#include<stdlib.h>
#include<math.h>
#include<time.h>
//#include <iostream.h>
//#include <string.h>
//#include <fstream.h>
#include <stdio.h>

#ifndef PI
#define PI 3.1415926535897932384626434
#endif 

/*
void Equal(double f1[3],double f2[3]);			//f2=f1
void cros(double f1[3],double f2[3],double f3[3]);	//f3=f1 X f2
void minus(double f1[3],double f2[3], double f3[3]);	//f3=f2-f1
void plus(double f1[3],double f2[3], double f3[3]);
double dot(double *Vec_1,double *Vec_2,int Dim);
double Norm(double *Vec,int Dim);
double factorMul(double Vec[3],double factor);
void Normalize(double *v1, double *v2,int Dim);

*/


double dot(double *Vec_1,double *Vec_2,int Dim)
{	
	double result=0;
	for(int i=0;i<Dim;i++)
	{
		result+=Vec_1[i]*Vec_2[i];
	}
	return result;
}

double Norm(double *Vec,int Dim)
{
	return sqrt(dot(Vec,Vec,Dim));
}

double factorMul(double Vec[3],double factor)
{
	for(int i=0;i<3;i++)
		Vec[i]*=factor;

}

void cros(double f1[3],double f2[3],double f3[3])
{
	f3[0]=f1[1]*f2[2]-f1[2]*f2[1];
	f3[1]=f1[2]*f2[0]-f1[0]*f2[2];
	f3[2]=f1[0]*f2[1]-f1[1]*f2[0];
}
void minus(double f1[3],double f2[3], double f3[3])
{
	f3[0]=f2[0]-f1[0];
	f3[1]=f2[1]-f1[1];
	f3[2]=f2[2]-f1[2];
}
void plus(double f1[3],double f2[3], double f3[3])
{
	f3[0]=f2[0]+f1[0];
	f3[1]=f2[1]+f1[1];
	f3[2]=f2[2]+f1[2];
}
void Equal(double f1[3],double f2[3])//f2=f1
{
	for(int i=0;i<3;i++)
		f2[i]=f1[i];
}
void Normalize(double *v1, double *v2,int Dim)
{
	double factor=Norm(v1,Dim);
	for(int i=0;i<Dim;i++)
		v2[i]=v1[i]/factor;
}