“Density contour plot”—plot solution surface using color

I would like to plot the solution of an equation in three variables via a color map, thus combining the functions of ContourPlot3D and DensityPlot.

That is, I have a plot of the form

ContourPlot3D[F(x,y,z)==0,{x,x1,x2},{y,y1,y2},{z,z1,z2}]


but I think it would look much better as a plot in (x,y) space where each point is assigned a color corresponding to a z value. Is there a way this can be done?

• Have you seen SliceContourPlot3D[] and SliceDensityPlot3D[]? – J. M. is away Jan 30 '17 at 7:46
• I don't think this is what I want....looks like this plots a function of three variables on a surface, whereas I'm simply looking to transform a surface into a 2D density plot. – mikefallopian Jan 30 '17 at 7:53
• Okay, so in the case of there being two or more $z$ values corresponding to an $x,y$ pair, what do you want to do? – J. M. is away Jan 30 '17 at 7:55
• That's a good question. Let's say that I've constrained the bounds on x, y, and z such that there's only one solution for any x and y, so that this won't be a problem – mikefallopian Jan 30 '17 at 7:59
• Do you have a sample F[x, y, z] and an appropriate domain in mind, so that we can try something out with actual examples? – MarcoB Jan 30 '17 at 19:31