I'm looking for help to understand how to find the parametric equations of this spring drawn in geogebra. Here's the link of the geogebra file which represents the perfect spring I was looking for, where I can move one or both ends of the spring to change its length and its coils width https://www.geogebra.org/m/AtDTCQGw.
The formula I don't understand is $curve(x(A)+(Lt+r+rcos(\pi-wt))e_1-2rsin(\pi-wt)e_2, y(A)+(Lt+r+rcos(\pi-wt))e_2+2rsin(\pi-wt)e_1, t, 0, 1)$.
The problem is not the curve command itself, but the parametric equations: $$ \left\{ \begin{array}{c} x=x(A)+(Lt+r+rcos(\pi-wt))e_1-2rsin(\pi-wt)e_2 \\ y=y(A)+(Lt+r+rcos(\pi-wt))e_2+2rsin(\pi-wt)e_1 \end{array} \right. $$
Most of all I'd like to understand how I can write the parametric equations of a curve (2D or 3D) in general case, simply looking at the drawing of the curve and I'd like to have some good resources at undergrad level (textbooks, preferably) where I can find this information.
Thanks