freediagram.nb

buildSegment[a_, xs_, x_] := 
 If[Length[xs] == 1, {}, 
  Join[{ { xs[[1]] + (x - a)*Sign[xs[[2]] - xs[[1]]], 
     a <= x <= a + Abs[xs[[1]] - xs[[2]]]}  }, 
   buildSegment[ a + Abs[xs[[1]] - xs[[2]]], Rest[xs], x]] ]
Curve[xs_, x_] := Piecewise[buildSegment[0, xs, x]]
MaxLength[xs_] := 
 Sum[ Abs[xs[[i]] - xs[[i + 1]]], {i, 1, Length[xs] - 1}]
FreeDiagram[xs_, ys_, epsilon_] := 
 RegionPlot[ 
  Abs[Curve[xs, x] - Curve[ys, y]] <= epsilon, {x, 0, 
   MaxLength[xs]}, {y, 0, MaxLength[ys]} , AspectRatio -> Automatic, 
  PerformanceGoal -> "Quality", PlotPoints -> 100]