">  ## Detailed Look into Mograph Formula Effector

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Detailed look into mograph formula effector and formula appendix for writing your own formulas…

### Practice

(We will create a example scene in order to test our formulas)

Create a cloner and feed it with a plane or poly object. Add formula effector. Your cloner mode would be Object in this example. Create a sphere an drag this object to cloner’s object field. Set distribution as Polygon Center. Now it’s time to set our formula.

On formulaeffector tab you’ll find an input text area titled as Formula. We would write any kind of formulas using Cinema 4D’s formula appendix.

In this example we have used clamp(0;1;(id<=t) * (t-id*f))  By default it’s explained several appendix usage under formula effector.

• px,py,pz – Position
• rx,ry,rz – Rotation
• sx,sy,sz – Scale
• id – Object Index
• count – Object Count
• falloff – Falloff weight

And also notice that we have one t and f values. T represents Time value and F represents Frequency which we might use in our formula string. If you use it Formula Node in Xpresso you would have a chance to add your custom inputs and read those values but in this example we will only use Formula Effector and a Cloner. So let’s look at formula appendix in depth according to Maxon Cinema 4D Formula Appendix Reference.

## Maxon Cinema 4D Formula Appendix Reference

Mathematical Operators

– Subtraction
* Multiplication
/ Division
( Left Parenthesis
) Right Parenthesis

Units

km Kilometer
m Meter
cm Centimeter
mm Milimeter
um Micrometer
nm Nanometer
mi Mile
yd Yard
ft Foot
in Inch
B Frame Number

Functions

sin(a) Sinus
cos(a) Cosinus
acos(a) Arcus Cosinus
asin(a) Arcus Sinus
tan(a) Tangent
atan(a) Arcus Tangent
cosh(a) Cosinus Hyerbolicus
sinh(a) Sinus Hyerbolicus
tanh(a) Tangent Hyerbolicus
floor(a) Round Down
ceil(a) Round Up
round(a) Round
abs(a) Absolute
sqr(a) Square Exponentiation
sqrt(a) Square Root
exp(a) Expontential Function
log10(a) Logarithm to the base of 10
log(a) Logarithm to the base of e
trunch(a) Truncates a number
rnd(a{;b}) Random between 0 and a, opt.b as seed value
pow(a;b) Exponentiation
mod(a;b) Modulo
clamp(a;b;c) Clamps val. of c btw. a & b
min(a;b) Minimum value a or b
max(a;b) Maximum value a or b
(a)<<(b) Bitwise shift to left
(a)shl(b) Bitwise shift to left
(a)<<(b) Bitwise shift to right
(a)shr(b) Bitwise shift to right
len(a;b{;…}) Vector Length

Logical Operators

= Equal Compare
== Equal Compare
> Greater Than
< Less Than
>= Greater than or Equal compare
<= Less than or Equal Compare
!= Not Equal Compare
! Not
|| bzw.or or
&& bzw. and and
& Bitwise And
| Bitwise Or
^ Bitwise Xor
~ Bitwise Not
?(a;b) Condition, If Statemtn: a, then b

Constants

e The Constant e ( Euler’s Number) = 2.71828
pi The Constant Pi (Ludolph’s Number) = 3.14159
pi05 Constant of Half of Pi
pi2 Constant of 2* Pi
piinv Constant of inverse Pi
pi05inv Constant of inverse of half of Pi
pi2inv Constant of Inverse of 2*Pi
Units

A custom value can be entered, independently of any preset values.

Tip:
If you change the basic units in the preferences, e.g., from meters to millimeters, only the measurement units are changed, not existing numerical values. For example, if an object has a width of 10 meters, but you then change the basic units to millimeters, the object will then have a width of 10 millimeters. If you wish to scale the objects to reflect the change in units, group all the objects and scale the group using the Coordinate manager.
Functions

Tip:
Function arguments must be bracketed. The number of open brackets must equal the number of close brackets. Functions may be nested: sin(sqr(exp(pi))).

Trigonometric function arguments will always be interpreted as degrees. Hence, the entry sin(2*pi) does not reflect the calculation of a sine of 360° but rather of approx. 6.283°.

General

When typing in a formula for the spline or Formula time curve, the arguments of trigonometric functions are in radians. However, when entering values in parameter text boxes, trigonometric functions always use degrees.

The function parser has the most important arithmetic operators built in. You can combine operations freely, for example: 2km + exp(sin(4mm*pi)) / ((sin(14cm))^2 + (cos(14cm))^2).

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