# Parametric Density Plot

I want to combine the features of the functions DensityPlot and ParametricPlot. That is, I have three functions $f(x,y)$, $g(x,y)$ and $h(x,y)$. I want to create a density plot that shows a color representing the magnitude of $h(x,y)$ at a point described by $(f(x,y), g(x,y))$ for some range of the input parameters x and y.

I have all the data analytically, so I would rather not like to use ListDensityPlot, since it takes a long time to create enough data for a useful plot and there is also some annoying extrapolation going on. (See also here.)

Is there anything built in I have overlooked? Is there an easy way to implement what I'm trying to do? Thanks for all suggestions!

• DensityPlot[h[f[x, y], g[x, y]], {x, -4, 4}, {y, -4, 4}]? – kglr Apr 5 '18 at 13:41
• No, that's not what I meant. I want to evaluate all the functions at {x,y} but plot the corresponding point at the position {f[x,y], g[x,y]}. I should say that while I have the functions in an analytical form, I don't want to invert them as that is going to be messy for sure. – Herr_Mitesch Apr 5 '18 at 13:46
• then, perhaps, DensityPlot[h[x, y], {x, -4, 4}, {y, -4, 4}] /. GraphicsComplex[a_, b___] :> GraphicsComplex[a /. {x_, y_} :> {f[x, y], g[x, y]}, b]? – kglr Apr 5 '18 at 13:48