从点到矩阵的螺旋环 [英] Spiral loop on a matrix from a point
问题描述
我有一个如下的2D网格，想从X，Y开始并保存窗口的角(W)和(OP)的重叠.我已经尝试过这些代码，但都不适合我的目的.
如所示，我想从一个随机点(黑色单元格)开始，并以螺旋循环的方式保存每个新窗口的角位置(以黑色圆圈显示).该算法应用于任何网格尺寸(不一定是正方形)和任何起点位置.
Matlab还具有与我想要的功能类似的功能(螺旋)，但它不需要网格，窗口大小和重叠(OP).
我希望该图具有以下输出:(8,12) (11,12) (11,9) (8,9) (4,9) (4,12) (4,15) ...
我正在使用以下代码，这些代码从一个角开始，并使用定义的W，OP和矩阵大小逐步填充矩阵:
W = [10 12];
OP = [4 3];
M = zeros(100,110);
for i=[1:W(1)-OP(1):size(M,1)-W(1), size(M,1)-W(1)+1]
for j=[1:W(2)-OP(2):size(M,2)-W(2), size(M,2)-W(2)+1]
block = rand(W(1),W(2));
M(i:i+W(1)-1, j:j+W(2)-1) = block;
imagesc(M); axis equal tight xy
pause(.1)
end;
end;
因此，以一种更清晰的方式，我应该如何更改上方"代码，以便从位置(x，y)开始并根据W，OP和size(M)螺旋填充整个矩阵. /p>
谢谢！
这是一段可产生预期输出的代码.在那里，只需对spiral_generic进行较小的更改即可满足您的要求:
function demo()
spiral_generic([10,11],[3,4])
W = [10 12];
OP = [4 3];
%make sure your start point is really on the grid of r and c, this is not checked!
start = [19,28];
M = zeros(100,110);
r=[1:W(1)-OP(1):size(M,1)-W(1), size(M,1)-W(1)+1];
c=[1:W(2)-OP(2):size(M,2)-W(2), size(M,2)-W(2)+1];
startindex=[find(r==start(1),1,'first'),find(c==start(2),1,'first')];
A=spiral_generic([numel(r),numel(c)],startindex);
[~,idx]=sort(A(:));
[ridx,cidx]=ind2sub(size(A),idx);
%blocks contains the lower left corners in order of processing.
blocks=[r(ridx);c(cidx)];
for blockindex=blocks
block = rand(W(1),W(2));
M(blockindex(1):blockindex(1)+W(1)-1, blockindex(2):blockindex(2)+W(2)-1) = block;
imagesc(M);
pause(.1)
end
end
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
M = permute(M,[2,1]); % changing start direction of the spiral
M = M(:,end:-1:1); % chaning spin orientation
C = r + 1 - (P - 1); % Top-left corner of A in M
A = M(C(1):C(1)+n(1)-1, C(2):C(2)+n(2)-1); % Get the submatrix
[~, order] = sort(A(:)); % Get elements' order
A(order) = 1:(n(1)*n(2)); % Fill with continous values
end
I have a 2D grid as follow and want to start from X, Y and save the corner of a window (W) and overlap of (OP). I have tried these codes, but non of them are fit to my purpose.
As it is demonstrated, I want to start from a random point (black cell) and save the corner locations (shown by black circles) of each new window in a spiral loop. The algorithm should be used for any grid sizes (not square necessarily) and any start point locations.
Matlab also has a function (spiral) that is similar to what I want, but it does not take a grid, window size and overlap (OP).
I expect to have the following output for this figure: (8,12) (11,12) (11,9) (8,9) (4,9) (4,12) (4,15) ...
I am using the following codes which starts from a corner and fill the matrix step-by-step using the defined W, OP and Matrix size:
W = [10 12];
OP = [4 3];
M = zeros(100,110);
for i=[1:W(1)-OP(1):size(M,1)-W(1), size(M,1)-W(1)+1]
for j=[1:W(2)-OP(2):size(M,2)-W(2), size(M,2)-W(2)+1]
block = rand(W(1),W(2));
M(i:i+W(1)-1, j:j+W(2)-1) = block;
imagesc(M); axis equal tight xy
pause(.1)
end;
end;
So, in a more clear way, how should I change the "above" code in order to start from a location(x,y) and spirally fill the whole matrix according to W, OP and size(M).
Thanks!
Here is a piece of code which produces the expected output. There where only minor changes to the spiral_generic necessary to match your requirements:
function demo()
spiral_generic([10,11],[3,4])
W = [10 12];
OP = [4 3];
%make sure your start point is really on the grid of r and c, this is not checked!
start = [19,28];
M = zeros(100,110);
r=[1:W(1)-OP(1):size(M,1)-W(1), size(M,1)-W(1)+1];
c=[1:W(2)-OP(2):size(M,2)-W(2), size(M,2)-W(2)+1];
startindex=[find(r==start(1),1,'first'),find(c==start(2),1,'first')];
A=spiral_generic([numel(r),numel(c)],startindex);
[~,idx]=sort(A(:));
[ridx,cidx]=ind2sub(size(A),idx);
%blocks contains the lower left corners in order of processing.
blocks=[r(ridx);c(cidx)];
for blockindex=blocks
block = rand(W(1),W(2));
M(blockindex(1):blockindex(1)+W(1)-1, blockindex(2):blockindex(2)+W(2)-1) = block;
imagesc(M);
pause(.1)
end
end
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
M = permute(M,[2,1]); % changing start direction of the spiral
M = M(:,end:-1:1); % chaning spin orientation
C = r + 1 - (P - 1); % Top-left corner of A in M
A = M(C(1):C(1)+n(1)-1, C(2):C(2)+n(2)-1); % Get the submatrix
[~, order] = sort(A(:)); % Get elements' order
A(order) = 1:(n(1)*n(2)); % Fill with continous values
end
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