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Determine the condition to find elements inside semi circular region in a rectangular mesh

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I have a rectangular mesh of 500000x500000. I extracted the coordinates of the mesh elements. Now I would like to remove elements in the semicircular form from this rectangular mesh. I have the function to remove elements. But I am struggling to set the condition for the semicircular region to determine all the elements inside the semicircular region. For example if ex and ey are the coordinates of elements in mesh, then I am using
find(ex<=R*cos(theta) & ey <=R*sin(theta)).
How to set this condition according to the grid points in the rectangular mesh. I have also attached the image for more clarity.
Thanks.

Accepted Answer

KSSV
KSSV on 6 Nov 2018
Edited: KSSV on 6 Nov 2018
Read about inpolygon. This should help you.
M = 100 ;
N = 100 ;
x = linspace(0,1,M) ;
y = linspace(0,1,N) ;
[X,Y] = meshgrid(x,y) ;
% semi circle
O = [0.5 0. ]; % origin of circle
R = 0.3 ; % RAdius of circle
th = linspace(0,2*pi) ;
xc = O(1)+R*cos(th) ;
yc = O(2)+R*sin(th) ;
% Get points lying inside circle
idx = inpolygon(X(:),Y(:),xc,yc) ;
% plot
figure
hold on
plot(X,Y,'.r') ;
plot(xc,yc,'b')
plot(X(idx),Y(idx),'.k')
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