Polyxpoly returns empty matrix

Question

I'm writing a code in which I have to use polyxpoly and I'm having some issues with the output.

My code:

x=[-286.1018 -363.2334];
y=[4617.4 4725.1];
xv=[-316.7 -128-9 -268.3 -1864.6 -840.4];
yv=[4694.4 4944.7 5641.7 6002.0 4519.9];
[xi,yi] = polyxpoly(x,y,xv,yv);

And it returns:

Empty matrix: 0-by-2

What am I doing wrong I can't understand why it is not working (it should return the intersection points)? Can someone help me? Is this a bug of the function polyxpoly?

Answer 1

You're getting an empty matrix because the polylines defined for (x,y) and (xv,yv) don't intersect. This can clearly be shown by the plotting the polylines:

x=[-286.1018 -363.2334];
y=[4617.4 4725.1];
xv=[-316.7 -128-9 -268.3 -1864.6 -840.4];
yv=[4694.4 4944.7 5641.7 6002.0 4519.9];
mapshow(xv, yv);
mapshow(x,y,'color','red')

We get:

As you can see, the bigger shape defined by xv and yv is not closed, so the smaller line defined by x and y never intersect the shape. If you want to find the intersection points, you'll need to close the larger polygon. This can simply be done by duplicating the first xv and yv point in the array and making sure these appear at the end of the xv and yv arrays so that you close the polygon:

x=[-286.1018 -363.2334];
y=[4617.4 4725.1];
xv=[-316.7 -128-9 -268.3 -1864.6 -840.4];
yv=[4694.4 4944.7 5641.7 6002.0 4519.9];
%// Change
xv = [xv xv(1)];
yv = [yv yv(1)];
mapshow(xv, yv);
mapshow(x,y,'color','red')

We get:

That's better! Now try polyxpoly on the new xv and yv values:

>> [xi,yi] = polyxpoly(x, y, xv, yv)

xi =

 -336.5178


yi =

   4.6878e+03

We can show this point of intersection by adding one more mapshow call to the already spawned figure:

mapshow(xi,yi,'DisplayType','point','Marker','o')

We get:

You can see that the point of intersection has been found, and that it is delineated by a red circle in the map.