Determine if a point lies between two lines

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Dave
Dave 2016-5-10
编辑： Chad Greene 2016-5-11
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?
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Roger Stafford
Roger Stafford 2016-5-11
If the lines intersect, how do you define 'between'? The lines, infinitely extended, divide two-dimensional space into four sections and the point must lie within one of these.

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Chad Greene
Chad Greene 2016-5-11
You can use inpolygon.
  2 个评论
Dave
Dave 2016-5-11
How can we define the region illustrated in the problem above using inpolygon?
Chad Greene
Chad Greene 2016-5-11
编辑：Chad Greene 2016-5-11
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')

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