Jump to content

Warframe And Curve Approximations (With Saryn's Boot) (Part 5.1)


Renegade343
 Share

Recommended Posts

So, since my laptop decided not to have its F6 button work (meaning no new pictures can be taken), I decided to do a quick consolation thread (again), this time with Saryn's boot. And so, using the Arsenal image from Part Four (with the same assumptions made with the function), I took this image (dashed box indicates the curve we will be approximating): 

 

XyWry3b.png

 

Then, cropping out that portion, I then placed it into Geogebra, and scaled the axis to be in meters, then made the image scale with the zoom button at the correct meter lengths (110.27 PPI, image size: 0.0129m x 0.0011m). Afterwards, since the curve does have one point of inflexion, I assumed it to be a cubic function first, and thus made four points (D, F, H, and J): 

 

TTypHUi.png

 

Afterwards, I used the technique of polynomial interpolation (the Monomial basis) (my scanner went kaput as well, so I cannot show the working here, but it does involve the use of a GDC to calculate the coefficients, since it gets very, very tedious for me to calculate by hand [not to mention that the room that an error could happen would be too high]). And thus, I obtained the function: 

 

GgxINSM.png

 

However, I was not satisfied with the accuracy of the approximation, and decided to plot more points to obtain higher degrees of polynomials in order to get an accurate curve. However, those attempts failed for me, and that got me thinking: 

 

What if I use a piecewise function, since I can see that part of the boot can be approximated to a (a*(x-b)^n) + c function, instead of having one function approximating the whole of the curve?

 

After debating about it whether it was cheating or not, I concluded that there may be some curves in which a piecewise function would be necessary, but I then cautioned myself into not using this technique unless absolutely needed. But anyways, for this time, I did trial and errors (since I am lazy today) with approximating the (a*(x-b)^n) + c function to fit as close to the front portion of Saryn's boot as possible, and obtained this result (Point K is the intersection point we will be interested in): 

 

zW8BSeK.png

 

And so, since I have point K (as it is the intersection point that will result in the piecewise function be approximated rather closely to Saryn's boot curve), I then made the piecewise function, and the result is below: 

 

07YZZLO.png

 

As it can be seen, the piecewise function does approximate the curve of Saryn's boot very closely, only deviating at the point x = 0.00755, as that is the end of the curve as far as we are concerned (since it then goes straight down).

 

However, I will state this again: Piecewise functions will only be used if I can identify that there are two or more functions making up the curve, either by eye or through repeated calculations. If possible, one function will be used to approximate the whole of the curve. 

 

But anyways, there is the result, and I will announce that I may (emphasis on may) take a short break. 

Link to comment
Share on other sites

I was going to ask about the functions you used before I saw them. Thanks for another entertaining read, Renegade. Bring us more of your mathematical genius.

 

Also, do you think that you would be able to derive a function/equation that allows you to approximate the heights of each Warframe in comparison to one another accurately? Or would that be a difficult matter, considering that the meshes are scaled to be the same height in-game (which I really dislike)?

Edited by Kashiki
Link to comment
Share on other sites

beside that the boot-plane is not parallel to the xy-plane ..

aslong you have fun with it ^^

I really want DE(L) to release the value of the angle of rotation in the Arsenal screen, just so I do not have to determine by eye. 

 

Besides, the F6 button was broken on my laptop, so I have to make do. 

 

either you work with a discontinuity on x=0.0075

or srew it and work with the Fourier transform *shudder*

The Fourier transform will make the curve approximation be quite inaccurate, judging by eye. 

Link to comment
Share on other sites

Also, do you think that you would be able to derive a function/equation that allows you to approximate the heights of each Warframe in comparison to one another accurately? Or would that be a difficult matter, considering that the meshes are scaled to be the same height in-game (which I really dislike)?

Now on my mathematics to-do list. 

Link to comment
Share on other sites

Well, I think that's what Llyssa was getting at; using the tool to just do screenshots.

Yeah. Printscreen copies the current monitor output to the clipboard.

 

To actually retrieve it, you'd have to paste it in somewhere.

 

That is/was the old-school way of taking screen shots--print screen, and paste.

 

Since, y'know, you said your F6 key is broken, you can still take new photos that way.

Link to comment
Share on other sites

Yeah. Printscreen copies the current monitor output to the clipboard.

 

To actually retrieve it, you'd have to paste it in somewhere.

 

That is/was the old-school way of taking screen shots--print screen, and paste.

 

Since, y'know, you said your F6 key is broken, you can still take new photos that way.

It is already fixed up in five minutes after that. Turned out it was just bad contact. 

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...