3 views (last 30 days)

In the Cartesian grid, the real structures are pixelized into the staircase approximation. To reduce the staircase error, the effective permittivity is computed, which is weighted by the fraction of the mesh step inside the material 1 or 2 (See the below figure). For instance, the structure is sphere. How I can compute the fraction ratio of four edges in each grid on the boundary of the sphere? Could you please give me some suggestions?

% build Cartesian grid

[Y1,X1]=meshgrid(y_1grid,x_1grid);

% build structure (sphere)

UCC= ((X1+dx/2).^2 + (Y1+dy/2).^2) <= (diam/2.0)^2;

eps_cc=eps(2)*(UCC==1)+eps(1)*(UCC==0);

% find the boundary

[Fx,Fy]=gradient(eps_cc);

boundary=(Fx~=0)|(Fy~=0);

% compute the ratio of intersection point

??

Big Thanks to you

Bruno Luong
on 9 Sep 2019

Edited: Bruno Luong
on 9 Sep 2019

Assuming the boundary has one connexed piece

x=-3:12;

y=-3:10;

[X,Y]=meshgrid(x,y);

cx = 4;

cy = 3;

r = 5;

Z = (X-cx).^2 + (Y-cy).^2 - r^2;

C = contourc(x,y,Z,[0 0]);

Cx = C(1,2:end);

Cy = C(2,2:end);

[Cx; Cy] % fractional crossing is grouped here

close all

hold on

plot(X,Y,'-b');

plot(X',Y','-b');

plot(Cx,Cy,'-r');

plot(cx,cy,'ko');

axis equal

Bruno Luong
on 16 Sep 2019

The pixels coordinates are

ii=interp1(x,1:length(x),Cx,'previous')

jj=interp1(y,1:length(y),Cy,'previous')

And the corresponding fractional are

ratio_x=interp1(x,1:length(x),Cx)-ii

ratio_y=interp1(y,1:length(y),Cy)-jj

Just loop on the list [ii; jj; ratio_x; ratio_y] and do whatever you need to do.

for pixel = [ii; jj; ratio_x; ratio_y]

i = pixel(1);

j = pixel(2);

rx = pixel(3);

ry = pixel(4):

% do something with i,j,rx,ry ...

end

Alternatively, to avoid using INTERP1 you can call contour with pixel coordinates

C = contourc(1:size(Z,2),1:size(Z,1),Z,[0 0]);

Cx = C(1,2:end);

Cy = C(2,2:end);

% these replace the INTERP1 stuffs

ii = floor(Cx);

jj = floor(Cy);

ratio_x = Cx-ii;

ratio_y = Cy-jj;

The process ii,jj,ratio_x,ratio_y

Sign in to comment.

Sign in to answer this question.

Opportunities for recent engineering grads.

Apply Today
## 2 Comments

## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/479460-how-to-compute-the-ratio-of-the-insection-point-in-each-grid-on-the-boundary-of-a-real-structure#comment_743796

⋮## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/479460-how-to-compute-the-ratio-of-the-insection-point-in-each-grid-on-the-boundary-of-a-real-structure#comment_743796

## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/479460-how-to-compute-the-ratio-of-the-insection-point-in-each-grid-on-the-boundary-of-a-real-structure#comment_744582

⋮## Direct link to this comment

https://se.mathworks.com/matlabcentral/answers/479460-how-to-compute-the-ratio-of-the-insection-point-in-each-grid-on-the-boundary-of-a-real-structure#comment_744582

Sign in to comment.