# How plot a grid of rectangles on an overlaid circle?

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JM on 20 May 2024 at 16:48
Moved: Matt J on 28 May 2024 at 12:33
How to plot a circle of radius R and an overlaid grid of rectangles (with each rectangle of dimensions LxW)?
Choice of dimensions are so that the rectangular grid is larger than the dimeter of the circle and the centre of the circle is on one of the rectangle corners within the grid. The circle fully sits within the rectangular grid.
Secondly, from the plot or otherwise can Matlab help count the full rectangles within the circle?

Matt J on 20 May 2024 at 18:04
Edited: Matt J on 20 May 2024 at 18:14
R = 5; % circle radius
H = 1; % rect height
W = 2; % rect width
circ=nsidedpoly(1000,"Radius",R); %polyshape for the circle
Grid=scale(nsidedpoly(4,'Side',1,'Center',[+1,+1]/2),[W,H]);
Grid=arrayfun(@(i)translate(Grid,H*[0,i]),-ceil(R/H):ceil(R/H)-1)';
Grid=arrayfun(@(i)translate(Grid,W*[i,0]),-ceil(R/W):ceil(R/W)-1,'uni',0);
Grid=vertcat(Grid{:}); %polyshape vector for grid rectangles
numContained=sum( area(intersect(Grid,circ))>=area(Grid(1))*0.9999 ) %count contained rectangles
numContained = 28
plot([circ; Grid],'FaceColor','w'); axis equal
JM on 22 May 2024 at 14:18
Edited: JM on 22 May 2024 at 14:33
Upgrade, as much as I would want it, is beyond my control I am afraid
JM on 22 May 2024 at 16:03
Moved: Matt J on 28 May 2024 at 12:33
@Matt J. Thanks

### More Answers (1)

Voss on 20 May 2024 at 17:31
R = 5; % circle radius
L = 1; % horizontal grid spacing
W = 2; % vertical grid spacing
C = [7 8]; % center of the circle
% calculate some points on the circle
th = linspace(0,2*pi,100);
xc = C(1)+R*cos(th);
yc = C(2)+R*sin(th);
% calculate the grid's x and y coordinates
xg = C(1)+W*(floor(-R/W):ceil(R/W));
yg = C(2)+L*(floor(-R/L):ceil(R/L));
% plot the circle
plot(xc,yc)
axis equal
% create the vertical grid lines
nx = numel(xg);
xdata = [xg;xg;NaN(1,nx)];
ydata = [repmat(yg([1 end]).',1,nx); NaN(1,nx)];
line(xdata,ydata,'Color','k')
% create the horizontal grid lines
ny = numel(yg);
ydata = [yg;yg;NaN(1,ny)];
xdata = [repmat(xg([1 end]).',1,ny); NaN(1,ny)];
line(xdata,ydata,'Color','k')
% count the rectangles completely inside the circle
n_rectangles_inside = nnz(conv2((xg-C(1)).^2+(yg.'-C(2)).^2 <= R^2,ones(2)) == 4)
n_rectangles_inside = 28

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