I'm currently working on a project which requires a lot of easing. A basic sine wave has worked for some parts, but most times I find myself needing a steeper curve. Unfortunately for my animation, I have a brain the size of a walnut, and can't figure out how to do this. I realize this is more of a math question, but still. How do I calculate a steeper curve?

Not quite sure what you mean by easing. What are you using the curve to do?

gor-dee wrote:

Not quite sure what you mean by easing. What are you using the curve to do?

I'm terribly bad at explaining things, sorry.

The red line is a sine wave, how do I calculate something more like the blue line?

y = (sin x)^1/3 looks quite good. Let me see how you would do that in Scratch…

set [X v] to [1]
repeat ()
go to x: (X) y: ([e^ v] of (((1) / (3)) * ([ln v] of ([sin v] of (X))))) //e^ should be green
change [X v] by (1)
end

This works but only for positive half…

gor-dee wrote:

y = (sin x)^1/3 looks quite good. Let me see how you would do that in Scratch…

Oh no… Curse you, Scratch's lack of exponents!!! (Seriously though, why don't they exist, they would take like five seconds to implement and save hours of programming)
Edit:

gor-dee wrote:

set [X v] to [1]
repeat ()
go to x: (X) y: ([e^ v] of (((1) / (3)) * ([ln v] of ([sin v] of (X))))) //e^ should be green
change [X v] by (1)
end

This works but only for positive half…

Positive half is all I'm probably going to need, actually.

What's a sine wave???

FashionMaven wrote:

What's a sine wave???

So imagine you're running around a circle. Now imagine that someone else is watching you from within a one dimensional plane. They can only see if something is moving left to right, not up or down. They would see that you're sort of swinging back and forth. That's basically what a sine wave is.

gor-dee wrote:

set [X v] to [1]
repeat ()
go to x: (X) y: ([e^ v] of (((1) / (3)) * ([ln v] of ([sin v] of (X))))) //e^ should be green
change [X v] by (1)
end

This works but only for positive half…

It worked! I'm not a fan of how long it has to be, but thanks so much for the solution! Do you want me to let you know when the project is done or are you not interested? I will give you credit.

I found that the function y = sin((pi/2) * sin(x)) works very well, and I think it's the shape that you're looking for. If you want it to be even steeper, you can just compose the function with itself, giving you y = sin((pi/2) * sin((pi/2) * sin(x))). Here's a link to a graph comparing the normal sine wave with these two alternatives. Hope this helped.

u8y7541 wrote:

I found that the function y = sin((pi/2) * sin(x)) works very well, and I think it's the shape that you're looking for. If you want it to be even steeper, you can just compose the function with itself, giving you y = sin((pi/2) * sin((pi/2) * sin(x))). Here's a link to a graph comparing the normal sine wave with these two alternatives. Hope this helped.

I just got finished implementing the other workaround but I'll give this one a shot tomorrow(?)

the2000 wrote:

It worked! I'm not a fan of how long it has to be, but thanks so much for the solution! Do you want me to let you know when the project is done or are you not interested? I will give you credit.

Thanks, no need for credit but I'm intrigued as to what you are doing, so I'd love to see it when it's done. However, I looked at @u8y7541's solution and it looks much more like what you were after!