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[])