MATLAB moving a point in the XY plane

Question

In MATLAB, I have an XY plane that is represented by finite number of points. The possible values of x are stored in a vector X and the possible values of y are stored in an

Answer 1

Consider the following code:

%# create grid of 2D coordinates
sz = [5 6];
[X,Y] = meshgrid(1:sz(2),1:sz(1));

%# point A
A = [1 2]

%# neighboring points
k = 2;                               %# hop size
[sx,sy] = meshgrid(-k:k,-k:k);       %# steps to get to neighbors
xx = bsxfun(@plus, A(1), sx(:));     %# add shift in x-coords
xx = min(max(xx,1),sz(2));           %# clamp x-coordinates within range
yy = bsxfun(@plus, A(2), sy(:));
yy = min(max(yy,1),sz(1));
B = unique([xx yy],'rows');          %# remove duplicates
B(ismember(B,A,'rows'),:) = [];      %# remove point itself

The result for the point A = (1,2) with k=2 hops:

B =
     1     1
     1     3
     1     4
     2     1
     2     2
     2     3
     2     4
     3     1
     3     2
     3     3
     3     4

and an illustration of the solution:

x A x x . .
x x x x . .
x x x x . .
. . . . . .
. . . . . .

Answer 2

lets say A = [Xcenter Ycenter]

for K-hop, you can access points:

pointsX = [];
pointsY = [];
for i=-k:k
  pointsX = [pointsX  Xcenter+i]; 
  pointsY = [pointsY  Ycenter+i];
end

Furthermore, you can filter these points by order coordinates and remove the outliers. e.g. consider

(1,1)  (1,2)  (1,3)
(2,1)  (2,2)  (2,3)
(3,1)  (3,2)  (3,3)

Now you know that minimum allowed X and Y are 1, so just filter out points with any ordinate and/or abscissa lesser than that.