Does a figure which has a contour plot have a systematic function to define it?

Question

Does a figure which has a contour plot have a systematic function to define it? I mean I am plotting a contour plot (the contour plot which shows z slices in x-y graph) of a figure like (suppose) mount everest. Does it necessary have a systematic function f(x, y) to define it?

Answer 1

In general, there is not a systematic way to plot the contour map of a terrain. In particular, many terrains are not a function of longitude and latitude; that is, there may be multiple heights at any point. So it's not a function at all.

However, for nicely behaved terrains (e.g. Mount Everest), one can make the contour plots in a systematic way.

A levelset of a function are all the points where the function equals a specific value. For example, the 0-levelset of a function f is the set $\{x: f(x)=0\}$. Any levelset can be drawn with the marching squares algorithm. So, to make a contour-map, one would choose the values of each contour that one would like to draw, and then use the marching-squares algorithm to draw those contours.

I hope that helps. :)