
xnor	Logical XNOR, True iff the biconditional of x and y is satisfied.	x xnor y
&	Similar to AND but with left to right expression short circuiting optimization.	(x & y) == (y and x)
|	Similar to OR but with left to right expression short circuiting optimization.	(x | y) == (y or x)

General Purpose Functions

Function	Definition	Use Examples
abs	Absolute value of x.	abs(x)
avg	Average of all the inputs.	avg(x,y,z,w,u,v) == (x + y + z + w + u + v) / 6
ceil	Smallest integer that is greater than or equal to x.
clamp	Clamp x in range between r0 and r1, where r0 < r1.	clamp(r0,x,r1)
equal	Equality test between x and y using normalized epsilon.
erf	Error function of x.	erf(x)
erfc	Complimentary error function of x.	erfc(x)
exp	e to the power of x.	exp(x)
expm1	e to the power of x minus 1, where x is very small.	expm1(x)
floor	Largest integer that is less than or equal to x.	floor(x)
frac	Fractional portion of x.	frac(x)
hypot	Hypotenuse of x and y.	hypot(x,y) = sqrt(x*x + y*y)
iclamp	Inverse-clamp x outside of the range r0 and r1. Where r0 < r1. If x is within the range it will snap to the closest bound.	iclamp(r0,x,r1)
inrange	In-range returns 'true' when x is within the range r0 and r1. Where r0 < r1.	inrange(r0,x,r1)
log	Natural logarithm of x.	log(x)
log10	Base 10 logarithm of x.	log10(x)
log1p	Natural logarithm of 1 + x, where x is very small.	log1p(x)
log2	Base 2 logarithm of x.	log2(x)
logn	Base N logarithm of x. where n is a positive integer.	logn(x,8)
max	Largest value of all the inputs.	max(x,y,z,w,u,v)
min	Smallest value of all the inputs.	min(x,y,z,w,u)
mul	Product of all the inputs.	mul(x,y,z,w,u,v,t) == (x*y*z*w*u*v*t)
ncdf	Normal cumulative distribution function.	ncdf(x)
nequal	Not-equal test between x and y using normalized epsilon.
pow	x to the power of y.	pow(x,y) == x ^ y
root	Nth-Root of x. where n is a positive integer.	root(x,3) == x^(1/3)
round	Round x to the nearest integer.	round(x)
roundn	Round x to n decimal places where n > 0 and is an integer.	roundn(x,3) roundn(1.2345678,4) == 1.2346
sgn	Sign of x, -1 where x < 0, +1 where x > 0, else zero.	sgn(x)
sqrt	Square root of x, where x >= 0.	sqrt(x)
sum	Sum of all the inputs.	sum(x,y,z,w,u,v,t) == (x + y + z + w + u + v + t)
swap <=>	Swap the values of the variables x and y and return the current value of y.	swap(x,y) or x <=> y
trunc	Integer portion of x.	trunc(x)

Trigonometry Functions

Function	Definition	Use Examples
acos	Arc cosine of x expressed in radians. Interval [-1,+1]	acos(x)
acosh	Inverse hyperbolic cosine of x expressed in radians.	acosh(x)
asin	Arc sine of x expressed in radians. Interval [-1,+1]	asin(x)
asinh	Inverse hyperbolic sine of x expressed in radians.	asinh(x)
atan	Arc tangent of x expressed in radians. Interval [-1,+1]	atan(x)
atan2	Arc tangent of (x / y) expressed in radians. [-pi,+pi]	atan2(x,y)
atanh	Inverse hyperbolic tangent of x expressed in radians.	atanh(x)
cos	Cosine of x.	cos(x)
cosh	Hyperbolic cosine of x.	cosh(x)
cot	Cotangent of x.	cot(x)
csc	Cosecant of x.	csc(x)
sec	Secant of x.	sec(x)
sin	Sine of x.	sin(x)
sinc	Sine cardinal of x.	sinc(x)
sinh	Hyperbolic sine of x.	sinh(x)
tan	Tangent of x.	tan(x)
tanh	Hyperbolic tangent of x.	tanh(x)
deg2rad	Convert x from degrees to radians.	deg2rad(x)
deg2grad	Convert x from degrees to gradians.	deg2grad(x)
rad2deg	Convert x from radians to degrees.	rad2deg(x)
grad2deg	Convert x from gradians to degrees.	grad2deg(x)

String Processing

Function	Definition	Use Examples
=, ==, !=, <>, <=, >=, >, <	All common equality/inequality operators are applicable to strings and are applied in a case sensitive manner. In the following example x, y and z are of type string.	not((x <= 'AbC') and ('1x2y3z' <> y)) or (z == x)
in	True only if x is a substring of y.	x in y or 'abc' in 'abcdefgh'
like	True only if the string x matches the pattern y. Available wildcard characters are '*' and '?' denoting zero or more and zero or one matches respectively.	x like y or 'abcdefgh' like 'a?d*h'
ilike	True only if the string x matches the pattern y in a case insensitive manner. Available wildcard characters are '*' and '?' denoting zero or more and zero or one matches respectively.	x ilike y or 'a1B2c3D4e5F6g7H' ilike 'a?d*h'
[r0:r1]	The closed interval [r0,r1] of the specified string. Given a string x with a value of 'abcdefgh' then (see example). Note: Both r0 and r1 are assumed to be integers, where r0 <= r1. They may also be the result of an expression, in the event they have fractional components truncation will be performed. (eg: 1.67 --> 1)	x[1:4] == 'bcde' x[ :5] == x[:10 / 2] == 'abcdef' x[2 + 1: ] == x[3:] =='defgh' x[ : ] == x[:] == 'abcdefgh' x[4/2:3+2] == x[2:5] == 'cdef'
:=	Assign the value of x to y. Where y is a mutable string or string range and x is either a string or a string range. Note: For options 7 and 8 the shorter of the two ranges will denote the number of characters that are to be copied.	y := x y := 'abc' y := x[:i + j] y := '0123456789'[2:7] y := '0123456789'[2i + 1:7] y := (x := '0123456789'[2:7]) y[i:j] := x y[i:j] := (x + 'abcdefg'[8 / 4:5])[m:n]
+	Concatenation of x and y. Where x and y are strings or string ranges.	x + y x + 'abc' x + y[:i + j] x[i:j] + y[2:3] + '0123456789'[2:7] 'abc' + x + y | | | 6. 'abc' + '1234567' (x + 'a1B2c3D4' + y)[i:2j]
+=	Append to x the value of y. Where x is a mutable string and y is either a string or a string range.	x += y x += 'abc' x += y[:i + j] + 'abc' x += '0123456789'[2:7]
<=>	Swap the values of x and y. Where x and y are mutable strings.	x <=> y
[]	The string size operator returns the size of the string being actioned.	'abc'[] == 3 var max_str_length := max(s0[],s1[],s2[],s3[]) ('abc' + 'xyz')[] == 6 (('abc' + 'xyz')[1:4])[] == 4

Control Structures

Structure	Definition	Use Examples
if	If x is true then return y else return z.	if (x, y, z) if ((x + 1) > 2y, z + 1, w / v) if (x > y) z; if (x <= 2*y) { z + w };
if-else	The if-else/else-if statement. Subject to the condition branch the statement will return either the value of the consequent or the alternative branch.	if (x > y) z; else w; if (x > y) z; else if (w != u) v; if (x < y) { z; w + 1; } else u; if ((x != y) and (z > w)) { y := sin(x) / u; z := w + 1; } else if (x > (z + 1)) { w := abs (x - y) + z; u := (x + 1) > 2y ? 2u : 3u; }
switch	The first true case condition that is encountered will determine the result of the switch. If none of the case conditions hold true, the default action is assumed as the final return value. This is sometimes also known as a multi-way branch mechanism.	switch { ase x > (y + z) : 2 * x / abs(y - z); case x < 3 : sin(x + y); default : 1 + x; }
while	The structure will repeatedly evaluate the internal statement(s) 'while' the condition is true. The final statement in the final iteration will be used as the return value of the loop.	while ((x -= 1) > 0) { y := x + z; w := u + y; }
repeat/until	The structure will repeatedly evaluate the internal until statement(s) 'until' the condition is true. The final statement in the final iteration will be used as the return value of the loop.	repeat y := x + z; w := u + y; until ((x += 1) > 100)
for	The structure will repeatedly evaluate the internal statement(s) while the condition is true. On each loop iteration, an 'incrementing' expression is evaluated. The conditional is mandatory whereas the initializer and incrementing expressions are optional.	for (var x := 0; (x < n) and (x != y); x += 1) { y := y + x / 2 - z; w := u + y; }
break break[]	Break terminates the execution of the nearest enclosed loop, allowing for the execution to continue on external to the loop. The default break statement will set the return value of the loop to NaN, where as the return based form will set the value to that of the break expression.	while ((i += 1) < 10) { if (i < 5) j -= i + 2; else if (i % 2 == 0) break; else | | | break[2i + 3]; }
continue	Continue results in the remaining portion of the nearest enclosing loop body to be skipped.	for (var i := 0; i < 10; i += 1) { if (i < 5) continue; j -= i + 2; }
return	Return immediately from within the current expression. With the option of passing back a variable number of values (scalar, vector or string).	return [1]; return [x, 'abx']; return [x, x + y,'abx']; return []; if (x < y) return [x, x - y, 'result-set1', 123.456]; else return [y, x + y, 'result-set2'];
?:	Ternary conditional statement, similar to that of the above denoted if-statement.	x ? y : z x + 1 > 2y ? z + 1 : (w / v) min(x,y) > z ? (x < y + 1) ? x : y : (w * v)
~	Evaluate each sub-expression, then return as the result the value of the last sub-expression. This is sometimes known as multiple sequence point evaluation.	~(i := x + 1, j := y / z, k := sin(w/u)) == (sin(w/u))) ~{i := x + 1; j := y / z; k := sin(w/u)} == (sin(w/u)))
[*]	Evaluate any consequent for which its case statement is true. The return value will be either zero or the result of the last consequent to have been evaluated.	[*] { case (x + 1) > (y - 2) : x := z / 2 + sin(y / pi); case (x + 2) < abs(y + 3) : w / 4 + min(5y,9); case (x + 3) == (y * 4) : y := abs(z / 6) + 7y; }
[]	The vector size operator returns the size of the vector being actioned.	v[] max_size := max(v0[],v1[],v2[],v3[])