How do I remove points which are far away from the boundary of domain?

Hi, I would like to know how do I remove points which are far away from the boundary of domain, for example

% Before

% Set points of domain:
x=  [ 0 0.5	0.5 1 1 0 0 0.5 0.75 0.25 0.25];
y = [0 0 0.5 0.5 1 1 0.5 1	0.75 0.75 0.25];
 
% Set center points:
xc = linspace(0,1,5);
yc = linspace(0,1,5);
[xcen,ycen]  = meshgrid(xc,yc);
 
% Plot
figure(1);
plot(x,y,'b.','MarkerSize',4);
hold on
corner = [0 0; 0.5 0; 0.5 0.5; 1 0.5; 1 1;0 1;0 0]; % visualize the boundary domain
plot(corner(:,1),corner(:,2),'-g','linewidth',0.5);
hold on
plot(xcen,ycen,'or');
hold off

% After

% % Remove center points which are  far away from the boundary of domain.
idx   = knnsearch(data_r,data_b,'k',1);
xc    = xc(:,unique(idx));
yc    = yc(:,unique(idx));

H           = min(diff(xc));

Xcen         = xc(1:end-1) + 0.5*H;
Ycen         = yc(1:end-1) + 0.5*H;

[xcen,ycen]  = meshgrid(Xcen,Ycen);
 
% Plot
figure(2);
plot(x,y,'b.','MarkerSize',7);
hold on
corner = [0 0; 0.5 0; 0.5 0.5; 1 0.5; 1 1;0 1;0 0]; % visualize the boundary domain
plot(corner(:,1),corner(:,2),'-g','linewidth',0.5);
hold on
plot(xcen,ycen,'or');
hold off

The problem : there is 4 red points which are out the boundary of domain!

Question : what can i do to remove any points which are out of the boundary nodes ?

Answer 1

[Matt J]

Question : what can i do to remove any points which are out of the boundary nodes ?

Use inpolygon to detect which points are within the boundaries. Then discard the others.

[Yamina chbak]

Thank you, @Matt J I followed your advice, but it didn't work.

% Set points of domain:
x=  [ 0 0.5	0.5 1 1 0 0 0.5 0.75 0.25 0.25];
y = [0 0 0.5 0.5 1 1 0.5 1	0.75 0.75 0.25];
 
% Set center points:
xc = linspace(0,1,15);
yc = linspace(0,1,15);

[in,on] = inpolygon(xc,yc,x,y); 
xc    = xc(:,in&~on);
yc    = yc(:,in&~on);
  
H           = min(diff(xc));

Xc         = xc(1:end-1) + 0.5*H;
Yc         = yc(1:end-1) + 0.5*H;
[in,on] = inpolygon(Xc,Yc,x,y); 
Xcen    = Xc(:,in&~on);
Ycen    = Yc(:,in&~on);

[xcen,ycen]  = meshgrid(Xcen,Ycen);
 
% Plot
figure();
plot(x,y,'b.','MarkerSize',10);
hold on
corner = [0 0; 0.5 0; 0.5 0.5; 1 0.5; 1 1;0 1;0 0]; % visualize the boundary domain
plot(corner(:,1),corner(:,2),'-g','linewidth',0.5);
hold on
plot(xcen,ycen,'or');
hold off

[Matt J]

Here is a similar idea that uses polyshape:

% Set points of domain:
x=  [ 0 0.5	0.5 1 1 0 0 0.5 0.75 0.25 0.25];
y = [0 0 0.5 0.5 1 1 0.5 1	0.75 0.75 0.25];
 
corner = [0 0; 0.5 0; 0.5 0.5; 1 0.5; 1 1;0 1;0 0];

% Set center points:
xc = linspace(0,1,5);
yc = linspace(0,1,5);
[xcen,ycen]  = meshgrid(xc,yc);

%Remove center points that are on or outside boundary
pgon=polybuffer( polyshape(corner), -1e-6);
keep=isinterior(pgon,xcen(:),ycen(:));
[xkeep,ykeep]=deal(xcen(keep),ycen(keep));


plot(corner(:,1),corner(:,2),'-g','linewidth',0.5);
hold on
plot(xcen,ycen,'or');
plot(xkeep,ykeep,'ok','MarkerFaceColor','k');
hold off

[Yamina chbak]

I want to thank you again and say that you have taught me something new.

I notice that you use polyshape(corner),which is nice idea and clear; but, if I have boundary node data that is complicated geometrically, it will appear like the red dots in the next picture:

and try out this idea polyshape(data_boundary) to get an etoile red like this picture, I discover that error:

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

What should i do ?

[Matt J]

It's a warning, not an error, so maybe nothing is wrong. You can plot it as a check,

plot(polyshape(data_boundary))

I suspect that the points in data_boundary are not listed in the proper order.

[Matt J]

It's a warning, not an error, so maybe nothing is wrong. You can plot it as a check,

plot(polyshape(data_boundary))

I suspect that the points in data_boundary are not listed in the proper order.

[Yamina chbak]

Thanks you again @Matt J.