public class HalfSpace {

  /*final*/ Point3d normal ; // normal to boundary plane
  /*final*/ double d; // eqn of half space is normal.x - d > 0
  
  /** Create a half space
   */
  public HalfSpace(Point3d a,Point3d b,Point3d c){
    normal = b.subtract(a).cross(c.subtract(a)).normalize();
    d = normal.dot(a);
  }

  /** Create a half space parallel to z axis
   */
  public HalfSpace(Point3d a,Point3d b){
    normal = b.subtract(a).cross(Point3d.k).normalize();
    d = normal.dot(a);
  }

  public boolean inside (Point3d x){
    return normal.dot(x) > d;
  }

  /** z coordinate of intersection of a vertical line through p and boundary plane */
  public double zint(Point3d p){
    return (d - normal.x()*p.x() - normal.y()*p.y()) / normal.z();
  }

}