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openMVS/vcglib/vcg/space/point3.h

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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004-2016 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
#ifndef __VCGLIB_POINT3
#define __VCGLIB_POINT3
#include <assert.h>
#include <algorithm>
#include <vcg/math/base.h>
namespace vcg {
/** \addtogroup space */
/*@{*/
/**
The templated class for representing a point in 3D space.
The class is templated over the ScalarType class that is used to represent coordinates. All the usual
operator overloading (* + - ...) is present.
*/
template <class T> class Box3;
template <class P3ScalarType> class Point3
{
protected:
/// The only data member. Hidden to user.
P3ScalarType _v[3];
public:
typedef P3ScalarType ScalarType;
enum {Dimension = 3};
//@{
/** @name Standard Constructors and Initializers
No casting operators have been introduced to avoid automatic unattended (and costly) conversion between different point types
**/
inline Point3 () { }
inline Point3 ( const P3ScalarType nx, const P3ScalarType ny, const P3ScalarType nz )
{
_v[0] = nx;
_v[1] = ny;
_v[2] = nz;
}
/** Default copy constructor */
inline Point3 ( Point3 const & p ) = default;
/** Copy from Point with different template */
template<class Q>
inline Point3 ( Point3<Q> const & p )
{
_v[0]= p[0];
_v[1]= p[1];
_v[2]= p[2];
}
inline Point3 ( const P3ScalarType nv[3] )
{
_v[0] = nv[0];
_v[1] = nv[1];
_v[2] = nv[2];
}
/** Default copy assignment */
inline Point3 & operator =(Point3 const & p) = default;
/** Copy assignment from Point with different template */
template<class Q>
inline Point3 & operator =(Point3<Q> const & p)
{
_v[0] = p[0]; _v[1] = p[1]; _v[2] = p[2];
return *this;
}
inline void SetZero()
{
_v[0] = 0;
_v[1] = 0;
_v[2] = 0;
}
/// Padding function: give a default 0 value to all the elements that are not in the [0..2] range.
/// Useful for managing in a consistent way object that could have point2 / point3 / point4
inline P3ScalarType Ext( const int i ) const
{
if(i>=0 && i<=2) return _v[i];
else return 0;
}
template <class Q>
inline void Import( const Point3<Q> & b )
{
_v[0] = P3ScalarType(b[0]);
_v[1] = P3ScalarType(b[1]);
_v[2] = P3ScalarType(b[2]);
}
template <class EigenVector>
inline void FromEigenVector( const EigenVector & b )
{
_v[0] = P3ScalarType(b[0]);
_v[1] = P3ScalarType(b[1]);
_v[2] = P3ScalarType(b[2]);
}
template <class EigenVector>
inline void ToEigenVector( EigenVector & b ) const
{
b[0]=_v[0] ;
b[1]=_v[1] ;
b[2]=_v[2] ;
}
template <class EigenVector>
inline EigenVector ToEigenVector(void) const
{
static_assert(EigenVector::RowsAtCompileTime == 3 || EigenVector::RowsAtCompileTime == 4,
"EigenVector type has not 3 or 4 components");
EigenVector b = EigenVector::Zero();
b[0]=_v[0];
b[1]=_v[1];
b[2]=_v[2];
return b;
}
template <class Q>
static inline Point3 Construct( const Point3<Q> & b )
{
return Point3(P3ScalarType(b[0]),P3ScalarType(b[1]),P3ScalarType(b[2]));
}
template <class Q>
static inline Point3 Construct( const Q & P0, const Q & P1, const Q & P2)
{
return Point3(P3ScalarType(P0),P3ScalarType(P1),P3ScalarType(P2));
}
static inline Point3 Construct( const Point3<ScalarType> & b )
{
return b;
}
static inline Point3 Zero(void)
{
return Point3(0,0,0);
}
static inline Point3 One(void)
{
return Point3(1,1,1);
}
//@}
//@{
/** @name Data Access.
access to data is done by overloading of [] or explicit naming of coords (x,y,z)**/
inline P3ScalarType & operator [] ( const int i )
{
assert(i>=0 && i<3);
return _v[i];
}
inline const P3ScalarType & operator [] ( const int i ) const
{
assert(i>=0 && i<3);
return _v[i];
}
inline const P3ScalarType &X() const { return _v[0]; }
inline const P3ScalarType &Y() const { return _v[1]; }
inline const P3ScalarType &Z() const { return _v[2]; }
inline P3ScalarType &X() { return _v[0]; }
inline P3ScalarType &Y() { return _v[1]; }
inline P3ScalarType &Z() { return _v[2]; }
inline const P3ScalarType * V() const
{
return _v;
}
inline P3ScalarType * V()
{
return _v;
}
inline P3ScalarType & V( const int i )
{
assert(i>=0 && i<3);
return _v[i];
}
inline const P3ScalarType & V( const int i ) const
{
assert(i>=0 && i<3);
return _v[i];
}
/** @name Classical overloading of operators
**/
inline Point3 operator + ( Point3 const & p) const
{
return Point3<P3ScalarType>( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2] );
}
inline Point3 operator - ( Point3 const & p) const
{
return Point3<P3ScalarType>( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2] );
}
inline Point3 operator * ( const P3ScalarType s ) const
{
return Point3<P3ScalarType>( _v[0]*s, _v[1]*s, _v[2]*s );
}
inline Point3 operator / ( const P3ScalarType s ) const
{
return Point3<P3ScalarType>( _v[0]/s, _v[1]/s, _v[2]/s );
}
/// Dot product
inline P3ScalarType operator * ( Point3 const & p ) const
{
return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] );
}
inline P3ScalarType dot( const Point3 & p ) const { return (*this) * p; }
/// Cross product
inline Point3 operator ^ ( Point3 const & p ) const
{
return Point3 <P3ScalarType>
(
_v[1]*p._v[2] - _v[2]*p._v[1],
_v[2]*p._v[0] - _v[0]*p._v[2],
_v[0]*p._v[1] - _v[1]*p._v[0]
);
}
inline Point3 & operator += ( Point3 const & p)
{
_v[0] += p._v[0];
_v[1] += p._v[1];
_v[2] += p._v[2];
return *this;
}
inline Point3 & operator -= ( Point3 const & p)
{
_v[0] -= p._v[0];
_v[1] -= p._v[1];
_v[2] -= p._v[2];
return *this;
}
inline Point3 & operator *= ( const P3ScalarType s )
{
_v[0] *= s;
_v[1] *= s;
_v[2] *= s;
return *this;
}
inline Point3 & operator /= ( const P3ScalarType s )
{
_v[0] /= s;
_v[1] /= s;
_v[2] /= s;
return *this;
}
// Norms
inline P3ScalarType Norm() const
{
return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
}
inline P3ScalarType SquaredNorm() const
{
return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
}
// Scalatura differenziata
inline Point3 & Scale( const P3ScalarType sx, const P3ScalarType sy, const P3ScalarType sz )
{
_v[0] *= sx;
_v[1] *= sy;
_v[2] *= sz;
return *this;
}
inline Point3 & Scale( const Point3 & p )
{
_v[0] *= p._v[0];
_v[1] *= p._v[1];
_v[2] *= p._v[2];
return *this;
}
// Normalization
inline Point3 & Normalize()
{
P3ScalarType n = P3ScalarType(math::Sqrt(_v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2]));
if (n > P3ScalarType(0)) { _v[0] /= n; _v[1] /= n; _v[2] /= n; }
return *this;
}
inline void normalize(void)
{
this->Normalize();
}
inline Point3 normalized(void) const
{
Point3<P3ScalarType> p = *this;
p.normalize();
return p;
}
/**
* Convert to polar coordinates from cartesian coordinates.
*
* Theta is the azimuth angle and ranges between [0, 2PI) degrees.
* Phi is the elevation angle (not the polar angle) and ranges between [-PI/2, PI/2] degrees.
*
* /note Note that instead of the classical polar angle, which ranges between
* 0 and PI degrees we opt for the elevation angle to obtain a more
* intuitive spherical coordinate system.
*/
void ToPolarRad(P3ScalarType &ro, P3ScalarType &theta, P3ScalarType &phi) const
{
ro = Norm();
theta = (P3ScalarType)atan2(_v[2], _v[0]);
phi = (P3ScalarType)asin(_v[1]/ro);
}
/**
* Convert from polar coordinates to cartesian coordinates.
*
* Theta is the azimuth angle and ranges between [0, 2PI) radians.
* Phi is the elevation angle (not the polar angle) and ranges between [-PI/2, PI/2] radians.
*
* \note Note that instead of the classical polar angle, which ranges between
* 0 and PI degrees, we opt for the elevation angle to obtain a more
* intuitive spherical coordinate system.
*/
void FromPolarRad(const P3ScalarType &ro, const P3ScalarType &theta, const P3ScalarType &phi)
{
_v[0]= ro*cos(theta)*cos(phi);
_v[1]= ro*sin(phi);
_v[2]= ro*sin(theta)*cos(phi);
}
Box3<P3ScalarType> GetBBox(Box3<P3ScalarType> &bb) const;
size_t MaxCoeffId() const
{
if (_v[0]>_v[1])
return _v[0]>_v[2] ? 0 : 2;
else
return _v[1]>_v[2] ? 1 : 2;
}
/** @name Comparison Operators.
Note that the reverse z prioritized ordering, useful in many situations.
**/
inline bool operator == ( Point3 const & p ) const
{
return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2];
}
inline bool operator != ( Point3 const & p ) const
{
return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2];
}
inline bool operator < ( Point3 const & p ) const
{
return (_v[2]!=p._v[2])?(_v[2]<p._v[2]):
(_v[1]!=p._v[1])?(_v[1]<p._v[1]):
(_v[0]<p._v[0]);
}
inline bool operator > ( Point3 const & p ) const
{
return (_v[2]!=p._v[2])?(_v[2]>p._v[2]):
(_v[1]!=p._v[1])?(_v[1]>p._v[1]):
(_v[0]>p._v[0]);
}
inline bool operator <= ( Point3 const & p ) const
{
return (_v[2]!=p._v[2])?(_v[2]< p._v[2]):
(_v[1]!=p._v[1])?(_v[1]< p._v[1]):
(_v[0]<=p._v[0]);
}
inline bool operator >= ( Point3 const & p ) const
{
return (_v[2]!=p._v[2])?(_v[2]> p._v[2]):
(_v[1]!=p._v[1])?(_v[1]> p._v[1]):
(_v[0]>=p._v[0]);
}
inline Point3 operator - (void) const
{
return Point3<P3ScalarType> ( -_v[0], -_v[1], -_v[2] );
}
//@}
}; // end class definition
template <class P3ScalarType>
inline P3ScalarType Angle( Point3<P3ScalarType> const & p1, Point3<P3ScalarType> const & p2 )
{
P3ScalarType w = p1.Norm()*p2.Norm();
if(w==0) return -1;
P3ScalarType t = (p1*p2)/w;
if(t>1) t = 1;
else if(t<-1) t = -1;
return (P3ScalarType) acos(t);
}
// versione uguale alla precedente ma che assume che i due vettori sono unitari
template <class P3ScalarType>
inline P3ScalarType AngleN( Point3<P3ScalarType> const & p1, Point3<P3ScalarType> const & p2 )
{
P3ScalarType w = p1*p2;
if(w>1)
w = 1;
else if(w<-1)
w=-1;
return (P3ScalarType) acos(w);
}
template <class P3ScalarType>
inline P3ScalarType Norm( Point3<P3ScalarType> const & p )
{
return p.Norm();
}
template <class P3ScalarType>
inline P3ScalarType SquaredNorm( Point3<P3ScalarType> const & p )
{
return p.SquaredNorm();
}
template <class P3ScalarType>
inline Point3<P3ScalarType> & Normalize( Point3<P3ScalarType> & p )
{
return p.Normalize();
}
template <typename Scalar>
inline Point3<Scalar> Normalized(const Point3<Scalar> & p)
{
return p.normalized();
}
template <class P3ScalarType>
inline P3ScalarType Distance( Point3<P3ScalarType> const & p1,Point3<P3ScalarType> const & p2 )
{
return (p1-p2).Norm();
}
template <class P3ScalarType>
inline P3ScalarType SquaredDistance( Point3<P3ScalarType> const & p1,Point3<P3ScalarType> const & p2 )
{
return (p1-p2).SquaredNorm();
}
template <class P3ScalarType>
P3ScalarType ApproximateGeodesicDistance(const Point3<P3ScalarType>& p0, const Point3<P3ScalarType>& n0,
const Point3<P3ScalarType>& p1, const Point3<P3ScalarType>& n1)
{
Point3<P3ScalarType> V(p0-p1);
V.Normalize();
const P3ScalarType C0 = V*n0;
const P3ScalarType C1 = V*n1;
const P3ScalarType De = Distance(p0,p1);
if(fabs(C0-C1)<0.0001) return De/sqrt(1-C0*C1);
const P3ScalarType Dg = ((asin(C0) - asin(C1))/(C0-C1));
return Dg*De;
}
// Dot product preciso numericamente (solo double!!)
// Implementazione: si sommano i prodotti per ordine di esponente
// (prima le piu' grandi)
template<class P3ScalarType>
double stable_dot ( Point3<P3ScalarType> const & p0, Point3<P3ScalarType> const & p1 )
{
P3ScalarType k0 = p0._v[0]*p1._v[0];
P3ScalarType k1 = p0._v[1]*p1._v[1];
P3ScalarType k2 = p0._v[2]*p1._v[2];
int exp0,exp1,exp2;
frexp( double(k0), &exp0 );
frexp( double(k1), &exp1 );
frexp( double(k2), &exp2 );
if( exp0<exp1 )
{
if(exp0<exp2)
return (k1+k2)+k0;
else
return (k0+k1)+k2;
}
else
{
if(exp1<exp2)
return(k0+k2)+k1;
else
return (k0+k1)+k2;
}
}
/// Point(p) Edge(v1-v2) dist, q is the point in v1-v2 with min dist
template<class P3ScalarType>
P3ScalarType PSDist( const Point3<P3ScalarType> & p,
const Point3<P3ScalarType> & v1,
const Point3<P3ScalarType> & v2,
Point3<P3ScalarType> & q )
{
Point3<P3ScalarType> e = v2-v1;
P3ScalarType t = ((p-v1)*e)/e.SquaredNorm();
if(t<0) t = 0;
else if(t>1) t = 1;
q = v1+e*t;
return Distance(p,q);
}
template <class P3ScalarType>
void GetUV( Point3<P3ScalarType> &n,Point3<P3ScalarType> &u, Point3<P3ScalarType> &v, Point3<P3ScalarType> up=(Point3<P3ScalarType>(0,1,0)) )
{
n.Normalize();
const double LocEps=double(1e-7);
u=n^up;
double len = u.Norm();
if(len < LocEps)
{
if(fabs(n[0])<fabs(n[1])){
if(fabs(n[0])<fabs(n[2])) up=Point3<P3ScalarType>(1,0,0); // x is the min
else up=Point3<P3ScalarType>(0,0,1); // z is the min
}else {
if(fabs(n[1])<fabs(n[2])) up=Point3<P3ScalarType>(0,1,0); // y is the min
else up=Point3<P3ScalarType>(0,0,1); // z is the min
}
u=n^up;
}
u.Normalize();
v=n^u;
v.Normalize();
}
template <class SCALARTYPE>
inline Point3<SCALARTYPE> Abs(const Point3<SCALARTYPE> & p) {
return (Point3<SCALARTYPE>(math::Abs(p[0]), math::Abs(p[1]), math::Abs(p[2])));
}
// probably a more uniform naming should be defined...
template <class SCALARTYPE>
inline Point3<SCALARTYPE> LowClampToZero(const Point3<SCALARTYPE> & p) {
return (Point3<SCALARTYPE>(std::max(p[0], (SCALARTYPE)0), std::max(p[1], (SCALARTYPE)0), std::max(p[2], (SCALARTYPE)0)));
}
template <typename Scalar>
inline Point3<Scalar> operator*(const Scalar s, const Point3<Scalar> & p)
{
return (p * s);
}
typedef Point3<short> Point3s;
typedef Point3<int> Point3i;
typedef Point3<float> Point3f;
typedef Point3<double> Point3d;
/*@}*/
} // end namespace
#endif