#include <iostream>
#include <string>
#include <cstdlib>
#include "vector.h"
using namespace std;

double * Add (double *A, double *B) {

 double *C = new double[3];
 C[0] = A[0]+B[0];
 C[1] = A[1]+B[1];
 C[2] = A[2]+B[2];
 return C;
}

double * Subtract (double *A, double *B) {

 double *C = new double[3];
 C[0] = A[0]-B[0];
 C[1] = A[1]-B[1];
 C[2] = A[2]-B[2];
 return C;
}

double Dot (double *A, double *B) {

 return A[0]*B[0] + A[1]*B[1] + A[2]*B[2];
}

double * ScaMult (double sca, double *A) {

 double *C = new double[3];
 C[0] = sca*A[0];
 C[1] = sca*A[1];
 C[2] = sca*A[2];
 return C;
}

double * Cross (double *A, double *B) {

 double *C = new double[3];
 C[0] = A[1]*B[2]-A[2]*B[1];
 C[1] = A[2]*B[0]-A[0]*B[2];
 C[2] = A[0]*B[1]-A[1]*B[0];
 return C;
}

double * Reflect (double *v, double *p1, double *p2, double *p3) {

//computes and returns the reflected vector when vector v bounces off a
//plane containing the points p1, p2, p3

 double *vec1 = Subtract (p2,p1);
 double *vec2 = Subtract (p3,p1);
 double *n = Cross (vec1,vec2);
 delete[] vec1;
 delete[] vec2;
 double ns = Dot (n,n);
 double vn = Dot (v,n);
 double *P  = ScaMult (2*vn/ns,n);
 double *R = Subtract (v,P);
 delete[] P;
 return R;
}