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

mesh

I have a rectangular mesh of 500000×500000. 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.

Best Answer

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')

Related Solutions

MATLAB: Remove points from a mesh

If you know the parameters of the circle that encompasses the area you'd like to remove (ie, the center coordinates and the radius), you could just calculate the distance of all points to the circle's center and then eliminate all dots whose distance is less than the radius. This would work if all of the dots are on the same plane as the circle's center which appears to be the case.

Here's an example where x and y are the coordinates of your dots. c is the (x,y) center of your circle and r is the radius.

% create data
x = rand(1000,1);     
y = rand(1000,1); 
c = [.5, .5];     %[x,y] center of circle
r = 0.2;          %radius
% Calculate distance to circle center
d = sqrt((x - c(1)).^2 + (y - c(2)).^2);
% find dots on/in circle
inCircleIdx = d <= r; 
% remove dots on/in circle
x(inCircleIdx) = []; 
y(inCircleIdx) = [];

MATLAB: How to draw circle with radius 1

Rad3Over2 = sqrt(3) / 2;
[X Y] = meshgrid(-.2:0.2:1.6);
n = size(X,1);
X = Rad3Over2 * X;
Y = Y + repmat([0 0.5],[n,n/2]);
% Plot the hexagonal mesh, including cell borders
[XV, YV] = voronoi(X(:),Y(:));
plot(XV,YV,'b')
axis equal,
axis([.2 1.2 .2 1])
zoom on ;
hold on
%%Get centers
[V,C] = voronoin([X(:) Y(:)]) ;
xc = cellfun(@(index) mean(V(index,1)),C);
yc = cellfun(@(index) mean(V(index,2)),C);
%%draw circles
th = linspace(0,2*pi) ; r = 0.1 ;
x = r*cos(th) ; y = r*sin(th) ;
for i = 1:length(xc)
    if ~isinf(xc(i))
        xx = x+xc(i) ;
        yy = y+yc(i) ;
        plot(xx,yy,'r')
    end
end

Best Answer

Related Solutions

MATLAB: Remove points from a mesh

MATLAB: How to draw circle with radius 1

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