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

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.

Answer 1

[KSSV]

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')

[Abhishek Saini]

Is it possible to do same for 3D meshgrid or cuboid? For example in a slice of 3D volume?

[KSSV]

Yes very much...but not with inpolygon.

[Abhishek Saini]

Could you please suggest for 3D also?

[KSSV]

For cuboid you want to get points which are inside sphere?

[Abhishek Saini]

No, It is like the flat semi-circular notch. I have attached the picture for the reference. Thanks!

[KSSV]

Do you have points for the above? I have to create and check..so asking..

[Abhishek Saini]

Yes, I have but that is quite a huge file. Maybe we could check by creating 3D meshgrid. I could create a smaller one.

[KSSV]

Yes..do it..and attach the data..3d points and semi circle. Actually, you can use the same inpolygon for this. YOu see the semi circle and the points lie on some plane..where you can discard one dimension which is common....and input the other 2d points.

[Abhishek Saini]

Hi,

Sorry for the dealy.

I have attached the data. I ahve generated the small data for the testing.

px, py and pz are the coordinate points in x, y and z direction.

I want to select points in semi circular pattern. Attacehd is the picture.

Cordinate system

x = horizontal

z = vertical

y = 3rd dimention i.e. width

[Image Analyst]

You've accepted an answer so we assume the problem has been solved.

[Abhishek Saini]

Whether this question will be considered or not?