Physics for Game Developers, 2nd Edition

Appendix A. Vector Operations

This appendix implements a class called Vector that encapsulates all of the vector operations that you need when writing 2D or 3D rigid-body simulations. Although Vector represents 3D vectors, you can easily reduce it to handle 2D vectors by eliminating all of the z terms or simply constraining the z terms to 0 where appropriate in your implementation.

Vector Class

The Vector class is defined with three components—x, y, and z—along with several methods and operators that implement basic vector operations. The class has two constructors, one of which initializes the vector components to 0, and the other of which initializes the vector components to those passed to the constructor:

//------------------------------------------------------------------------
// Vector Class and vector functions
//------------------------------------------------------------------------
class Vector {
public:
     float x;
     float y;
     float z;

     Vector(void);
     Vector(float xi, float yi, float zi);

     float Magnitude(void);
     void  Normalize(void);
     void  Reverse(void);

     Vector& operator+=(Vector u);
     Vector& operator-=(Vector u);
     Vector& operator*=(float s);
     Vector& operator/=(float s);

     Vector operator-(void);

};

// Constructor
inline Vector::Vector(void)
{
     x = 0;
     y = 0;
     z = 0;
}

// Constructor
inline Vector::Vector(float xi, float yi, float zi)
{
     x = xi;
     y = yi;
     z = zi;
}

Magnitude

The Magnitude method simply calculates the scalar magnitude of the vector according to the formula:

|v| =

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