Is there a standard algorithm for calculating the envelope of a family of piecewise linear functions?

Question

Algorithms

Given: a set of continuous piecewise linear functions, each with its own set of breakpoints, for example (dotted lines are a special case, you should not pay attention to them):

Required: calculate the upper envelope of the family, that is, such a piecewise linear function, value which at each point is equal to the maximum of the values ​​of the functions of the family at this point. It is required to find the red line in the picture:

For the solution, of course, it is enough to build a set of break points of the desired function. Own algorithm is thought up and even written, but it would not be desirable to reinvent bicycles. Therefore, the question is: is there a problem that can be solved by standard algorithms, to which this problem would be reduced?

Answer 1

_{Points (x 1} ; 0) and (x _n ; 0) are added to each line (projections of extreme points on the X axis), a polygon is obtained. Next is the algorithm for adding polygons.