Surface plot with different z and contour axes

[#1]

I would like to plot a surface plot with x, y, and z axes as the positions in the graph "cube" but use a different axis (I'll call this axis "p") to overlay data on top of the surface.

However, when I plot a surface using my 4 axes, as soon as I put Z as my response and choose surface as a style, the surface fill defaults to Z's values which isn't very useful. It's basically plotting the same variable in two ways.

Is it possible to script my way out of this? Could a different column be used as a continuous/discrete gradient surface fill?

Example:

I want the surface to look exactly like this with XYZ as coordinates but use column P as the continuous fill not Z:

Ignore "Column 4" in the example screenshot. It's empty and serves no purpose.

I have attached a prototype data table to this message that I was trying things on.

[#2]

Further context: if P is a formula column, I can achieve a close-enough effect but the graph is not contained within the data ranges and the sheet basically extends to a rectangular bounds of xmin,xmax and ymin,ymax. As you can see, I'm trying to get a custom shape with my coordinates with bits and pieces missing from the x and y ranges.

[#3 · Accepted solution]

Custom Visualization uses the Scene3D/OpenGL underpinnings of the surface plot to make a visualization similar to what you describe. The surface coloring and surface height are from two different functions. The surface height is animated across time. You could also just render a single frame and try using an ArcBall to rotate it with the mouse. The example uses a lot of polygons with color specified for each corner and might need better hardware or fewer polygons to perform well. There are also examples in the scene3D example folder; you may need to add an axis and other labeling.

Crater

Also, you can display multiple functions, and you can make one of the functions be a contour plot on the floor of the cube.

Two different functions, one as a surface, one as a contour

The contour lines of one function can't be mapped onto the surface of another function with this platform.

[#4]

Also, if you want to create a hole in the surface, arrange for the formula to return missing values for Z.

[#5]

Thanks a lot! You've saved me countless hours of further trials.

I was hoping not to go into the 3D scenes but it appears to be the only solution. I'll look into your example as well. I've done very little with 3D Scenes so I got some things to learn.

Anyway, thanks for the reply.