# Warframe And Curve Approximations (With Zephyr's Breast Area) (Part Six)

## Recommended Posts

So, from Part Four, I have received this request:

Zephyr breast feathers fluff

And since I do have a Zephyr, I decided to do it.

So, doing the Arsenal screen manipulations again (see all the other parts to know what I am talking about), I obtained the following picture (dashed box indicates area we will be approximating a curve on): Then, I turned the image π/4 radians clockwise to obtain a function, placed the image into Geogebra and scaled it (110.27 PPI, image size: 0.0304m x 0.01566m). Afterwards, I first used the method of polynomial interpolation (Monomial basis, and obtained the curve from points D, F, G, I, and L (scanner is still broken, so I cannot show the working out): Since that curve is not accurate enough, I then used the Taylor series (since this time, there are no points where x = 0), using points D, F, G and I, and selecting the x-coordinate of point D to be a (see Taylor series formula), and obtained this result (first image is the first derivative of the Taylor series curve):  However, that curve is not accurate as well, which leads me to use a piecewise function to approximate the curve of Zephyr's breast area. So, I first split the curve into two areas: x > 0.015995, and x ≤ 0.015995. The image for the curve approximation when x > 0.015995 is below (using Taylor series [a = 0.02602]):   Afterwards, I then plotted points H, J and L, in which all of them have their x-coordinate ≤ 0.015995, and used polynomial interpolation (Monomial basis) to determine the curve at these points. The result is below (and my calculator died when I tried to calculate five simultaneous equations with it, so I had to make do with four points and some inaccuracy with a cubic function): Once I obtain these two curves, I then found the intersection point that will give me the most accurate curve approximation for a piecewise function, and obtained point N: So, using point N, I finally obtained this piecewise function for Zephyr's breast area: This whole thing took me three hours to calculate, check for errors and such (and I think my calculator is totalled too).

So, next time, this request:

Nova's shiny buttocks~

2muchmath4me

##### Share on other sites

Huh so not even with your skills you could not get the perfect answer ,huh maybe that's why no one draws Zephyr. . .

##### Share on other sites

Huh so not even with your skills you could not get the perfect answer ,huh maybe that's why no one draws Zephyr. . .

To be honest, if my calculator did not die, I could plot an accurate curve using more points and Monomial basis.