class Point3{
public:
float x,y,z;
void set(float dx, float dy, float dz){x = dx; y = dy; z = dz;}
void set(Point3& p){x = p.x; y = p.y; z = p.z;}
Point3(float xx,float yy, float zz){x = xx; y = yy; z = zz;}
Point3(){x = y = z = 0;}
void build4tuple(float v[])
{// load 4-tuple with this color: v[3] = 1 for homogeneous
v[0] = x; v[1] = y; v[2] = z; v[3] = 1.0f;
}
};

class Vector3{
public:
float x,y,z;
void set(float dx, float dy, float dz){ x = dx; y = dy; z = dz;}
void set(Vector3& v){ x = v.x; y = v.y; z = v.z;}
void flip(){x = -x; y = -y; z = -z;} // reverse this vector
void setDiff(Point3& a, Point3& b)//set to difference a - b
{ x = a.x - b.x; y = a.y - b.y; z = a.z - b.z;}
void normalize()//adjust this vector to unit length
{
double sizeSq = x * x + y * y + z * z;
if(sizeSq < 0.0000001)
{
//cerr << "\nnormalize() sees vector (0,0,0)!";
return; // does nothing to zero vectors;
}
float scaleFactor = 1.0/(float)sqrt(sizeSq);
x *= scaleFactor; y *= scaleFactor; z *= scaleFactor;
}
Vector3(float xx, float yy, float zz){x = xx; y = yy; z = zz;}
Vector3(Vector3& v){x = v.x; y = v.y; z = v.z;}
Vector3(){x = y = z = 0;} //default constructor
Vector3 cross(Vector3 b) //return this cross b
{
Vector3 c(y*b.z - z*b.y, z*b.x - x*b.z, x*b.y - y*b.x);
return c;
}
float dot(Vector3 b) // return this dotted with b
{return x * b.x + y * b.y + z * b.z;}
};