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


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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~


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