I have a 3D point cloud (XYZ) where the Z
can be position or energy. I want to project them on a 2D surface in a n-by-m grid (in my problem n = m
) in a manner that each grid cell has a value of the maximum difference of Z
, in case of Z
being position, or a value of summation over Z
, in case of Z
being energy.
For example, in a range of 0 <= (x,y) <= 20
, there are 500 points. Let's say the xy-plane has n-by-m partitions, e.g. 4-by-4; by which I mean in both x
and y
directions we have 4 partitions with an interval of 5
(to make it 20
at maximum. Now, each of these cells should have a value of the summation, or maximum difference, of the Z
value of those points which are in the corresponding column in the defined xy-plane.
I made a simple array of XYZ just for a test as follows, where in this case, Z
denotes the energy of the each point.
n=1;
for i=1:2*round(random('Uniform',1,5))
for j=1:2*round(random('Uniform',1,5))
table(n,:)=[i,j,random('normal',1,1)];
n=n+1;
end
end
How can this be done without loops?
Remarks:
What you can do is
meshgrid
, kd-tree
search, i.e. label your data associating to each cloud point a grid nodeaccumarray
).Here's a working example:
samples = 500;
%data extrema
xl = 0; xr = 1; yl = 0; yr = 1;
% # grid points
sz = 20;
% # new random cloud
table = [random('Uniform',xl,xr,[samples,1]) , random('Uniform',yr,yl,[samples,1]), random('normal',1,1,[samples,1])];
figure; scatter3(table(:,1),table(:,2),table(:,3));
% # grid construction
xx = linspace(xl,xr,sz); yy = linspace(yl,yr,sz);
[X,Y] = meshgrid(xx,yy);
grid_centers = [X(:),Y(:)];
x = table(:,1); y = table(:,2);
% # kd-tree
kdtreeobj = KDTreeSearcher(grid_centers);
clss = kdtreeobj.knnsearch([x,y]); % # classification
% # defintion of local statistic
local_stat = @(x)sum(x) % # for total energy
% local_stat = @(x)max(x)-min(x) % # for position off-set
% # data_grouping
class_stat = accumarray(clss,table(:,3),[],local_stat );
class_stat_M = reshape(class_stat , size(X)); % # 2D reshaping
figure; contourf(xx,yy,class_stat_M,20);