I have a set of curves (n set of m points in 3D Cartesian space). For instance, here I have plotted the data in x direction over the number of points:
I want to find the curves that describe the upper or lower bound for this set of points in each direction. If I simply use max/min the result is as follows:
The problem is that the resulting curve is not smooth and breaks at the points that the max or min switches from one curve to another. I can think of applying smoothing process to the resulting curve in the cost of loosing shape and precision. Is there a more legitimate and elegant way to do this?
You could just use the points in the upper and lower bounds and search for a best fitting trendline. If you do this in excel, you can choose from linear, log, polynomial, power etc and it will give you an equation as well as an $R^2$ value which will tell you how good that fit is to the data.