Creating a three dimensional grid

I want to create a three dimensional grid (x,y,z) in mathematica and plot a function f(x,y,z) on it. I am not worried about the plotting part now; for that I will probably use ListContourPlot3D or something like that. But, I am having problem in creating the grid itself. In matlab, one can achieve this by Meshgrid command which takes either two or three variable. There are many nice ways to reproduce the two variable meshgrid equivalent in mathematica as discussed in this stackexchange question: Simulate MATLAB's meshgrid function

However, what should be the equivalent for 3D case? I am trying a combination of Riffle and Partition, but it's getting too long and confusing. Any help will be much appreciated. Thanks!!

Answer

There are better ways to make this list that don't involve emulating MATLAB, but what you want is straightforward:

meshgrid3D[xxx_List, yyy_List, zzz_List] := 

 Table[#, {x, xxx}, {y, yyy}, {z, zzz}] & /@ {x, y, z}

{xxx, yyy, zzz} = 
  meshgrid3D[Range[-2, 2, .1], Range[-2, 2, .1], Range[-2, 2, .1]];

ListContourPlot3D[xxx^2 + yyy^2 - zzz^2, Contours -> {0}, 
 Mesh -> None]

Mathematica graphics

For example, it is better to use

grid3D = Table[{x, y, z}, {x, -2, 2, .1}, {y, -2, 2, .1}, {z, -2, 
    2, .1}];
func[x_, y_, z_] := x^2 + y^2 - z^2;
ListContourPlot3D[
 Apply[func,
  grid3D, {3}], Contours -> {0}, Mesh -> None]

Comments

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functions - Get leading series expansion term?

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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}]

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