Number of grid points inside circle

I have my radius being between 1 and 10 and my angle from 0 to 2pi. I defined an uniform rectangular grid with 10 points (10 by 10) and I want to find how many points fall into the circle. This is my code but when I run it I do not get the figure that I want. Thanks a lot.

xq=-10:10;

yq=-10:10;

a=0:0.01:2*pi; %angle

r = 10; % radius

xv = r*cos(a); % cartesian x coordinate

yv = r*sin(a); % cartesian y coordinate

in = inpolygon(xq,yq,xv,yv);

figure(1)

plot(xv,yv) % circle

axis equal

hold on

plot(xq(in),yq(in),'r+') % points inside

plot(xq(~in),yq(~in),'bo') % points outside

hold off

[Star Strider]

The code you posted —

xq=-10:10;
yq=-10:10;
a=0:0.01:2*pi; %angle 
r = 10;           % radius
xv = r*cos(a);    % cartesian x coordinate
yv = r*sin(a);    % cartesian y coordinate
in = inpolygon(xq,yq,xv,yv);
figure(1)
plot(xv,yv) % circle
axis equal
hold on
plot(xq(in),yq(in),'r+') % points inside
plot(xq(~in),yq(~in),'bo') % points outside
hold off

The code I posted previously in Find all the grid points that are inside of the circle does this differently —

r = 1:10;
% r = pi*[1:3];
a = linspace(0, 2*pi);
x = r(:)*cos(a)+5.5;
y = r(:)*sin(a)+5.5;
[Xg,Yg] = ndgrid(1:numel(r));
Xv = Xg(:);
Yv = Yg(:);

for k = 1:size(Xg,1)
    [incirc(:,k),oncirc(:,k)] = inpolygon(Xv,Yv,x(k,:),y(k,:));
end
circtot = [nnz(incirc) nnz(oncirc)]

circtot = 1×2

676 0

CircleRad = 3;

figure
hp{1} = plot(x.', y.', '--b');
hold on
hp{2} = plot(Xv, Yv, '.k');
hp{3} = plot(Xv(incirc(:,CircleRad)), Yv(incirc(:,CircleRad)), 'or');
hp{4} = plot(Xv(oncirc(:,CircleRad)), Yv(oncirc(:,CircleRad)), 'og');
hold off
axis('equal')
text(cosd(30)*r+5.5, sind(30)*r+5.5,compose('$%d$',r), 'Horiz','center','Vert','middle', 'Interpreter','latex')
legend([hp{1}(1),hp{2}(1),hp{3}(1)],'Circles', 'Grid', sprintf('In Circle r = %d (N = %d)', CircleRad, nnz(incirc(:,CircleRad))), sprintf('On Circle r = %d (N = %d)', CircleRad, nnz(oncirc(:,CircleRad))), 'Location','best')

Warning: Ignoring extra legend entries.

Is there a problem with what it does?

Answer 1

[Scott MacKenzie]

I only changed the 1st two lines. Is this what you are looking for?

xq = repmat(-10:10,21,1);
yq = xq';
a = 0:0.01:2*pi;  % angle 
r = 10;           % radius
xv = r*cos(a);    % cartesian x coordinate
yv = r*sin(a);    % cartesian y coordinate

in = inpolygon(xq,yq,xv,yv);

figure(1)

plot(xv,yv) % circle
axis([-11 11 -11 11]);
hold on
plot(xq(in),yq(in),'r+')   % points inside
plot(xq(~in),yq(~in),'bo') % points outside
hold off

[Scott MacKenzie]

Marina: Oops, that was my mistake. I just corrected the solution. I changed the first line from

xq = repmat(-10:10,10,1); % Oops. Wrong number of repetitions of the vector

to

xq = repmat(-10:10,21,1); % 21 repetitions needed!

[Marina Markaki]

I just wrote xq = repmat(-10:10,100) and I got exactly the figure that I wanted. Thank you a lot for your help.