Using parameter from ParametricPlot as parameter in ColorFunction

Questions
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1

Hey

I’m new to this site, so bear with me if I posted in the wrong forum.

I’m trying to make a ParametricPlot with parameters r and t, and then color that plot with a ColorFunction, so that the plot becomes more red for increasing r, and more green for increasing t. I can however only make the ColorFunction do this for increasing x[r,t] and y[r,t], meaning that the plot becomes more red the the left and more green towards the top.

Minimal (non-)working example. for simplicity my x and y just swaps r and t wrt my ColorFunction.

x[t_, r_] = r;
y[t_, r_] = t;
ParametricPlot[{x[t, r], y[t, r]}, {r, 0, 1}, {t, 0, 1}, 
 ColorFunction -> Function[{t, r}, RGBColor[t, r, 0]], 
 ColorFunctionScaling -> True, AspectRatio -> 1/1]

In this case, I get green in top left corner, red in bottom right, and yellow in top right corner. What I expected was for (y=0,x=1 => t=0,r=1) lower right to be green, and similar upper left to be red.
If I change variables for the ColorFunction this does not change, suggesting that the ColorFunction is independed of my parameters r and t from ParametricPlot.

So how do I get ColorFuction to use my parameters and not my coordinates ?

Thanks

2

Go to the main documentation page for ColorFunction and look under Details.
For ParametricPlot, the arguments passed are x, y, u or x, y, u, v where
x and y are the directions and u and v are the first and second parameters.

In

 ColorFunction -> Function[{t, r}, RGBColor[t, r, 0]],

it does not matter what names you gave the function internal variables;
the first two variables passed to the function are the x and y positions.

To include the two parameters, include all four arguments in the header and ignore the first two.

ParametricPlot[{x[t, r], y[t, r]}, {r, 0, 1}, {t, 0, 1}, 
 ColorFunction -> Function[{x, y, r, t}, RGBColor[t, r, 0]],
 ColorFunctionScaling -> True, AspectRatio -> 1/1,
 FrameLabel -> {"x", "y"}]

and make sure the order of variables is correct in the RGBColor call.

3

Thanks. Worked perfectly.