2D Surface Random Number Plot

The 2D square surface has 1m length in each side and splitted into 10 grid(Total grid is 10x10). A ball is hitting the surface 1000 times. The hit is random. The exact position of each hit is determined by random number. How can I find the total hit count in each grid? Each grid will be named as

A0101, A0201 . . . .A1001

A0102, A0202 . . . .A1002

.........................................

A1001, A1002 . . . A1010

Initial codes are as followings -

x = rand;
y = rand;

x1 = linspace(0,1,11)
y1 = linspace(0,1,11)

for i = 1:1000
    [x,y];
end

Answer 1

[KSSV]

% Make grid 
x = linspace(0,1,11) ;
y = linspace(0,1,11) ;
[X,Y] = meshgrid(x,y) ; 
% Get mid points  of each element 
mx = linspace(0.05,0.95,10) ; 
my = linspace(0.05,0.95,10) ; 
[MX,MY] = meshgrid(mx,my) ; 
plot(X,Y,'.r',MX,MY,'.b')

MZ = zeros(size(MX)) ;   % Initialize the hit count 
for i = 1:1000
    hit = rand(1,2) ; 
    % Check where it is hit 
    idx = knnsearch([MX(:) MY(:)],hit) ;
    % UPdate the count 
    MZ(idx) = MZ(idx)+1 ; 
end
figure
hold on
plot(X,Y,'k',X',Y','k')
scatter(MX(:),MY(:),[],MZ(:),'filled') ; 
colormap(jet) ; 
cb = colorbar ;
ylabel(cb,'Number of hits')

[Syed Arafun Nabi]

• The Ball will hit boundary too in some other cases. So in this case I want to consider the scenerio of boundary too. For the outer most grid the boundary line will be considered too.
• I want to have the final data in Table format. Grid Number & Count. So I will have more control in data to plot in different graph (x axis vs count, contour plot, etc)

[KSSV]

Z is in matrix already you can plot a contour.

About boundary, we need to change the strategy.

[Syed Arafun Nabi]

If the probablity of hitting the bondary is 20% & inside the surface is 80%. The boundary hit will be consider in the corresponding grid. How can we modify? Can you please assist?

My actual code is more than 250 lines. so this is just a template

a = rand

a = 0.8406

if a<.05 
    %hit y=0 plane
    x=rand
    y=0
elseif a<.10
    %hit y=0 plane
    x=rand
    y=1
elseif a<.15
    %hit x=0 plane
    x=0
    y=rand
elseif a<.20
    %hit x=1 plane
    x=1
    y=rand
else 
    %inside the surface
    x=rand
    y=rand
end

x = 0.4815

y = 0.4564

Answer 2

[Steven Lord]

I recommend using histogram2.

Answer 3

[John]

The best way to do this is to use sequential indices, rather than row, column. Then you're just keeping track of a single number. If you do need the x, y coordinates (row, column), you can try this:

hit_count = zeros(10);
hits = randi(numel(hit_count), 1, 1000); %Randomly hit an cell index between 1 and 100, 1000 times

for i = 1:10
    for j = 1:10
        seq_index = (i-1) * 10 + j;
        hit_count(i, j) = sum(hits == seq_index);
    end
end

This would be the same as doing the following:

hit_count = zeros(10);
hits = randi(numel(hit_count), 1, 1000); %Randomly hit an cell index between 1 and 100, 1000 times

for i = 1:numel(hit_count)
    hit_count(i) = sum(hits == i);
end

As for the name of the cells, I'm not sure how you want to access them. You can easily make up a calling function though that returns the hits per cell based on an inputted name though...

hits_at_3_5 = getNumberOfHitsPerCell('A0305', hit_count);
disp(hits_at_3_5)

     8

function [num_hits] = getNumberOfHitsPerCell(cell_name, hit_count)
    x = str2num(cell_name(2:3));
    y = str2num(cell_name(4:5));
    num_hits = hit_count(x, y);
end

You'd probably want to do some more intense string validation if you go this route though. Good luck!