How can I create a 2D array of 3D points

The purpose is to render 2D image of gestner waves

https://developer.nvidia.com/gpugems/gpugems/part-i-natural-effects/chapter-1-effective-water-simulation-physical-models

So I think these equations add Offset not only in vertical direction, but also squeeze points horizontally to make crests choppy

I know that meshgrid can create a group of evenly distributed grid points and we can assign a vertical values to each of the (x,y) discrete locations.

(https://www.mathworks.com/help/matlab/ref/meshgrid.html?lang=en)

But this is far from drawing gestner waves.

I need to create a 2D array of points. Each element of the array is a point (or a point's 3D-location), and then I can offset each of these points and then visualize the surface.

If I write this code: points will be a 16384*3 array. Just storing 3d points in a row vector for 16384 times. I cannot access them via x,y,z index. How can I do that?

vector_of_x = 1:128;
vector_of_y = 1:128;
[X, Y] = meshgrid(vector_of_x, vector_of_y);
Z=zeros(128,128);
surf(X,Y);
points = [X(:), Y(:), Z(:)];
ptCloud = pointCloud(points);%%case

Answer 1

[Jeremy Perez]

Hi,

Read this:

https://www.mathworks.com/help/matlab/math/multidimensional-arrays.html

https://www.mathworks.com/matlabcentral/answers/242280-3-dimension-array

What you want is creating a pxyt array with 3 pages.

Each page contains the values at each step t.

The code you know:

n = 128;
vector_of_x = 1:n;
vector_of_y = 1:n;
[X, Y] = meshgrid(vector_of_x, vector_of_y);
Z=zeros(n,n);

Your surface at t0:

pxyt = zeros(n,n);
pxyt(:, :, 1) = X(:, :);
pxyt(:, :, 2) = Y(:, :);
pxyt(:, :, 3) = Z(:, :);

Your surface at t:

% pxyt = myfunctionP(pxyt)
pxyt(:, :, 3) = rand(n,n);

X = pxyt(:, :, 1);
Y = pxyt(:, :, 2);
Z = pxyt(:, :, 3);

%figure()
%surf(X,Y,Z);

Your point at t:

p = [0;0;0];
kx = 1; % index x
ky = 1; % index y
p(:) = pxyt(kx, ky, :);

Hope it helps,