Warframe And Taylor's Expansion (With Oberon's Front Bulge) (Part Three)

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(I will start to post the link of this series onto my profile page)

So, based on Part Two of this series, I asked viewers what curve do they want me to approximate, and one (the only one) replied with this:

Unfortunately, since I do not have Vauban yet, I promised to make a consolation thread to approximate a function for Oberon's front bulge. So, going to the Arsenal, making Oberon have no animation set, and turning him approximately π/4 radians to his right, I obtained the following picture (dashed box indicates the area we will be approximating the function on [the front bulge]):

Then, I cropped out the area selected, rotated it π/4 clockwise, placed it into Geogebra, set the axis to be in meters, and manipulated it so that the image will scale (110.27 PPI, image size: 0.02511m x 0.01428m) when I zoom in or out. Afterwards, I started to find the tangent of the end limits of the cropped image, and find the point where dy/dx = 0. The result is below:

Then, using the tangent gradients of Points E, G, and I, I plotted a dy/dx vs. x graph, and obtained this function:

I differentiated that function again to obtain f''(x) = -18.01962.

Now, with all the data obtained, I used the Taylor series (actually, for the more mathematically aware people, they will know that I am actually using a variant of the Taylor series known as the Manclaurin series, which is still basically the Taylor series, but with a = 0. Besides, the word 'Taylor' is easier to spell than 'Manclaurin' from memory):

f(x) = f(a) + f'(a)*(x-a) + (f''(x)/2!)*(x-a)^2 + ... (we will only be interested in up to f''(x), since based on the data obtained, f'''(x) = 0, and thus anything higher than f''(x) = 0)

Let a = 0,

f(0) = 0.00584

f'(0) = 0.24393

f''(0) = -18.01962

f(x) = -(9.00981x^2) +  0.24393x + 0.00584

And so, here is the result:

Now, as we can see, the approximate function does fit rather well with Oberon's front bulge, only deviating slightly at and near the vertex, so it can be said that this time, the Taylor series has managed to approximate a pretty accurate polynomial function for Oberon's front bulge.

However, some members may argue that based on the first image, I have not taken the full image of the bulge, and that can be a valid argument, depending on how the member see where is the end of the bulge. So, next time, I will take a wider image, and use polynomial interpolation (the Monomial basis method) to check on Oberon's front bulge (and see if I can replicate the result using Taylor series).

But all in all, a pretty relaxing activity.

And I shall ask again: What curve in Warframe do you want me to approximate next time?

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Saryn's underboob or Rhino's codpiece

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Saryn's underboob or Rhino's codpiece

I do not have Rhino, but I do have Saryn. So at least you can get that probably next weekend, or maybe on Tuesday.

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This is very confusing.

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This is very confusing.

Which part?

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This is ,I don't understand why tho but this is just something that is why ,WHAT IS THIS AND WHY!?

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This is ,I don't understand why tho but this is just something that is why ,WHAT IS THIS AND WHY!?

Approximating a polynomial function to a curve. In this case, it is approximating a polynomial function to Oberon's front bulge, and the steps to do it (as well as the result) is art.

I... uh... I...

uh.

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I... uh... I...

uh.

Next round, it will be more interesting, since I am taking in Angius's request for approximating a polynomial function for Saryn's breasts.

At least, I hope it does.

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Yet in 10th grade, I'm still being taught about theorems of angles...

-.-

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Yet in 10th grade, I'm still being taught about theorems of angles...

-.-

This is what I do in my spare time: Study the areas of mathematics that are not taught by my school course, then apply it to something.

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This is what I do in my spare time: Study the areas of mathematics that are not taught by my school course, then apply it to something.

Oh god, can't imagine how you have the energy.

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*Maclaurin ;-)

Really a shame that these things are not taught in your school. This is when math starts getting fun!

Edited by Dhrekr
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(I will start to post the link of this series onto my profile page)

But all in all, a pretty relaxing activity.

And I shall ask again: What curve in Warframe do you want me to approximate next time?

If not the curve of the reaper prime.

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If not the curve of the reaper prime.

I am going to need a good view of it (and definitely need to get one, since I do not have it anyways).

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I am going to need a good view of it (and definitely need to get one, since I do not have it anyways).

Edited by Jacate
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but on math it is

MATH

not even once