import java.applet.Applet;
import java.awt.event.*;
import java.awt.*;

public class Energy {


    /**This is the basic routine.  It computes the quantity 1/d^e, 
       where d is the E3-distance between the vectors V1 and V2. **/

    public static double interaction(double e,Vector V1,Vector V2) {
	double d=Vector.dist(V1,V2);
	d=Math.pow(d,-e);
	return(d);
    }

    /**This routine computes the total energy of 4 points in the plane, plus the point at
          infinity.  These 4 points are  mapped stereographically to the unit sphere, and
          the vector (0,0,1) is included as the image of infinity.  */

    public static double energy(double e,Complex[] z) {
	Vector[] V=new Vector[5];
	for(int i=0;i<4;++i) V[i]=Stereo.inverseStereo(z[i]);
	V[4]=new Vector(0,0,1);

	double total=0;
	for(int i=0;i<5;++i) {
	    for(int j=i+1;j<5;++j) {
		total=total+interaction(e,V[i],V[j]);
	    }
	}
	return(total);
    }

    /**This is the energy lower bound based on the distance upper bound from the paper**/

    public static double energyLowerBound(double e,Box B1,Box B2) {
	double dist=Separation.psiMax(B1,B2);
	double t=Math.pow(dist,-e);
	return(t);
    }



    /**This is a formula for the energy of the TBP**/

    public static double minEnergy(double E) {
	double y=Math.pow(.5,E)+6*Math.pow(.5,E/2)+3*Math.pow(1.0/3.0,E/2);
	return(y);
    }

    /**This is used in the tetrahedral eliminator**/

    public static double tetrahedralComplement(double E) {
	double e1=minEnergy(E);
	double e2=6*Math.pow(3.0/8.0,E/2);
	double t=e1-e2;
	return(t);
    }





}