// 3D vectorclass Vector3
{public:
Vector3(float fx, float fy, float fz)
:x(fx), y(fy), z(fz)
{
}

// Subtract    Vector3 operator - (const Vector3& v) const
{return Vector3(x - v.x, y - v.y, z - v.z) ;
}

// Dot product    float Dot(const Vector3& v) const
{return x * v.x + y * v.y + z * v.z ;
}

// Cross product    Vector3 Cross(const Vector3& v) const
{return Vector3(
y * v.z - z * v.y,
z * v.x - x * v.z,
x * v.y - y * v.x ) ;
}

public:float x, y, z ;
};

// Determine whether two vectors v1 and v2 point to the same direction// v1 = Cross(AB, AC)// v2 = Cross(AB, AP)bool SameSide(Vector3 A, Vector3 B, Vector3 C, Vector3 P)
{
Vector3 AB = B - A ;
Vector3 AC = C - A ;
Vector3 AP = P - A ;

Vector3 v1 = AB.Cross(AC) ;
Vector3 v2 = AB.Cross(AP) ;

// v1 and v2 should point to the same direction    return v1.Dot(v2) >= 0 ;
}

// Same side method// Determine whether point P in triangle ABCbool PointinTriangle1(Vector3 A, Vector3 B, Vector3 C, Vector3 P)
{return SameSide(A, B, C, P) &&
SameSide(B, C, A, P) &&
SameSide(C, A, B, P) ;
}

// Determine whether point P in triangle ABCbool PointinTriangle(Vector3 A, Vector3 B, Vector3 C, Vector3 P)
{
Vector3 v0 = C - A ;
Vector3 v1 = B - A ;
Vector3 v2 = P - A ;

float dot00 = v0.Dot(v0) ;float dot01 = v0.Dot(v1) ;float dot02 = v0.Dot(v2) ;float dot11 = v1.Dot(v1) ;float dot12 = v1.Dot(v2) ;

float inverDeno = 1 / (dot00 * dot11 - dot01 * dot01) ;

float u = (dot11 * dot02 - dot01 * dot12) * inverDeno ;if (u < 0 || u > 1) // if u out of range, return directly    {return false ;
}

float v = (dot00 * dot12 - dot01 * dot02) * inverDeno ;if (v < 0 || v > 1) // if v out of range, return directly    {return false ;
}

return u + v <= 1 ;
}