# Determine if a point lies between two lines

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Dave on 10 May 2016
Edited: Chad Greene on 11 May 2016
Assume there are two lines and each line is defined by two points.(e.g. (x1a,y1a) and (x2a,y2a) for line 1, (x1b,y1b) and (x2b,y2b) for line 2.). Consider also a square centered at the origin therefore these points are inside the square. How can we test whether a point inside the square (xu,yu) lies between these lines? Lines can be either parallel or intersecting (in such case, lines intersect outside the square).
%line 1
x1a=-2.5;
y1a=-1.8;
x2a=0.8;
y2a=-2.5;
%line2
x1b=-2.5;
y1b=- 1.4;
x2b=2.5;
y2b=1.4;
%square
xs=[-2.5 -2.5 2.5 2.5 -2.5] ;
ys=[-2.5 2.5 2.5 -2.5 -2.5];
figure;
plot([x1a x2a],[y1a y2a])
hold on
plot([x1b x2b],[y1b y2b])
hold on
plot(xs,ys,'-k','Linewidth',2)
axis([-3 3 -3 3])
Assume the lines and square created above. How can we exactly test if (2,-2) is between lines inside the square but (-1,1) is not?
Dave on 11 May 2016
Question is revised.

Chad Greene on 11 May 2016
You can use inpolygon.
##### 2 CommentsShowHide 1 older comment
Chad Greene on 11 May 2016
Edited: Chad Greene on 11 May 2016
Try this:
polygonx = [x1a x2a x1b x2b];
polygony = [y1a y2a y1b y2b];
k = convhull(polygonx,polygony);
plot(polygonx(k),polygony(k),'r-','linewidth',3)
% 100 random points:
randx = randn(100,1);
randy = randn(100,1)-1;
plot(randx,randy,'bx')
% Find random points inside the polygon:
in = inpolygon(randx,randy,polygonx(k),polygony(k));
plot(randx(in),randy(in),'ro') ### Categories

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