order making for a matrix in matlab

问题

I am doing a simulation on a matrix (suppose a 5x5 matrix). One of the elements of this matrix is known (the back square in below; this location will not be always in center) and I want to start from that location and spirally visit the other elements (I have shown the orders in number). How I can define this order in a large matrix (e.g. 1000x1000)? Because I cannot do it manually and I am looking for a more heuristic way.

I used bwdist in matlab and then sort the obtained matrix, but the results were not as what I want.

Any better solution?

回答1:

When element is in the center, just use the spiral command:

>> spiral(5)

ans =

    21    22    23    24    25
    20     7     8     9    10
    19     6     1     2    11
    18     5     4     3    12
    17    16    15    14    13

For arbitrary position of the starting point we'll need to do something by hands

Let's exploit this fancy spiral function. To obtain the answer matrix A, make the bigger matrix M where the starting point is in the center. Note that relative order of the elements in A and in M is the same. All we need is to get A as a submatrix from M and fill it with continuous array of elements in the same order:

function A = spiral_generic(n, P)
% Makes NxN matrix filled up spirally starting with point P
  r = max([P - 1, n - P]);              % Radius of the bigger matrix
  M = spiral(2 * r + 1);                % Bigger matrix itself
  C = r + 1 - (P - 1);                  % Top-left corner of A in M
  A = M(C(1):C(1)+n-1, C(2):C(2)+n-1);  % Get the submatrix
  [~, order] = sort(A(:));              % Get elements' order
  A(order) = 1:n^2;                     % Fill with continous values
end

And here's how it works:

>> spiral_generic(5, [3 2])

ans =

    17    18    19    20    21
     7     8     9    10    22
     6     1     2    11    23
     5     4     3    12    24
    16    15    14    13    25

>> spiral_generic(6, [2 5])

ans =

    36    25    16     7     8     9
    35    24    15     6     1     2
    34    23    14     5     4     3
    33    22    13    12    11    10
    32    21    20    19    18    17
    31    30    29    28    27    26

This is not the fastest solution since it requires sorting and thus takes O(N^2 logN) time comparing to direct O(N^2) implementation. But it is very short and works fast enough for matrices around 1000x1000.

来源：https://stackoverflow.com/questions/20259818/order-making-for-a-matrix-in-matlab