[TOMAJA Micro Video Tutorial] Simple Sinusoidal Function Explanation on Realistic Animation as Example

Resources Expressions
1

Hi there!

after reading this discussion about the sinusoidal function using for different effects (breathing, shaking , wave production, floating , movements, animated objects, etc.) I decided to try to explain it in a simple picture and video (gif) form.

Here is the example expression for a moving part in the X Axis (X Position).

(160 + ( 120 * ( sin ( #DWE# * 2 * pi ) ) ) )

And here is a kind of graphic description of this formula.

2.png1651Ă—924 145 KB

The original speed (2*pi) in the facer creator could be seen at the following gif picture.

34dc4c23e6299cec4c0e55aa8814bd28.gif678Ă—522 882 KB

If somebody is more interested to the mathematical explanation, you could find a great explanation here and here .

Please let me know if you :heart: this kind of TOMAJA Micro Tutorials :wink: Thanks.

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2

This visual aid is awesome. Really clear as opposed to my dense, wordy attempt at explanation :laughing:

3

Your description, however, has also more information… :wink:

4

Putting this here in case someone is looking for a similar alternative with slightly different behavior:

Linear Function, Cycled Motion, but with the same parameters
(where you see 160 that is the “start point”, where you see 120 that is the “distance” and where you see 2*#DWE# that is the “speed”. As you can see, the linear version requires all these inputs more than once :blush:)

Original: (160 + ( 120 * ( sin ( #DWE# * 2 * pi ) ) ) )
vs
Linear: $ (round( floor( 2 * #DWE#+.5 ) / 2 )) = (floor( (2 * #DWE#+.5 ) / 2 )) ? 160 + 120 * (-1 + 2 * ( ( 2 * #DWE#+.5 ) - (floor( 2 * #DWE#+.5 )) ) ) : 160 - 120 * (-1 + 2 * ( ( 2 * #DWE#+.5 ) - (floor( 2 * #DWE#+.5 )) ) ) $

(the +.5 to each #DWE# starts the cycle from the middle rather than from the left side)

Waveform comparison:

Movement comparison:

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