I want to combine the features of the functions
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!