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

Question

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.'s missing motivation, Mar 27 '19 at 06:53
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

Esme_ · Accepted Answer · 2019-04-14T22:49:54.347

2

This post https://mathematica.stackexchange.com/a/21726/34694 gave me the solution - essentially set the z-axis viewpoint to infinity and you will have a 2D projection.

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

Mathematica graphics

Edit: Note that removing the AxesLabel -> Automatic, gets rid of the z axis label issue in the bottom left hand corner

edited Apr 14 '19 at 22:49

answered Apr 12 '19 at 04:57

Esme_

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You could also combine these two options ...ViewPoint -> Top, ViewProjection -> "Orthographic"... to get the same effect. – Pinti Apr 12 '19 at 07:04

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

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