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[])
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