plotting - 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!

Comments

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I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Adding a thick curve to a regionplot

Suppose we have the following simple RegionPlot: f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}] Now I'm trying to change the curve defined by $y=g[x]$ into a thick black curve, while leaving all other boundaries in the plot unchanged. I've tried adding the region $y=g[x]$ and playing with the plotstyle, which didn't work, and I've tried BoundaryStyle, which changed all the boundaries in the plot. Now I'm kinda out of ideas... Any help would be appreciated! Answer With f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 You can use Epilog to add the thick line: RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}, PlotPoints -> 50, Epilog -> (Plot[g[x], {x, 0, 2}, PlotStyle -> {Black, Thick}][[1]]), PlotStyle -> {Directive[Yellow, Opacity[0.4]], Directive[Pink, Opacity[0.4]],

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