Intersection of circles and polygons?

I am a bit lost on how I can get the points where a circle intersects a polygon. The circle was created using the rectangle() function and the polygon was plotted using the polyshape() function.

[Star Strider]

The inpolygon function could be helpful here.

.

Answer 1

[Matt J]

If you approximate the circle as a polyshape as well, it is very easy to do with

https://www.mathworks.com/matlabcentral/fileexchange/93470-intersections-of-multiple-2d-lines-or-line-segments

Example:

pgon=polyshape(     [2.8259    1.8997
    1.3496    4.4206
    3.3552    3.4178
    4.3719    4.6992
    4.8872    2.1226
    3.2298    2.7214
    3.3134    1.1337
    1.1685    1.1616] );  %hypothetical polygon

R=1.5; [x0,y0]=deal(3,3); %Circle radius and center
t=linspace(0,360,1000).'; t(end)=[]; %circle angular samples

circle=polyshape([cosd(t), sind(t)]*R+[x0,y0]); 

plot([pgon,circle]); axis equal

%find intersections

V=pgon.Vertices;
N=size(V,1);
V=V([1:N,1],:);

hold on
for i=1:N
    xy=linexlines2D(circle,V(i,:),V(i+1,:));
    plot(xy(1,:),xy(2,:),'or','MarkerFaceColor','r');
end
hold off

[Steven Lord]

One easier way to approximate the circle by a polyshape is to create a regular N-sided polygon for a large value of N.

P = nsidedpoly(1000, 'Center', [3 3], 'Radius', 2);
plot(P)
axis equal

That looks pretty circular to me, though if you want you could increase 1000 to 10k or even higher.

Answer 2

[Matt J]

This is similar to my other answer, but instead of approximating the circle as a polygon, it does an exact theoretical calculation of the intersections. It will probably be much faster.

pgon=polyshape(     [2.8259    1.8997
    1.3496    4.4206
    3.3552    3.4178
    4.3719    4.6992
    4.8872    2.1226
    3.2298    2.7214
    3.3134    1.1337
    1.1685    1.1616] );  %hypothetical polygon

R=1.5; [x0,y0]=deal(3,3); %Circle radius and center


plot(pgon); axis equal  %plot polygon
hold on
fimplicit(@(x,y)(x-x0).^2+(y-y0).^2-R^2); %plot circle



%find intersections

V=pgon.Vertices;
N=size(V,1);
V=V([1:N,1],:);


for i=1:N % loop over the polygon edges
    
    v0=V(i,:)-[x0,y0];
    
    d=V(i+1,:)-V(i,:);

    Ax=d(1); Bx=v0(1);
    Ay=d(2); By=v0(2);
    
    q=[Ax.^2+Ay.^2, 2*(Ax*Bx+Ay*By), Bx.^2+By.^2-R^2];
    
    t=roots(q);
    t(abs(imag(t))>1e-8*abs(real(t)))=[];
    t=t(0<=t &t<=1);
    
    if isempty(t), continue; end
    
    
    
    xy=V(i,:)+t*d; %intersection(s) with current polygon edge
    
    plot(xy(:,1),xy(:,2),'or','MarkerFaceColor','r');
end
hold off