# Intersection between line and circle when line ends inside circle (using geom2d)

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John Disandolo on 20 Nov 2019
Commented: John Disandolo on 21 Nov 2019
I have a circle and a line drawn like so... Using the createLine function in the geom2d collection, the line is treated like this (i.e. continuous)... Therefore, when finding the intersection points between the line and the circle, two points are returned instead of one.
How can I solve this problem of showing an extra incorrect point, and is there a workaround you could suggest, either using geom2d or otherwise?
Many thanks.

John Disandolo on 21 Nov 2019
Position of line:
0.1947 0.4388
0.5173 0.5933
Center point of circle:
0.4850 0.6239
0.2035
darova on 21 Nov 2019
% Position of line:
x1 = [0.1947
0.5173];
y1 = [0.4388
0.5933];
% Center point of circle:
x0 = 0.4850;
y0 = 0.6239;
r = 0.2035;
t = linspace(0,2*pi,30);
x2 = r*cos(t) + x0;
y2 = r*sin(t) + y0;
[xc,yc] = polyxpoly(x1,y1,x2,y2)
Adam Danz on 21 Nov 2019
To demonstrate both methods,
% Define circle
ang=0:0.1:2*pi;
xyr = [5 2 4]; %(xCenter,yCenter,radius)
xp=xyr(:,3)*cos(ang) + repmat(xyr(:,1),1,numel(ang)); %changed 190901 to work with r2016a
yp=xyr(:,3)*sin(ang) + repmat(xyr(:,2),1,numel(ang));
% Define line endpoints
xln = [1 6];
yln = [-1 1];
% plot it
clf()
plot(xp,yp,'k-') %circle
axis equal; grid on; hold on
plot(xln,yln,'b-') %line
% Method 1 uses this FEX:
% https://www.mathworks.com/matlabcentral/fileexchange/11837-fast-and-robust-curve-intersections
[x0,y0] = intersections(xp,yp,xln,yln);
plot(x0,y0,'r*','MarkerSize',9,'LineWidth',2) %intersection point(s)
% Method 2
[xi,yi] = polyxpoly(xp,yp,xln,yln);
plot(xi,yi,'gh','MarkerSize',15,'LineWidth',2) %intersection point(s) Someone should copy their comment to the answers section so it can be accepted.

darova on 21 Nov 2019
• Someone should copy their comment to the answers section so it can be accepted.
It should be me
% Position of line:
x1 = [0.1947
0.5173];
y1 = [0.4388
0.5933];
% Center point of circle:
x0 = 0.4850;
y0 = 0.6239;
r = 0.2035;
t = linspace(0,2*pi,30);
x2 = r*cos(t) + x0;
y2 = r*sin(t) + y0;
[xc,yc] = polyxpoly(x1,y1,x2,y2)

John Disandolo on 21 Nov 2019
Thanks for demonstrating it.
Adam Danz on 21 Nov 2019
2 Changes you need to make.
1) you're not extracting the x and y coordinates of the line correctly.
% x1 = [h.Position(1) h.Position(3)]; wrong
% y1 = [h.Position(2) h.Position(4)]; wrong
x1 = h.Position(:,1);
y1 = h.Position(:,2);
2) This one is minor. As long as your ROI line and circle objects are still on the plot, new lines will be plotted under them. If you mark the intersection with a small marker, you won't see it.
% solution one: make the marker large
plot(xc, yc, 'ro','markersize',12)
% solution two: remove the cirlce ROI object and replace it with your
% computed circle
delete(c)
hold on
plot(x2,y2,'b-', 'LineWidth',4)
% Plot intersection point on top
plot(xc, yc, 'ro')
John Disandolo on 21 Nov 2019
Thanks, I realised this after I posted it!