# Warframe And Curve Approximations (With A Gif)

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So, I delayed this series for two weeks due to various computer and program problems, and I said this:

I promise by the next weekend, it will be fixed, and I will do something to make up for it.

The first promise is done, so I went and fulfil the second promise (warning: Since this is rather, for a lack of a better acronym, NSFW, I have hidden the images and the gif in spoilers.):

Now, this gif came from a place (and also appears in various threads):

While I did cringe a bit from viewing this, the mathematical part of my mind took over, and analysed it. It then noticed that this gif seems to be executing simple harmonic motion (look it up if you do not know) (at least on the horizontal plane), and thus raised this question:

What is the approximate sinusoidal wave of this motion (horizontal component only)?

Thus, I took the gif, went into Final Cut Pro 7, and slowly analysed the clip frame by frame, finding the maximum and minimum values of the motion (and their associated times [30FPS]), as well as the equilibrium point. Afterwards, I took still images of these points (four in total, but only took three still images, as the fourth one is also the equilibrium point [but when time = 0.45s]), then pasted them into Geogebra (first image is at first equilibrium point, second is at minimum point, and third is at maximum point):

Taking the x-values of these points, then shifting it by 0.111 (so that equilibrium point can be 0), I then plotted a graph of time vs. distance from equilibrium point. I then used the equation:

a * sin(bx + c) + d

And started to find the function:

a * sin(bx + c) + d

a = (First max or min point - Second min or max point) / 2

a = (-0.01326 - 0.01365) / 2

a = -0.013455

Period = 2π/b

14/15 = 2π/b

b = 5.864

d = (Max + min) / 2

d = (0.01365 - 0.01326) / 2

d = 0.000195

Let x = 0.0333, y = 0,

0.01346 * sin(0.195 + c) + 0.000195 = 0

-0.0146 = sin(0.195 + c)

arcsin(-0.0146) = 0.195 + c

Since arcsin(θ) ≈ θ when θ is very, very small,

-0.0146 = 0.195 + c

c = -0.21

And so, I plotted the graph, and the result is thus:

It is relatively accurate (and thus does prove that the horizontal motion executes simple harmonic motion [to a good degree]), although it could be improved with installing better programs to track a certain point in a clip (or maybe I could play around with Final Cut Pro 7 more).

But anyways, here is my artwork of combining Warframe and mathematics.

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This is bvery good, I will be able to use the function to imitate the same butt physics in a game I am making

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and slowly analysed the clip frame by frame

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What else can I do?

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This is perhaps the first time I've ever seen the concept of oscillations used to deduce something related to games.

Albeit in the end, the question repeats itself : Was that absolutely necessary or profitable in some way?

I feel like I just lost both time and brain cells reading this. xD

(the concept of using up time to remember things that have no considerable value)

Well, good job deducing that. I guess.

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This is perhaps the first time I've ever seen the concept of oscillations used to deduce something related to games.

Albeit in the end, the question repeats itself : Was that absolutely necessary or profitable in some way?

Practice makes perfect in mathematics.

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Practice makes perfect in mathematics.

This is where I can finally say : I hate maths particularly for this.

It's the most mechanical way of developing logical processing. D:

Practice never makes perfect.

Effort does not equal an end.

It just adds up. Well, I guess I didn't learn anything reading this, except that there are other programs I did not know of to plan graphs with.

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Practice never makes perfect.

Effort does not equal an end.

It just adds up. Well, I guess I didn't learn anything reading this, except that there are other programs I did not know of to plan graphs with.

At least you know how to calculate the function of a sine wave given some points.

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Mathemagic, at its finest...

Edited by Ognj

huehuehue

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dat &amp;#&#33; o_o

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Mathemagic, at its finest...

It does beat textbook math questions, right?

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Contents from post #13.

Why would they lock it for?

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Why would they lock it for?

reasons, lol

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reasons, lol

It is a mathematical approach to something questionable (and the approach is considered normal art, not to mention the approach is nothing questionable).

After all, I did not make the gif. I just approximated the formula for the horizontal oscillation of the gif.

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Now, this gif came from a place

Was that a horrible place?

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Was that a horrible place?

I do not know.

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Ok now... am i the only who stopped at "dat &amp;#&#33;" ??!

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its a little NSFW I would put a tag, I just got a dirty look from a coworker/friend lol, but this is.. interesting. and headache inducing. I will never be able to math like this.

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Was that a horrible place?

well yes... only a horrible place could possibly bring this up and a bout...

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you're thinking too much about &amp;#&#33; yo

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Was that a horrible place?

I see what you did there. It's a horrible place indeed *wink*

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