Determine if a point lies between two lines

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?

[Donny Liu]

Please look for 'intersect' in the library.

[Roger Stafford]

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.

[Dave]

Question is revised.

Answer 1

[Chad Greene]

You can use inpolygon.

[Dave]

How can we define the region illustrated in the problem above using inpolygon?

[Chad Greene]

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')