hilbert曲线序编码matlab

以下是Hilbert曲线序编码的Matlab代码示例：

function coord = hilbert_curve_order(n, d)
%HILBERT_CURVE_ORDER Hilbert curve order numbers
%   COORD = HILBERT_CURVE_ORDER(N, D) returns the coordinates
%   of the Hilbert curve of order N and dimension D.
%
%   Examples:
%
%   % plot a 2D Hilbert curve of order 3
%   coord = hilbert_curve_order(3, 2);
%   plot(coord(:,1), coord(:,2));
%
%   % plot a 3D Hilbert curve of order 3
%   coord = hilbert_curve_order(3, 3);
%   plot3(coord(:,1), coord(:,2), coord(:,3));
%
%   See also HILBERT, PEANO_CURVE_ORDER.

if d < 1
    error('Dimension D must be greater than or equal to 1.');
end

if n < 0
    error('Order N must be a non-negative integer.');
end

if n == 0
    coord = zeros(1, d);
    return;
end

m = 2^d;
m2 = m / 2;

coord = hilbert_curve_order(n-1, d);
new_coord = zeros(size(coord));

for i = 1:size(coord, 1)
    switch mod(floor((i-1)/m), 4)
        case 0
            new_coord(i,:) = [coord(i,2) coord(i,1)];
        case 1
            new_coord(i,:) = [coord(i,1) coord(i,2)+m2];
        case 2
            new_coord(i,:) = [coord(i,1)+m2 coord(i,2)+m2];
        case 3
            new_coord(i,:) = [m2-coord(i,2)+1 m2-coord(i,1)+1];
    end
end

coord = new_coord + repmat((m2 .* [mod(floor((0:m^d-1)/m),m); ...
    mod(floor((0:m^d-1)/m^2),m)])',1,d);

end

该函数返回Hilbert曲线上每个点的坐标，您可以使用这些坐标进行编码或解码。