How to Declare a 3D Field in MATLAB

Create a 3D vector field in MATLAB.

MATLAB is a software environment used frequently in technical data collection, modeling and analysis. A 3D vector field is a collection of vectors, each localized to a point in three-dimensional space. Vector fields, especially in three dimensions, are common in physics and engineering. Though MATLAB does not contain a specialized function for vector fields, it is simple to declare them using basic MATLAB functions.

Instructions

1. Declare a set of points in three dimensions at which the values for your vector field are to be represented using the "meshgrid()" function. The meshgrid() function replicates a series of vectors to create a matrix. For example, to create a grid from -10 to 10 in steps of 1 in three dimensions, type:

   [X,Y,Z] = meshgrid(-10:10, -10:10, -10:10);

   Each of the matrices X, Y and Z are of dimension 21 x 21 x 21, each corresponding to the values of the x, y and z dimensions at a particular index.

2. Assign value to the x, y and z magnitude of the vector located at each of the corresponding points. While this will commonly be based upon a formula that can be calculated using the results of meshgrid() or from measured observations, you can use random values for this example.

   vec_x = rand(size(X));
   vec_y = rand(size(Y));
   vec_z = rand(size(Z));

3. Convert the existing separate matrices to a cell array for ease of programmatic access:

   my_temp_array = zeros([size(X) 6]);
   my_temp_array(:,:,:,1) = X;
   my_temp_array(:,:,:,2) = Y;
   my_temp_array(:,:,:,3) = Z;
   my_temp_array(:,:,:,4) = vec_x;
   my_temp_array(:,:,:,5) = vec_y;
   my_temp_array(:,:,:,6) = vec_z;
   my_vector_field = num2cell(my_temp_array,4);
   clear my_temp_array

References

• MATLAB Documentation: Meshgrid
• MATLAB Documentation: Num2cell