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Warframe And Curve Approximations (With Nova's Buttocks) (Part Seven)


Renegade343
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So, from Part Four, I received the following request: 

 

Nova's shiny buttocks~

And so, now that I have a Nova, I shall complete this now. 

 

So, doing the routine Arsenal screen manipulations (read previous parts if you do not get what I mean), I obtained the following image (dashed box indicates the area we will be focusing on) (and for the record, almost white on white makes for a very difficult time to determine whether a point is on the curve of Nova's buttocks): 

 

e18xAGS.png

 

And then, rotating the image π/4 radians anticlockwise, scaling the axes to be in meters (110.27 PPI, image size: 0.03133m x 0.02188m), I then first plotted three points (D, F, and H): 

 

A9RE1gc.png

 

Then, using polynomial interpolation (Monomial Basis), I obtained the following function (and my calculator has been revived. Turned out that the calculator was suffering from low memory) (and the scanner is still broken) (and if you do not know what polynomial interpolation is, either read part four or this: Given a set of points, find a polynomial function that passes said set of points): 

 

roPqHKs.png

 

However, this is not accurate enough, so I then made another point, known as point E = (0.02213, 0.01303), and used the Monomial Basis again to obtain this function (now a cubic): 

 

yz66Em6.png

 

This curve is more accurate, but still not enough (by my standards). So, I plotted another point, known as point G = (0.00187, 0.00853), and used the Monomial Basis (yet again) to obtain this function (now a quadric [and see the pattern now?]): 

 

L3lTv8C.png

 

As it can be seen, this is very, very accurate, only deviating at around x = 0.0028, but if I were to plot another point at the end, the polynomial function calculated will be almost, if not exactly, identical to the curve of Nova's buttocks (but I think my calculator would die if I have to do that [and it is already at its limit with trying to solve five simultaneous equations already]) (and not to mention that I am lazy). 

 

And so, the quartic function is the final version of this piece of art. And next time, this request: 

 

How about approximating Lokis famous 'grin'? 

 

And at this point, I feel a bit like Wizard Howl, in terms of being skilled and lazy.

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