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I want to reproduce these plots for further development in Mathematica:

enter image description here

To do so I defined the functions A and B as following

A[x_ /; 0 < x < 200] := Piecewise[{{65, 0 < x < 100}, {110, 100 < x < 200}}]

B[x_ /; 0 < x < 200] := Piecewise[{{40, 0 < x < 100}, {90 , 100 < x < 200}}]

Now when I plot their sum the domain is fixed and the ranges are added together.

In the graph above the domains of A and B are added. Then in a try in each step of the new domain the minimum of A or B or A+b is returned. How one can make this graph below from A and B?

EDIT: The domain of the functions are not necessarily unique. Take this example:

A[x_ /; 0 < x < 200] := Piecewise[{{65, 0 < x < 100}, {110, 100 < x < 200}}]

B[x_ /; 0 < x < 300] := Piecewise[{{40, 0 < x < 170}, {90 , 170< x < 300}}]

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    $\begingroup$ ……Where's your "graph below"? $\endgroup$
    – xzczd
    Commented Jan 23, 2014 at 11:20
  • $\begingroup$ typo...Corrected!! $\endgroup$
    – Morry
    Commented Jan 23, 2014 at 12:21
  • $\begingroup$ I think Piecewise[] is bad for this problem, because the arguments should be simpler. How about defining some sort of Line[] object. Like: line[points_,options_]:=Line[blah]. Then you can choose how points should be entered. $\endgroup$
    – Coolwater
    Commented Jan 23, 2014 at 12:53
  • $\begingroup$ I would like to have a solution which elaborates on general concepts of Mathematics, not graph analysis or other tricks! $\endgroup$
    – Morry
    Commented Jan 23, 2014 at 13:03
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    $\begingroup$ I don't understand the desired output. You state that the output is the Min of a[x/2], b[x/2] and a[x/2]+b[x/2], but this is inconsistent with the region between 300 and 400 where the output is shown as the same as a[x/2], even though b[x/2] is smaller. $\endgroup$
    – bill s
    Commented Jan 23, 2014 at 17:29

2 Answers 2

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a[x_ /; 0 < x < 200] := Piecewise[{{65, 0 < x < 100}, {110, 100 < x < 200}}]

b[x_ /; 0 < x < 200] := Piecewise[{{40, 0 < x < 100}, {90, 100 < x < 200}}]

c[x_ /; 0 < x < 400] := Switch[Mod[Quotient[x, 100], 2], 1, Max@#, 0, Min@#] &@{a[x/2], b[x/2]}

Plot[{a[x], b[x], c[x]}, {x, 0, 400}, 
      PlotRange -> {{0, 400}, {0, 120}}, 
      PlotStyle -> {{Dashed, Thick, Blue}, {Dashed, Thick, Magenta}, {Black}}, 
      GridLines -> {None, Automatic}]

Mathematica graphics

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  • $\begingroup$ What if the domains are different? Something like a[x_ /; 0 < x < 300] := Piecewise[{{65, 0 < x < 170}, {110, 170< x < 300}}] $\endgroup$
    – Morry
    Commented Jan 23, 2014 at 12:25
  • $\begingroup$ @Morry We can't prescience your needs. Please try to state all your requirements in the question! $\endgroup$
    – Dr. belisarius
    Commented Jan 23, 2014 at 12:36
  • $\begingroup$ This is the solution to my problem, but the solution is not a general one.... I think there should be a more general way! $\endgroup$
    – Morry
    Commented Jan 23, 2014 at 12:39
  • $\begingroup$ @Morry I think it's as general as the question. It can be generalized in a large number of different ways (more intervals, more piecewise functions, more operations between the functions, etc)- Please state what kind of generalizations you need and we could try to fulfill those $\endgroup$
    – Dr. belisarius
    Commented Jan 23, 2014 at 12:45
  • $\begingroup$ I will edit the question..... $\endgroup$
    – Morry
    Commented Jan 23, 2014 at 13:00
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Another way to define your functions is via Interpolation. Since you want the functions to be flat, you can use the option InterpolationOrder->0 which simply connects the points with a horizontal line. Using belisarius' definition of the desired output function, this would be:

aa = Interpolation[{{0, 65}, {100, 65}, {200, 110}, {400, Infinity}}, InterpolationOrder -> 0];
bb = Interpolation[{{0, 40}, {100, 40}, {200, 90}, {400, Infinity}}, InterpolationOrder -> 0];
cc[x_] := Switch[Mod[Quotient[x, 100], 2], 1, Max@#, 0, Min@#] &@{a[x/2], b[x/2]};
Plot[{aa[x], bb[x], cc[x]}, {x, 0, 400}, PlotRange -> {0, 120}]

enter image description here

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