In a tutorial in Online Help we learn that +- 100 as Accel and Decel level will make a sinus form, as it does perfectly well. But I am trying to figure out the math behind it. Can anyone enlighten me a bit please?
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Just to be clear, the +/- button in the calculator is the negation key, so following the keypresses in the tutorial means that you entered the value -100%.
This is not easy to explain with just text but let's try....
- to my understanding:
An Acceleration of 0% represents a linear transition to the next step, the exit vector, has the same angle as the direction to the next stepvalue.
An Acceleration of -100% represents a ease-out towards the next stepvalue, the exit vector is horizontal.
A Deceleration of 0% represents a linear transition from previous stepvalue, the entry vector has same angle as direction from the previous stepvalue.
A Deceleration of -100% represents an ease-in from previous stepvalue, the entry vector, is is horizontal.
When entry and exit vector both are horizontal the transition is smooth, as a sinewave
Acc/Dec with even lower value than -100% represents direction vectors further away than horizontal, in other words in the wrong direction of the target.
Acc/Dec with positive values represents the equivalent vectors on the other side of the vector of the linear transition, representing a more aggressive entry/exit
for testing try the following with some fixtures selected:
Step 1 + 2
When the sum of Accel and Decel = -200, the entry and exit vectors are parallel
When entry and exit vector are parallel, the transition is stepless/smooth
The math behind is bezier curves, the valueranges are normalized for easier interaction.
Ok, so step 1 has a Beziere where point 1 and 3 are fixed and point 2 is variable, and with 2 steps point 1,3 and 5 are fixed and 2 and 4 are variable? And if I am right, does the variations in point 2 and 4 influence the common point 3?
I see that when I use your excample 2 on my leftside fixtures and excample 3 on my righthand fixtures I am getting close to sin/cosine. It seems like commandline is the only way to input levels <-100 >100.
- seems like the calculator is currently limited to +- 100%
both encoderturn and commandline can be used to over/undershoot.
if you select the "Move Handles" tool in phaser editor, you can see the bezier control vectors, - also in 1D-layout
the visualization of bezier vectors has some glitches in 1D layout, when next step also is previous step.
- so add a third step, to properly visualize in 1D layout the vectors for step 1