Second I have a problem with the graph scale which goes to logMin (1E-150) whatever I do.
Uwe can answer about Qwt, but this problem could well be due to your comparison in line 7. A floating point value, especially one measured experimentally, is never exactly equal to zero unless it is set to exactly zero. So your comparison is probably only rarely true for your data. A better solution is to define some "epsilon" value, where if the absolute value of the number is less than epsilon, you treat it as zero. For experimental data, this is typically the minimum resolution of the intensity scale - where two measured values are treated as equal if their difference is less than the measurement error (the ability of the measurement to distinguish them).

Qt Code: 
  1. double epsilon = 1.0e-6;
  2. if ( std::abs( value ) < epsilon ) return 0;
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First this is not very flexible since the method is "const".
It is perfectly appropriate that these methods are defined as "const". A const method does not change the state of the class instance when it is called. In this case, transform() simply returns a new value based on the input (changing nothing), and copy() returns a new instance, again changing nothing in the class instance.

If you need to store some value in the class instance as a member variable that changes its value when transform() or copy() are called, then declare that variable as "mutable". It is designed for that purpose - to preserve the const-ness of the interface while allowing minor side-effect changes to occur in member variables.