MATLAB: An error while using polyxpoly for finding (xi,yi) of an intersecting line and circle

intersectionpolyxpoly

Hello,
I need to connect point 2 and point 1 and find all the intersecting points(between red line and blue line/circle), So, I used polyxpoly. My problem is why polyxpoly function generates an extra intersecting point which is not on the line or the circle (I show it in the below image)?
My data
%Data
clear variables
clc
% points
x_points=[1;3];
y_points=[1;5];
% line coordinates
x_line=[3;2];
y_line=[3;5];
% Circle coordinates
xcenter = 2;
ycenter = 2;
radius = 1;
circr = @(radius,rad_ang)  [radius*cos(rad_ang)+xcenter;  radius*sin(rad_ang)+ycenter];
N = 2000;
rad_ang = linspace(0, 2*pi, N);
xy_r = circr(radius,rad_ang);
x_circle= radius * cos(rad_ang) + xcenter;
y_circle= radius * sin(rad_ang) + ycenter;
circle=round([x_circle',y_circle'],2);
% all points
All(:,1)=[x_points;x_line];
All(:,2)=[y_points;y_line];
% I want to calculate the intersection coordinates between a line contacting curret point/next point and
% circle/line
current_point=2
next_point=1
[xi,yi]=polyxpoly(All([next_point;current_point],1),...
    All([next_point;current_point],2),[x_line;circle(:,1)], [y_line;circle(:,2)])

Best Answer

Hi,
The x co-ordinates as well as the y co-ordinates of the line and the circle should not be combined as this generates a complicated polygon and a new solution is found other than the expected ones.
As a workaround one can use the polyxpoly function twice to generate two sets of solutions which together will provide the expected solution. 
[xi,yi]= polyxpoly(All([next_point;current_point],1),...
 All([next_point;current_point],2),circle(:,1),circle(:,2));
[xj,yj]=polyxpoly(All([next_point;current_point],1),...
 All([next_point;current_point],2),x_line,y_line);
Here [xi,yi] will give us the points of intersection between the line and the circle and [xj,yj] will give us the point of intersection between the two lines.
Hope this helps!
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