////////  Vector2D.java  //////////

public class Vector2D
{ 
     public Vector2D() {}
     public Vector2D(float x, float b)
     {   this.x = x;  
         y = b;
     }
     public boolean equals(Vector2D v)
     {   return( x == v.x && y == v.y ); }

     public String toString()
     {     return( "(" + x + ",  " + y + ')' );
     }

     public boolean nonzero()
         { return ( x != 0.0f || y != 0.0f ); }

     public float inner(Vector2D a)
     {  return(x * a.x + y * a.y);   }

     public Vector2D minus(Vector2D a)
     {    Vector2D tmp = new Vector2D();
          tmp.x = x - a.x;
          tmp.y = y - a.y;
          return(tmp);
     }

     // test if the host is parallel to b 
     //  (pointing in the same direction)
     public boolean isParallel(Vector2D b)
     {   return( nonzero() && b.nonzero() &&
                 x*b.x >= 0.0f &&
                 y*b.y >= 0.0f &&
         Math.abs(x*b.y-y*b.x) < delta );
     }

     public boolean isPerpendicular(Vector2D b)
     {   return ( nonzero() && b.nonzero()
                  && Math.abs(x*b.x + y*b.y) < delta );
     }

     private static float delta = 0.00000001f;
     private float x, y;
}