Create a vec3 class that implements a 3-dimensional vector. It also implements basic vector functionality: addition, subtraction, scaling, negation, dot product, cross product, etc.

Provide the vec3.cpp file that contains the body for the vec3 class declared in the header file vec3.h provided below.

Header file declaring vec3 class.

// vec3.h #ifndef __vec3_h__ #define __vec3_h__ #include  using namespace std; class vec3 { private: float m[3]; public: // constructors vec3(); vec3(const vec3& v); vec3(float x, float y, float z); // indexing float& operator[](int i); const float& operator[](int i) const; // assignment const vec3& operator=(const vec3& v); // multiplication with a scalar void operator*=(float s); friend vec3 operator*(const vec3& v, float s); // addition void operator+=(const vec3& v); friend vec3 operator+(const vec3& v1, const vec3& v2); // subtraction void operator-=(const vec3& v); friend vec3 operator-(const vec3& v1, const vec3& v2); // negation vec3 operator-(); // dot product friend float operator*(const vec3& v1, const vec3& v2); // cross product friend vec3 operator^(const vec3& v1, const vec3& v2); // length float length(); // io friend ostream& operator<<(ostream& o, const vec3& v); friend istream& operator>>(istream& o, vec3& v); }; #endif 

Using vec3 class

Consider the following main.cpp file that is using the vec3 class declared above

#include  #include "vec3.h" using namespace std; int main() { vec3 a; cout << "a:" << a << endl; a += vec3(2,3,5); cout << "a+=vec3(2,3,5): " << a << endl; a[0] = 22; cout << "a[0]=22: " << a << endl; vec3 b(1,2,3); cout << "b: " << b << endl; cout << "b-a: " << b - a << endl; cout << "b*a: " << b*a << endl; cout << "b^a: " << (b^a) << endl; cout << "-b: " << -b << endl; return 0; } 

Compilation

We compile the code as follows:

$ g++ main.cpp vec3.cpp -o v 

Note that you are to provide the vec3.cpp file.

Execution

The output is

$ ./v a:0 0 0 a+=vec3(2,3,5): 2 3 5 a[0]=22: 22 3 5 b: 1 2 3 b-a: -21 -1 -2 b*a: 43 b^a: 1 61 -41 -b: -1 -2 -3