Jump to content

Warframe And Curve Approximations (With A Gif)


Renegade343
 Share

Recommended Posts

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): 

a3jTlcm.gif

 

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): 

 

w2gc9kH.png

BZxsgI3.png

YdbKnHT.png

 

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: 

 

Eov6CYj.png

 

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. 

Link to comment
Share on other sites

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.

Link to comment
Share on other sites

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.

Link to comment
Share on other sites

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. 

Link to comment
Share on other sites

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. 

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
 Share

×
×
  • Create New...