title: Calculation of intersections between line segments
body: <p>There's a lot of questions about intersections between line segments here at stackowerflow and here is one more! Sorry, but I need help to understand how to calculate intersections. I have read several of the questions here and looked at several examples on other websites, but I'm still confused and don't get it! I don't like to copy and paste code without how things work. </p>
  
  <p>So far I know that I'm going to compare the points of each line segments like Ax, Ay, Bx, By, Cx, Cy, Dx, Dy. Could someone explain for me what I'm going to calculate, what would the result of the calculating be if there is an intersection?</p>
  
  <p>This is one of the example code I seen. I guess I don't need the intersecting point, just to know if the lines intersect or not.</p>
  
  <pre><code>   public static Point lineIntersect(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {
    double denom = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1);
    if (denom == 0.0) { // Lines are parallel.
       return null;
    }
    double ua = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3))/denom;
    double ub = ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3))/denom;
      if (ua &gt;= 0.0f &amp;&amp; ua &lt;= 1.0f &amp;&amp; ub &gt;= 0.0f &amp;&amp; ub &lt;= 1.0f) {
          // Get the intersection point.
          return new Point((int) (x1 + ua*(x2 - x1)), (int) (y1 + ua*(y2 - y1)));
      }
  
    return null;
    }
  </code></pre>
  
  <p>Do I also need to calculate some median value like in this code example?</p>
  
  <pre><code>For lines through points (x0,y0) and (x1,y1), let xm = (x0+x1)/2, ym = (y0+y1)/2 (median of line segment). 
  Then a = (y1-y0) and b = (x0-x1). 
  If you evaluate c = a(x-xm)+b(y-ym), c=0 for (x,y) on the line, and the sign(c) tells you which side a point is on
  </code></pre>