// file Line.java

class DegenerateLine extends Exception {}
class ParallelException extends Exception {}

public class Line {   


// An unbounded line of the parameterized form { p + t*v | -infty < t < infty }
// is implemented as the pair [p,v] where p is the point and v is the direction

    public double[] point;
    public double[] direction;

// Constructor
    public Line (double[] p, double[] d) throws DegenerateLine {
       if (VecMagSquared(d) < epsilon*epsilon)
         throw new DegenerateLine();
       point = p;
       direction = d;
      }

    public String toString() {
        return "L: [" + point[0] + ", " + point[1] + 
               "]  [" + direction [0] + ", " + direction [1] + "]";
       }


// Computes the intersection of Line this with Line l2. Returns a quadruple:
// xi, yi, the coordinates of the intersection
// and t1, t2, the associated parameters on each line.
// That is, [x1,y1} = this.point + t1*this.direction = 
//                    l2.point + t2*this.direction
// Throw an exception if the lines are parallel.

  public double[] intersect(Line l2) throws ParallelException {
      double det = direction[0]*l2.direction[1] - direction[1]*l2.direction[0];
      if (- epsilon < det && det < epsilon) 
         throw new ParallelException();
      double[] ans = new double[4];
      ans[2] = ((l2.point[0]-point[0])*l2.direction[1] -
                (l2.point[1]-point[1])*l2.direction[0]) 
               / det;
      ans[3] = ((l2.point[0]-point[0])*direction[1] -
                (l2.point[1]-point[1])*direction[0]) 
               / det;
      ans[0] = point[0] + ans[2] * direction[0];
      ans[1] = point[1] + ans[2] * direction[1];
      return ans;
    }  // end intersect

public static final double epsilon = 0.001;  // Small distance

// Magnitude of vector v squared. 
public static double SumSquared(double x, double y) {
     return x*x + y*y;
  }

public static double VecMagSquared(double[] v) {
     return SumSquared(v[0],v[1]);
  }
     
public static double DistSquared(double[] p1, double[] p2) {
     return SumSquared(p2[0]-p1[0], p2[1]-p1[1]);
    }

} // end Line