public class Plane extends Surface{

    Vector extNormal;//the normal pointing *out* of the surface   

    Plane(double[] coeffs){
	m=new material();
	coefficients=new double[4];
	origCoeff=new double[4];
	extNormal=new Vector(new double[] {coeffs[0], coeffs[1], coeffs[2]});
	double norm=extNormal.norm;	
	extNormal.normalize();
	if (norm==0) norm=1;	
	origCoeff[0]=coefficients[0]=coeffs[0]/norm;
	origCoeff[1]=coefficients[1]=coeffs[1]/norm;
	origCoeff[2]=coefficients[2]=coeffs[2]/norm;
	origCoeff[3]=coefficients[3]=coeffs[3]/norm;	
	
    }

    Plane(double[] coeffs, material ms){
	m=new material();
	coefficients=new double[4];
	origCoeff=new double[4];	
	extNormal=new Vector(new double[] {coeffs[0], coeffs[1], coeffs[2]});
	double norm=extNormal.norm;
	extNormal.normalize();	
	if (norm==0) norm=1;
	origCoeff[0]=coefficients[0]=coeffs[0]/norm;
	origCoeff[1]=coefficients[1]=coeffs[1]/norm;
	origCoeff[2]=coefficients[2]=coeffs[2]/norm;
	origCoeff[3]=coefficients[3]=coeffs[3]/norm;
	m.copy(ms);
    }

    Plane(Plane s){
	//	new Plane(s.coefficients, s.m);
	double[] coeffs=s.coefficients;
	origCoeff=new double[4];
	m=new material();
	coefficients=new double[4];
	extNormal=new Vector(new double[] {coeffs[0], coeffs[1], coeffs[2]});
	extNormal.normalize();	
	origCoeff[0]=coefficients[0]=coeffs[0];
	origCoeff[1]=coefficients[1]=coeffs[1];
	origCoeff[2]=coefficients[2]=coeffs[2];
	origCoeff[3]=coefficients[3]=coeffs[3];	
	m.copy(s.m);
    }

    void setTransfo(Matrix3D tfs){
	tf=new Matrix3D();
	tf.copy(tfs);    
	tf.invert();
	tf.transpose();
	tf.transform(origCoeff, coefficients);
	extNormal=new Vector(new double[] {coefficients[0], coefficients[1], coefficients[2]});
	double norm=extNormal.norm;
	extNormal.normalize();	
	if (norm==0) norm=1;
	coefficients[0]/=norm;
	coefficients[1]/=norm;
	coefficients[2]/=norm;
	coefficients[3]/=norm;
    }

    void updateNormal(){
	extNormal=new Vector(new double[] {coefficients[0], coefficients[1], coefficients[2]});
	extNormal.normalize();
    }

    Vector getNormal(double[] position){
	return extNormal;
    }

    double[] intersections(double[] v, double[] w){
	double vs0=extNormal.dotP(v)+coefficients[3];	
	double vs1=extNormal.dotP(w);
	
	if (vs1==0) {// normal orthogonal to w
	    if (vs0>=0) return new double[]{INFTY+1,-1};// always out
	    else return new double[]{0,INFTY};//always in
	}
	else{
	    double t=-vs0/vs1;
	    if (vs1>0) {//w going away from the plane
		return new double[]{-1,t};

	    }
	    else {//w going into the plane
		return new double[]{t,INFTY};

	    }

	}	


    }

}