So, I remember a while back there was a maths competition and we were given a curve that we needed to write an equation for. I just skipped the question since I didn't even know where to begin. I remember it was one among the last few questions of the paper and it was worth a lot of points.
I don't really remember what the curve looked like; it was something spirally, but I can't recall it to save my life right now.
So, I drew this curve in Inkscape (it's a Bézier curve. Or a few of them linked together, according to Wikipedia. If it's required I will post the whole path). And I would like to write the equation for it (with someone's help, obviously).
I was always a bit bad with curves, graphs and lines, but I want to understand them better. So, I was hoping someone could explain the process of deriving the equation for a curve.
P.S: I'd like it if you could use another curve (it can be something simpler, but try avoiding something overly complicated) so I can crack this one on my own, but if you feel like using this curve as an example I won't mind.
EDIT
So have been browsing the internet, read a few Wikipedia entries about Bazier curves, and I understand how they're drawn (mostly the GIFs helped, haha), but I am still stumped when it comes to mathematically representing a Bézier curve. Also, I will add this image, which is the path and its control points (at the end of the blue lines; I didn't paint them in):
And also, the contents of the .tex file for the shape.
%LaTeX with PSTricks extensions %%Creator: 0.48.2 %%Please note this file requires PSTricks extensions \psset{xunit=.5pt,yunit=.5pt,runit=.5pt} \begin{pspicture}(451.46875,34.25392151) { \newrgbcolor{curcolor}{1 0 0} \pscustom[linewidth=3,linecolor=curcolor] { \newpath \moveto(450.48448,1.10834551) \curveto(404.89404,41.45133951)(333.34998,42.21654151)(281.90128,9.03018551) \curveto(258.09407,-6.32636849)(228.42388,9.91159551)(202.75741,15.38398551) \curveto(145.68728,27.55199551)(85.852286,40.32786151)(28.08402514,26.23698551) \curveto(18.5710181,23.91656551)(9.403556,20.24334551)(0.681686,15.78116551) } } \end{pspicture}
Thanks!