/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* 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. *
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****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
Revision 1.26 2006/11/13 13:03:45 ponchio
Added GetBBox in Point3 (declaration) the body of the function is in box3.h
Revision 1.25 2006/10/13 12:59:24 cignoni
Added **explicit** constructor from three coords of a different scalartype
Revision 1.24 2006/09/28 13:37:35 m_di_benedetto
added non const * V()
Revision 1.23 2005/11/09 16:11:55 cignoni
Added Abs and LowClampToZero
Revision 1.22 2005/09/14 14:09:21 m_di_benedetto
Added specialized Convert() for the same scalar type.
Revision 1.21 2005/05/06 14:45:33 spinelli
cambiato parentesi nel costruttore di GetUV per rendere compatibile tale costruttore con MVC e borland
Revision 1.20 2005/04/27 16:05:19 callieri
line 466, added parentesis on default value creator getUV [borland]
Revision 1.19 2004/11/09 15:49:07 ganovelli
added GetUV
Revision 1.18 2004/10/13 12:45:51 cignoni
Better Doxygen documentation
Revision 1.17 2004/09/10 14:01:40 cignoni
Added polar to cartesian
Revision 1.16 2004/03/21 17:14:56 ponchio
Added a math::
Revision 1.15 2004/03/07 22:45:32 cignoni
Moved quality and normal functions to the triangle class.
Revision 1.14 2004/03/05 17:55:01 tarini
errorino: upper case in Zero()
Revision 1.13 2004/03/03 14:22:48 cignoni
Yet against cr lf mismatch
Revision 1.12 2004/02/23 23:42:26 cignoni
Translated comments, removed unusued stuff. corrected linefeed/cr
Revision 1.11 2004/02/19 16:12:28 cignoni
cr lf mismatch 2
Revision 1.10 2004/02/19 16:06:24 cignoni
cr lf mismatch
Revision 1.8 2004/02/19 15:13:40 cignoni
corrected sqrt and added doxygen groups
Revision 1.7 2004/02/17 02:08:47 cignoni
Di prova...
Revision 1.6 2004/02/15 23:35:47 cignoni
Cambiato nome type template in accordo alla styleguide
Revision 1.5 2004/02/10 01:07:15 cignoni
Edited Comments and GPL license
Revision 1.4 2004/02/09 13:48:02 cignoni
Edited doxygen comments
****************************************************************************/
#ifndef __VCGLIB_POINT3
#define __VCGLIB_POINT3
#include <assert.h>
#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;
}
inline Point3 ( Point3 const & p )
{
_v[0]= p._v[0];
_v[1]= p._v[1];
_v[2]= p._v[2];
}
inline Point3 ( const P3ScalarType nv[3] )
{
_v[0] = nv[0];
_v[1] = nv[1];
_v[2] = nv[2];
}
inline Point3 & operator =( Point3 const & p )
{
_v[0]= p._v[0]; _v[1]= p._v[1]; _v[2]= p._v[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 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;
}
//@}
//@{
/** @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
Note
**/
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;
}
// Norme
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;
}
// Normalizzazione
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;
}
// for compatibility with eigen port
inline Point3 & normalized() { return Normalize(); }
/**
* 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) degrees.
* Phi is the elevation angle (not the polar angle) and ranges between [-90, 90] 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 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;
//@}
//@{
/** @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 - () 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 )
{
p.Normalize();
return p;
}
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();
}
// 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();
Point3<P3ScalarType> uv=u^v;
}
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>(math::Max(p[0], (SCALARTYPE)0), math::Max(p[1], (SCALARTYPE)0), math::Max(p[2], (SCALARTYPE)0)));
}
typedef Point3<short> Point3s;
typedef Point3<int> Point3i;
typedef Point3<float> Point3f;
typedef Point3<double> Point3d;
/*@}*/
} // end namespace
#endif