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[adaburton]

Added free function bezier to calculate the bezier coefficient for a given point in an animations cycle to resolve #9

[AldaronLau]

I think it would be good to add some tests for this function (check for expected values).

We'll also need a function needs to get the animation progress based on time using std::time::Duration for both time delta and animation speed. Then, adding a test that makes sure the beginning and end of the animation are slower than the middle.

Let me know if you have any questions.

[adaburton]

I based the function off of the red curve pictured in this graph. https://en.wikipedia.org/wiki/B%C3%A9zier_curve#/media/File:Bezier_basis.svg

You could convert a linear animation to this curve by first rasterizing the animation into discrete frames, and then converting as follows:

for frame in frames param * = bezier(frame/sizeof(frames))

something like that. This is a pretty hacky solution though, and I understand the need for tests. But this was the only solution I could think of that was as simple as taking a single f32 and returning one back.

[AldaronLau]

Yeah, I guess there's a few options:

• Calculate all frames
• Use DeCastlejau algorithm to split the curve into parts, to only calculate some frames and use linear interpolation
• There's also a simplified bezier equation I came up with for the Twang crate - if you set some constants, you can simplify it to a piecewise function. I just made a graph of it, if you want to try implementing it (I haven't gotten around to implementing it yet for twang): https://www.desmos.com/calculator/wcqr57xzpn

[AldaronLau]

I should mention that the Twang bezier function is less tunable than the CSS bezier animations. That might be ok for this project though. Just something to keep in mind.

[AldaronLau]

Actually, I just did some experimenting and it's more or less basically an x² algorithm.

[AldaronLau]

Here's what I'm going to use for bezier curve in twang if you choose to base it on that implementation (where performance is big concern): https://www.desmos.com/calculator/3gf8alz4zy (time from -1 start to +1 end)

A nice benefit is that it's a linear function.

[adaburton]

I'm wondering if the way we implement this should depend on how animations are implemented, and therefore we should wait until then to worry about this.

[AldaronLau]

Possibly. I'll let you make the call if you want to wait until more things are in place to implement this.