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

public class IntervalEnergy {


    /**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 Interval interaction(double e,IntervalVector V1,IntervalVector V2) {
	Interval d=IntervalVector.dist(V1,V2);
	Interval ONE=new Interval(1.0);
	if(e<1.5) return(Interval.divide(ONE,d));
	return(Interval.divide(ONE,Interval.times(d,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 Interval energy(double e,IntervalComplex[] z) {
	IntervalVector[] V=new IntervalVector[5];
	for(int i=0;i<4;++i) V[i]=IntervalStereo.inverseStereo(z[i]);
	V[4]=IntervalVector.northPole();

	Interval total=new Interval(0.0);
	for(int i=0;i<5;++i) {
	    for(int j=i+1;j<5;++j) {
		total=Interval.plus(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 Interval energyLowerBound(double e,IntervalBox B1,IntervalBox B2) {
	Interval dist=IntervalSeparation.psiMax(B1,B2);
	if(dist.l<=0.0) return(new Interval(10000000));
	Interval ONE=new Interval(1.0);
	if(e>1.5) {
	    Interval t=Interval.divide(ONE,Interval.times(dist,dist));
	    return(t);
	}
	Interval t=Interval.divide(ONE,dist);
	return(t);
    }

    /**These intervals give UPPER bounds to the minimum energy.**/

    public static Interval minEnergy(double e) throws ProofException {
 	if(e==1) return(new Interval(6.4746914946882));
	if(e==2)	return(Interval.fat(4.25));
	throw new ProofException("IntervalEnergy: exponent not 1 or 2");
    }

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

    public static Interval tetrahedralComplement(double e) throws ProofException {
	if(e==1) return(new Interval(2.800457));
	if(e==2) return(Interval.fat(2.0));
	throw new ProofException("IntervalEnergy: exponent not 1 or 2");

    }

}