Renegade343 Posted September 13, 2014 Share Posted September 13, 2014 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~ Link to comment Share on other sites More sharing options...
-FrostByte- Posted September 13, 2014 Share Posted September 13, 2014 wow, some of your maths went over my head. +1 Link to comment Share on other sites More sharing options...
(XBOX)UndyingNoble6 Posted September 13, 2014 Share Posted September 13, 2014 2muchmath4me Link to comment Share on other sites More sharing options...
Oxin Posted September 13, 2014 Share Posted September 13, 2014 Huh so not even with your skills you could not get the perfect answer ,huh maybe that's why no one draws Zephyr. . . Link to comment Share on other sites More sharing options...
Renegade343 Posted September 13, 2014 Author Share Posted September 13, 2014 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. Link to comment Share on other sites More sharing options...
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