how can I sweep a triangle area using two loops

Hello,

I want to sweep all points inside a triangle by coordinates (0,0), (2*pi/(3*a),0) and (0,4*pi/(3*a)) and by deviding this into two triangles and calculating line equations i wrote this code

for j=1:101

x=2*(j-1)*pi/(100*sqrt(3)*a);

for l=1:101

y=-(l-1)*x/(100*sqrt(3))+2*pi*(l-1)/(3*a*100);

for k=1:101

x=2*(k-1)*pi/(100*sqrt(3)*a);

for m=1:101

y=-(m-1)*x/(100*sqrt(3))+2*pi*(m-1)/(100*3*a)+2*pi/(3*a);

But this code doesn't cover some y points inside the triangle. What can i do for solving this problem?

[Scott MacKenzie]

Please provide code that can execute and clarify what you mean by "sweep". Also, by "points", do you mean "points with integer coordinates"?

[mohammad mortezaie]

This is code:

acc=1.42;

a=sqrt(3)*acc;

c=3.3;

gama0=3.16;

gama1=0.39;

gama2=-0.020;

gama3=0.315;

gama4=0.044;

gama5=-0.04;

V=0.;

iform=complex(0.0,1.0);

iden= eye([6 6]);

delta=0.0015;

eta=0.05;

for i=1:201

e=-0.5+4*(i-1)*delta;

Density=0;

for j=1:101

k_x=2*(j-1)*pi/(100*sqrt(3)*a);

for l=1:101

k_y=-(l-1)*k_x/(100*sqrt(3))+2*pi*(l-1)/(3*a*100);

f0=exp(-iform*acc*k_x)+2*cos(sqrt(3)*k_y*acc)*exp(iform*k_x*acc);

f1=exp(iform*k_x*c);

f3=f0*exp(iform*c*k_x);

H6=[-V gama0*f0 gama4*f3 gama3*f3 gama2*f1 0;

gama0*conj(f0) -V gama1*f1 gama4*f3 0 gama5*f1;

gama4*conj(f3) gama1*conj(f1) 0 gama0*f0 gama4*conj(f3) gama1*f1;

o vv gama3*conj(f3) gama4*conj(f3) gama0*conj(f0) 0 gama3*conj(f3) gama4*conj(f3);

gama2*conj(f1) 0 gama4*f3 gama3*f3 V gama0*f0 ;

0 gama5*conj(f1) gama1*conj(f1) gama4*f3 gama0*conj(f0) V];

G=(e*iden+eta*iform*iden)-eig(H6).*iden;

Green=inv(G);

Den=trace(Green);

Density=Density-imag(Den)/pi;

end

end

for k=1:101

k_x=2*(k-1)*pi/(100*sqrt(3)*a);

for m=1:101

k_y=-(m-1)*k_x/(100*sqrt(3))+2*pi*(m-1)/(100*3*a)+2*pi/(3*a);

f0=exp(-iform*acc*k_x)+2*cos(sqrt(3)*k_y*acc)*exp(iform*k_x*acc);

f1=exp(iform*k_x*c);

f3=f0*exp(iform*c*k_x);

H6=[-V gama0*f0 gama4*f3 gama3*f3 gama2*f1 0;

gama0*conj(f0) -V gama1*f1 gama4*f3 0 gama5*f1;

gama4*conj(f3) gama1*conj(f1) 0 gama0*f0 gama4*conj(f3) gama1*f1;

gama3*conj(f3) gama4*conj(f3) gama0*conj(f0) 0 gama3*conj(f3) gama4*conj(f3);

gama2*conj(f1) 0 gama4*f3 gama3*f3 V gama0*f0 ;

0 gama5*conj(f1) gama1*conj(f1) gama4*f3 gama0*conj(f0) V];

G=(e*iden+eta*iform*iden)-eig(H6).*iden;

Green=inv(G);

Den=trace(Green);

Density=Density-imag(Den)/pi;

end

end

i

T(i,1)=e;

T(i,2)=Density/8000;

end

plot(T(:,1),T(:,2))

Yes from points i mean (x,y) coordinate.

[mohammad mortezaie]

this is triangle that I mean. Strip area is needed to be sweep or broom.

Answer 1

[Scott MacKenzie]

No need for loops. The tests are built in to the inpolygon function when you provide matrices as input. Assuming you want to find points inside the triangle, given a "sweep" grid of x-y test points (integers or reals), then I think this achieves what you are after:

% your triangle points 
a = 0.1;
xt = [0, 2*pi / (sqrt(3)*a), 0, 0];
yt = [0, 2*pi/(3*a), 4*pi/(3*a), 0];

% plot triangle with margin around edges
margin = 5;
x1 = round(min(xt)- margin);
x2 = round(max(xt)+ margin);
y1 = round(min(yt)- margin);
y2 = round(max(yt)+ margin);
axis([x1 x2 y1 y2]);
hold on;
plot(xt,yt);

% make a grid of points to find points inside and outside triangle
delta = 1; % granularity of grid (adjust as desired)
[X,Y] = ndgrid(x1:delta:x2,y1:delta:y2);

% test the points (logical matrix 'in' identifies points in/out)
in = inpolygon(X,Y,xt,yt);

% output number of points inside triangle
sum(sum(in))

% plot the points inside (blue) and outside (light blue)
plot(X(in),Y(in),'.b') % points inside
plot(X(~in),Y(~in),'.', 'color', [.7 .7 1]) % points outside

[mohammad mortezaie]

Thank you so much. But I need all of x and y points in a "for" loop since I should use these points inside the matrix and calculating "Density". Please help me for writing this code using loops.

[mohammad mortezaie]

I was doing some similar problem by finding line equations(as I mentioned in the top code. But it is not correct), but in this case I faced with a problem which has I can't broom all appropriate y coordinates for x=0-2*pi/(sqrt(3)*a) and restricted in the triangle.

[Scott MacKenzie]

I'm not sure what you mean by "all points" or "all appropriate y coordinates". The number of points inside the triangle is infinite. I included a variable delta for setting up ndgrid. The lower the value of delta the greater the number of points inside the triangle. Some stats here are...

Delta Number of Points inside triangle

1 781

0.1 76186

0.01 7599720

[mohammad mortezaie]

Thank you so much