ContourPlot and Colorfunction

Question

I have the following code:

ContourPlot[
(2.7` (-3.8099999999999996` + 7.24` x - 3.24` x^2 + 3.62` y - 6.48` x y + 6.48` x^2 y))/
( 11.43` - 6.48` x + 3.24` x^2 - 3.24` y + 6.48` x y) - 
( 3 (-(-1 + x)^2 + (1 + 2 (-1 + x) x) y))/( 3 + (-2 + x) x + (-1 + 2 x) y) , 
{x, 0.5, 1}, {y, 0, 0.5},
 ContourStyle -> {Black, Thick}, Contours -> {0}, 
 ColorFunction -> 
(If[#1 > 0, Directive[Lighter[Lighter[Lighter[Yellow]]]], White] &)]

which gives me

But my color function should color the area above the black line white while color area below the black line yellow.

However, if I use the colorfunction Rainbow, then it will give me the correct coloring result:

What should I do to make my 1st color function behave as expected?

Answer 1

I always forget about ColorFunctionScaling too:

ContourPlot[(2.7` (-3.8099999999999996` + 7.24` x - 3.24` x^2 + 3.62` y - 6.48` x y + 
            6.48` x^2 y))/(11.43` - 6.48` x + 3.24` x^2 - 3.24` y + 6.48` x y) - (
            3 (-(-1 + x)^2 + (1 + 2 (-1 + x) x) y))/(3 + (-2 + x) x + (-1 + 2 x) y),
            {x, 0.5, 1}, {y, 0, 0.5}, 
    ContourStyle -> {Black, Thick}, Contours -> {0}, 
    ColorFunction -> (If[#1>0, Directive[Lighter[Lighter[Lighter[Yellow]]]], White] &), 
    ColorFunctionScaling -> False]

Answer 2

The argument to the ColorFunction shouldn't be scaled, because if it is then the zero passed to the ColorFunction depends on whether the minimum and maximum of the plot values are symmetric with respect to zero or not.

So we have to add the option ColorFunctionScaling -> False to the ContourPlot as follows:

ContourPlot[(2.7` (-3.8099999999999996` + 7.24` x - 3.24` x^2 + 
       3.62` y - 6.48` x y + 6.48` x^2 y))/(11.43` - 6.48` x + 
     3.24` x^2 - 3.24` y + 
     6.48` x y) - (3 (-(-1 + x)^2 + (1 + 2 (-1 + x) x) y))/(3 + (-2 + 
        x) x + (-1 + 2 x) y), {x, 0.5, 1}, {y, 0, 0.5}, 
 ContourStyle -> {Black, Thick}, Contours -> {0}, 
 ColorFunction -> (If[#1 > 0, 
     Directive[Lighter[Lighter[Lighter[Yellow]]]], White] &), 
 ColorFunctionScaling -> False]

This produces the correct result.

Answer 3

This is more of very long comment than an answer, but I hope it cast more murk on the problem.

If I evaluate

ContourPlot[
  (2.7` (-3.8099999999999996` + 7.24` x - 3.24` x^2 + 3.62` y - 6.48` x y + 6.48` x^2 y))/
    (11.43` - 6.48` x + 3.24` x^2 - 3.24` y + 6.48` x y) - 
    (3 (-(-1 + x)^2 + (1 + 2 (-1 + x) x) y))/(3 + (-2 + x) x + (-1 + 2 x) y),
  {x, 0.5, 1}, {y, 0, 0.5}, 
  ContourStyle -> {Black, Thick}, 
  Contours -> {0}, 
  ColorFunction -> (If[#1 > 0, Directive[Lighter[Lighter[Lighter[Yellow]]]], White] &)]

I get

all.yellow.png

However, If I change -3.8099999999999996` to -3.81` and only that and then evaluate

ContourPlot[
  (2.7` (-3.81` + 7.24` x - 3.24` x^2 + 3.62` y - 6.48` x y + 6.48` x^2 y))/
    (11.43` - 6.48` x + 3.24` x^2 - 3.24` y + 6.48` x y) - 
    (3 (-(-1 + x)^2 + (1 + 2 (-1 + x) x) y))/(3 + (-2 + x) x + (-1 + 2 x) y),
  {x, 0.5, 1}, {y, 0, 0.5}, 
  ContourStyle -> {Black, Thick}, 
  Contours -> {0}, 
  ColorFunction -> (If[#1 > 0, Directive[Lighter[Lighter[Lighter[Yellow]]]], White] &)]

I get

So both of the previously posted answers may be right, but they don't seem to tell the whole story.