intersection points between random polygon and a circle

Hi, I have a random polygon (with known coordinates of the vertices) and a circle(with know center coordinates and center). I want to find the intersection points in between them. I have used linecirc function, but the problem is it also gives the intersection points which does not lie on the polygon. I have developed the following program, but sometimes it does not provide all the intersection points. Please help me to find out where I went wrong. Thanks

for i=1:length(V_x) %closed polygon with 7 vertices

V_x(8)=V_x(1);

V_y(8)=V_y(1);

m(i)=(V_y(i)-V_y(i+1))/(V_x(i)-V_x(i+1));

b(i)=-m(i)*V_x(i)+V_y(i);

[xout,yout] = linecirc(m(i),b(i),C_x,C_y,R);

crossX(i,1)=xout(1,1);

crossX(i,2)=xout(1,2);

crossY(i,1)=yout(1,1);

crossY(i,2)=yout(1,2);

DistCircleVertex(i)=distance(C_x,V_x(i),C_y,V_y(i));

EdgeLength(i)=distance(V_x(i),V_x(i+1),V_y(i),V_y(i+1));

DistPoint1Vertex1(i)=distance(V_x(i),crossX(i,1),V_y(i),crossY(i,1));

DistPoint1Vertex2(i)=distance(V_x(i+1),crossX(i,1),V_y(i+1),crossY(i,1));

DistPoint2Vertex1(i)=distance(V_x(i),crossX(i,2),V_y(i),crossY(i,2));

DistPoint2Vertex2(i)=distance(V_x(i+1),crossX(i,2),V_y(i+1),crossY(i,2));

%checking if intersection points lies on the polygon

if EdgeLength(i)==DistPoint1Vertex1(i)+DistPoint1Vertex2(i)& EdgeLength(i)==DistPoint2Vertex1(i)+DistPoint2Vertex2(i)

InpointX(i,1)=crossX(i,1);

InpointY(i,1)=crossY(i,1);

InpointX(i,2)=crossX(i,2);

InpointY(i,2)=crossY(i,2);

else if EdgeLength(i)==DistPoint1Vertex1(i)+DistPoint1Vertex2(i)

InpointX(i,1)=crossX(i,1);

InpointY(i,1)=crossY(i,1);

InpointX(i,2)=NaN;

InpointY(i,2)=NaN;

else if EdgeLength(i)==DistPoint2Vertex1(i)+DistPoint2Vertex2(i)

InpointX(i,1)=NaN;

InpointY(i,1)=NaN;

InpointX(i,2)=crossX(i,2);

InpointY(i,2)=crossY(i,2);

else

InpointX(i,1)=NaN;

InpointY(i,1)=NaN;

InpointX(i,2)=NaN;

InpointY(i,2)=NaN;

end

end

end

end

Answer 1

[Matt J]

I have used linecirc function, but the problem is it also gives the intersection points which does not lie on the polygon.

Why not just discard the points that do not lie on the polygon? You can test this with inpolygon or with one of several File Exchange submissions, e.g.,

http://www.mathworks.com/matlabcentral/fileexchange/10226-inhull

http://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-polyhedra-in-terms-of-vertices-or--in-equalities

[KalMandy]

Hi Matt, Thank you for the suggestion, I have tried inpolygon, but as far as I understood it can only differentiate if the point lies inside or outside the polygon, but not ON one of it's edges. I looked at the other two options you gave, But I cannot figure out how it can help me. Can you please help me with that. Thanks again

[KalMandy]

Hi Matt, I figured out the way to use inpolygon for my case. Thank you very much!

[Khouloud Eledlebi]

Hello KalMandy, I am working on a project and I got stuck at how to find the intersection between polygon and circle. Can you please send me your final version of the code which you have adjusted earlier please. I would really appreciate your help very much