# Project RegionPlot3D to 2D using hue/color function to show third dimension

I would like to project the output of RegionPlot3D onto a 2D plane. Basically I'd like to turn this

f = a^2  + b^3 + c;
RegionPlot3D[f <= 0.5, {a, 0, 1}, {b, 0, 1}, {c, 0, 1},
AxesLabel -> Automatic, ColorFunction -> "Rainbow",
ViewPoint -> Above, Mesh -> None]


into something more like a contour plot (colour showing what the c value is). I am only interested in the maximum value for c that will satisfy the constraints - so I would like to project onto a 2D plane.

My actual functions are considerably more complex, and the 3D image makes it harder to see the detail.

• Can you always solve for a, b, or c, or are they trapped in a complicated implicit relationship? – J. M. is in limbo Mar 27 '19 at 6:53
• Complicated implicit relationships unfortunately. There are also multiple conditions within the Region plot to ensure what is returned is physical as well. – Esme_ Mar 27 '19 at 23:04

f = a^2 + b^3 + c;

• You could also combine these two options ...ViewPoint -> Top, ViewProjection -> "Orthographic"... to get the same effect. – Pinti Apr 12 '19 at 7:04