# 3D plot from lists

I'm trying to generate a 3D plot of some functions a,b,c, under certain inequality constraints. I have earlier defined the functions

a[x,y,z],b[x,y,z],c[x,y,z]


and

f[a[x,y,z],b[x,y,z],c[x,y,z]]


So far I have:

RegionPlot3D[
0 < f[a[x, y, z], b[x, y, z], c[x, y, z]] &&
0 < a[x, y, z] < 1 && 0 < b[x, y, z] < 1 && 0 < c[x, y, z] < 1,
{x, -Pi/2, Pi/2}, {y, 200, 2000}, {z, 100, 1000}]


This works great, and gives me a 3D plot showing the region in x, y, z space for which the constraint holds.

Now, I have lists of a,b,c from another calculation, i.e.,

mat=Table[{a[i],b[i],c[i]},{i,0,10}]
alist=mat[[All,1]]


Essentially I want to use a similar RegionPlot3D code to plot the space in x, y, z for which the a,b,c values from the dataset fulfill the conditions (inequalities).

I'm struggling with:

• Properly ordering/pairing my data sets, such as to thread each set of corresponding a, b and c values together

• Calling values from the data table in the RegionPlot3D, i.e. running it for every data point in the table a, b, c

• Plotting this on a 3D plot in terms of x,y,z. So essentially I have the functions a[x,y,z],b[x,y,z],c[x,y,z] and separately lists of a, b, c values.

Any help would be much appreciated!

• Is {x,y,z} -> {a,b,c} an invertible transformation? It may not be possible to determine the appropriate {x,y,z} points for plotting if they are not and the original {x,y,z} points are not otherwise available. Otherwise consider using ListPointPlot3D and Select. – eyorble May 28 '18 at 2:45
• @eyorble - I am not sure they are. What is the procedure if they are? ListPointPlot3D looks like it could be useful. I'm not sure how I could enforce the inequality condition though (which I have in the region plot). I'm also struggling with the general task of choosing data sets as my dependent and independent variables, for a plot, particularly the latter.. – SarahThompson May 28 '18 at 12:48
• Possible duplicate of RegionPlot from list – MarcoB Jun 11 '18 at 4:26