Can someone review a problem I am having related to coordinates and curve fitting
Part 1
I have a curve in the coordinate frame XY. This curve is represented by a list of $(x,y)$ coordinates
I also have a list of "distances" calculated as the distance between $(x_1,y_1)$ and $(x_0,y_0)$ and so on
For example, let's say I have the points:
$(0,0), (1,1), (1,2), (3,1), (5,5)$ then the list of distance would be $[\sqrt 2, 1, \sqrt 3 ,\sqrt 6]$
Part2
If I take only the X component $([0,1,1,3,5])$ and I try to fit a cuadratic equation $y=a+bx+cx^2$ with y being the distances, am I representing the curve parametrically?
I mean I can understand curve fitting when y is y and x is x but can someone understand what kind of coefficients I am finding if I curve fit only one component (x or y) versus the distance?
I am sorry for the confused question, I am confused.
EDIT: I made a huge mistake of interpretation. Here
I try to fit a cuadratic equation $y=a+bx+cx^2$ with y being the distances, am I representing the curve parametrically?
the correct way was
I try to fit a cuadratic equation $y=a+bx+cx^2$ with y being the coordinates and x the distances, am I representing the curve parameticaly?
And the answer is yes. The distance acts as the parameter and the coordinates are $x=x(d),y=y(d)$