Do two lines intersect? Processing/Java

gistfile1.pde

//adapted from http://wiki.processing.org/w/Line-Line_intersection

//I do not understand how or why this works.

boolean intersects(float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4) { 
  float bx = x2 - x1; 
  float by = y2 - y1; 
  float dx = x4 - x3; 
  float dy = y4 - y3;
  float b_dot_d_perp = bx * dy - by * dx;
  if (b_dot_d_perp == 0) {
    return false;
  }
  float cx = x3 - x1;
  float cy = y3 - y1;
  float t = (cx * dy - cy * dx) / b_dot_d_perp;
  if (t < 0 || t > 1) {
    return false;
  }
  float u = (cx * by - cy * bx) / b_dot_d_perp;
  if (u < 0 || u > 1) { 
    return false;
  }
  return true;
}