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MathGroup Archive 1995

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Re: Problems with defintion of a ContourFunction

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1578] Re: [mg1557] Problems with defintion of a ContourFunction
  • From: twj (Tom Wickham-Jones)
  • Date: Sat, 1 Jul 1995 03:18:08 -0400


Martina Giarre writes:

>I have some problems in defining a ContourFunction. I cannot
>specify a color for a certain z-value in a ListContourPlot.

The values passed to the ColorFunction are scaled from the values 

of the contour lines and the minimum and maximum z values of the 

PlotRange.   The lowest value is the midpoint between the lowest
contour and z_{min; this gets scaled to 0.  The highest value is 

the midpoint between the highest contour and z_max; this gets scaled 

to 1.   The intermediate points are the midpoints between the appropriate 

contour lines.  All the values are scaled with a linear function
so that the minimum  and maximum values are 0 and 1 respectively.
This can be represented by the Mathematca function where vals are 

the contour lines and z1 and z2 are respectively the minimum and maximum 

z values of the PlotRange.

ColorFunctionValues[vals_List, {z1_, z2_}] :=
  Module[{p1, p2, pf, res},
    p1 = (z1 + First[vals])/2. ;
    p2 = (z2 + Last[vals])/2. ;
    pf = p2 - p1 ;
    res =
      Table[
        ((Part[vals, i] + Part[vals, i+1])/2. - p1)/pf,
        {i,Length[vals] - 1}] ;
    Join[{0}, res, {1}]
    ]      



In the example given:

>test = Transpose[{{1,2,3,4,5,6},{1,2,3,4,5,6},
>		{1,2,3,4,5,6},{1,2,3,4,5,6},
>		{1,2,3,4,5,6},{1,2,3,4,5,6}}];
>
>g = {1,2,3,4,5,6};
>tc = Table[{Hue[d]},{d,0.4,1,0.1}];
>c[f_]:=While[f<=1,Hue[0.9]]
>ListContourPlot[test,	PlotRange->{1,6}, 

>			Contours->g, 

>			ContourStyle->tc,
>			ContourShading->True,
>			ContourLines->True,
>			ColorFunction->c];

The c[f_] function must be wrong,  this has a While, changing this
to an If defines a color function that will always return Hue[0.9],
which also probably is wrong since generally the levels 


Here is a different color function, (this one prints out the argument),
and then uses the argument to pick out a color from a list.

In[19]:= c[f_] := (Print[f]; Part[ tc, Floor[6f +1.5],1])

In[20]:= test = Transpose[{{1,2,3,4,5,6},{1,2,3,4,5,6},
                {1,2,3,4,5,6},{1,2,3,4,5,6},
                {1,2,3,4,5,6},{1,2,3,4,5,6}}];
                  

In[21]:= g = {1,2,3,4,5,6};

In[22]:= tc = Table[{Hue[d]},{d,0.4,1,0.1}];

In[23]:= ListContourPlot[test,  PlotRange->{1,6}, 

                        Contours->g, 

                        ContourStyle->tc,
                        ContourShading->True,
                        ContourLines->True,
                        ColorFunction->c];
0.1
0.3
0.5
0.7
0.9
0.
1.


which prints out the values past to the ColorFunction.
Now using the ColorFunctionValues function defined above
these values can be confirmed.

In[24]:= ColorFunctionValues[vals_List, {z1_, z2_}] :=
  Module[{p1, p2, pf, res},
    p1 = (z1 + First[vals])/2. ;
    p2 = (z2 + Last[vals])/2. ;
    pf = p2 - p1 ;
    res =
      Table[
        ((Part[vals, i] + Part[vals, i+1])/2. - p1)/pf,
        {i,Length[vals] - 1}] ;
    Join[{0}, res, {1}]
    ]      

                                                                                          

In[25]:= ColorFunctionValues[ g, {1,6}]

Out[25]= {0, 0.1, 0.3, 0.5, 0.7, 0.9, 1}



Tom Wickham-Jones
WRI




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