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point - vertex of a mesh

point(2rheolef) rheolef-6.7 point(2rheolef)

NAME

point - vertex of a mesh

DESCRIPTION

Defines geometrical vertex as an array of coordinates. This array is also used as a vector of the three dimensional physical space.

IMPLEMENTATION

template <class T>
class point_basic {
    public:
// typedefs:
typedef size_t size_type; typedef T element_type; typedef T scalar_type; typedef T float_type;
// allocators:
explicit point_basic () { _x[0] = T(); _x[1] = T(); _x[2] = T(); }
explicit point_basic ( const T& x0, const T& x1 = 0, const T& x2 = 0) { _x[0] = x0; _x[1] = x1; _x[2] = x2; }
template <class T1> point_basic<T>(const point_basic<T1>& p) { _x[0] = p._x[0]; _x[1] = p._x[1]; _x[2] = p._x[2]; }
template <class T1> point_basic<T>& operator = (const point_basic<T1>& p) { _x[0] = p._x[0]; _x[1] = p._x[1]; _x[2] = p._x[2]; return *this; }
#ifdef _RHEOLEF_HAVE_STD_INITIALIZER_LIST point_basic (const std::initializer_list<T>& il); #endif // _RHEOLEF_HAVE_STD_INITIALIZER_LIST
// accessors:
T& operator[](int i_coord) { return _x[i_coord%3]; } const T& operator[](int i_coord) const { return _x[i_coord%3]; } T& operator()(int i_coord) { return _x[i_coord%3]; } const T& operator()(int i_coord) const { return _x[i_coord%3]; }
// interface for CGAL library inter-operability: const T& x() const { return _x[0]; } const T& y() const { return _x[1]; } const T& z() const { return _x[2]; } T& x(){ return _x[0]; } T& y(){ return _x[1]; } T& z(){ return _x[2]; }
// inputs/outputs:
std::istream& get (std::istream& s, int d = 3) { switch (d) { case 0 : _x[0] = _x[1] = _x[2] = 0; return s; case 1 : _x[1] = _x[2] = 0; return s >> _x[0]; case 2 : _x[2] = 0; return s >> _x[0] >> _x[1]; default: return s >> _x[0] >> _x[1] >> _x[2]; } } // output std::ostream& put (std::ostream& s, int d = 3) const;
// algebra:
bool operator== (const point_basic<T>& v) const { return _x[0] == v[0] && _x[1] == v[1] && _x[2] == v[2]; }
bool operator!= (const point_basic<T>& v) const { return !operator==(v); }
point_basic<T>& operator+= (const point_basic<T>& v) { _x[0] += v[0]; _x[1] += v[1]; _x[2] += v[2]; return *this; }
point_basic<T>& operator-= (const point_basic<T>& v) { _x[0] -= v[0]; _x[1] -= v[1]; _x[2] -= v[2]; return *this; }
point_basic<T>& operator*= (const T& a) { _x[0] *= a; _x[1] *= a; _x[2] *= a; return *this; }
point_basic<T>& operator/= (const T& a) { _x[0] /= a; _x[1] /= a; _x[2] /= a; return *this; }
point_basic<T> operator+ (const point_basic<T>& v) const { return point_basic<T> (_x[0]+v[0], _x[1]+v[1], _x[2]+v[2]); }
point_basic<T> operator- () const { return point_basic<T> (-_x[0], -_x[1], -_x[2]); }
point_basic<T> operator- (const point_basic<T>& v) const { return point_basic<T> (_x[0]-v[0], _x[1]-v[1], _x[2]-v[2]); }
template <class U> typename std::enable_if< details::is_rheolef_arithmetic<U>::value ,point_basic<T> >::type operator* (const U& a) const { return point_basic<T> (_x[0]*a, _x[1]*a, _x[2]*a); } point_basic<T> operator/ (const T& a) const { return operator* (T(1)/T(a)); } point_basic<T> operator/ (point_basic<T> v) const { return point_basic<T> (_x[0]/v[0], _x[1]/v[1], _x[2]/v[2]); }
// data: // protected: T _x[3]; // internal: static T _my_abs(const T& x) { return (x > T(0)) ? x : -x; } }; typedef point_basic<Float> point;
// algebra: template <class T, class U> inline typename std::enable_if< details::is_rheolef_arithmetic<U>::value ,point_basic<T> >::type operator* (const U& a, const point_basic<T>& u) { return point_basic<T> (a*u[0], a*u[1], a*u[2]); } template<class T> inline point_basic<T> vect (const point_basic<T>& v, const point_basic<T>& w) { return point_basic<T> ( v[1]*w[2]-v[2]*w[1], v[2]*w[0]-v[0]*w[2], v[0]*w[1]-v[1]*w[0]); } // metrics: template<class T> inline T dot (const point_basic<T>& x, const point_basic<T>& y) { return x[0]*y[0]+x[1]*y[1]+x[2]*y[2]; } template<class T> inline T norm2 (const point_basic<T>& x) { return dot(x,x); } template<class T> inline T norm (const point_basic<T>& x) { return sqrt(norm2(x)); } template<class T> inline T dist2 (const point_basic<T>& x, const point_basic<T>& y) { return norm2(x-y); } template<class T> inline T dist (const point_basic<T>& x, const point_basic<T>& y) { return norm(x-y); } template<class T> inline T dist_infty (const point_basic<T>& x, const point_basic<T>& y) { return max(point_basic<T>::_my_abs(x[0]-y[0]), max(point_basic<T>::_my_abs(x[1]-y[1]), point_basic<T>::_my_abs(x[2]-y[2]))); } template <class T> T vect2d (const point_basic<T>& v, const point_basic<T>& w);
template <class T> T mixt (const point_basic<T>& u, const point_basic<T>& v, const point_basic<T>& w);
// robust(exact) floating point predicates: return the sign of the value as (0, > 0, < 0) // formally: orient2d(a,b,x) = vect2d(a-x,b-x) template <class T> int sign_orient2d ( const point_basic<T>& a, const point_basic<T>& b, const point_basic<T>& c);
template <class T> int sign_orient3d ( const point_basic<T>& a, const point_basic<T>& b, const point_basic<T>& c, const point_basic<T>& d);
// compute also the value: template <class T> T orient2d( const point_basic<T>& a, const point_basic<T>& b, const point_basic<T>& c);
// formally: orient3d(a,b,c,x) = mixt3d(a-x,b-x,c-x) template <class T> T orient3d( const point_basic<T>& a, const point_basic<T>& b, const point_basic<T>& c, const point_basic<T>& d);
template <class T> std::string ptos (const point_basic<T>& x, int d = 3);
// ccomparators: lexicographic order template<class T, size_t d> bool lexicographically_less (const point_basic<T>& a, const point_basic<T>& b) { for (typename point_basic<T>::size_type i = 0; i < d; i++) { if (a[i] < b[i]) return true; if (a[i] > b[i]) return false; } return false; // equality }
 
rheolef-6.7 rheolef-6.7