如何使函数使用不同大小的网格/线性空间输入

问：

我有一个名为函数的函数，它将网格向量作为输入，并计算在这些网格点上评估的一些输出。总共有网格点。[U,V,W] = my_function(x,y,z)N

问题是我希望我的函数能够容忍不同大小的输入。例如

THIS:
[Y,Z] = meshgrid(0:10,-10:20); X = 6.3;

OR THIS:
[X,Y,Z] = meshgrid(0:10,-10:20,-2:2);

OR THIS:
Z = linspace(-1,1,10); X = 4.2; Y = 1;
etc

但是在函数内部，我需要将 x y z 变量转换为 3 x 数组，如下所示：N

r = [X(:) Y(:) Z(:)]

（这是因为我需要应用一些旋转矩阵，然后对旋转的坐标进行一些进一步的操作）。如果 X、Y 和 Z 的大小不同，则这不起作用。

我试图制作一个预处理坐标的辅助函数，如下面的 MWE 所示，但它非常混乱。我想知道是否有更简洁/更干净/更标准的方法来实现这一目标？

x = linspace(-10,10,100);
Y = 3;
z = linspace(-12,12,80);
[X,Z] = meshgrid(x,z);

[U,V,W] = my_function(X,Y,Z);




%%% MAIN FUNCTION %%%
function [U,V,W] = my_function(X,Y,Z)

[X,Y,Z] = preprocess_gridvectors(X,Y,Z);  % Make sure grid vectors are all same size
N1 = size(X,1); N2 = size(X,2); N3 = size(X,3);
X = X(:); Y = Y(:); Z = Z(:);

%%% Do some transformation and processing here (rotate coordinates and use them)
R = [cos(pi) -sin(pi) 0;sin(pi) cos(pi) 0;0 0 1]; rotXYZ = R*[X Y Z].';
U = rotXYZ(1,:); V = rotXYZ(2,:); W = rotXYZ(3,:);
%%%

% Put the outputs back into the same shape as the original inputs
U = reshape(U, N1,N2,N3);
V = reshape(V, N1,N2,N3);
W = reshape(W, N1,N2,N3);
end



%%% HELPER FUNCTION %%%
function [X,Y,Z] = preprocess_gridvectors(X,Y,Z)

unique_array_sizes = unique([size(X) size(Y) size(Z)]);  % Determine dimensions to use
unique_array_sizes(unique_array_sizes==1) = [];          % Disregard scalar dimension
N_expected = prod(unique_array_sizes);                   % Total number of unique grid points expected

sizes = zeros(3,3);
if numel(X)==N_expected     % X already has the right dimensions
    sizes(1,1) = size(X,1); % Get the dimensions of X
    sizes(1,2) = size(X,2);
    sizes(1,3) = size(X,3);
end

if numel(Y)==N_expected    % Y already has the right dimensions
    sizes(2,1) = size(Y,1);
    sizes(2,2) = size(Y,2);
    sizes(2,3) = size(Y,3);
end

if numel(Z)==N_expected    % Z already has the right dimensions
    sizes(3,1) = size(Z,1);
    sizes(3,2) = size(Z,2);
    sizes(3,3) = size(Z,3);
end

inds = sizes~=0; % Anything which is non-zero has correct dimensions already
ind_dir = find(inds(:,1),1); % Choose the first axis that has good dimensions

% These should be the correct final dimensions now
N1 = sizes(ind_dir,1);
N2 = sizes(ind_dir,2);
N3 = sizes(ind_dir,3);

if ~any(sizes(1,:)) % X direction needs replicating
    X = repmat(X,[N1 N2 N3]);
end
if ~any(sizes(2,:)) % Y direction needs replicating
    Y = repmat(Y,[N1 N2 N3]);
end
if ~any(sizes(3,:)) % Z direction needs replicating
    Z = repmat(Z,[N1 N2 N3]);
end

end