"dimensionally unified" version: first commit

This commit is contained in:
mtarini 2004-03-16 03:07:38 +00:00
parent e4cf5549cd
commit 223902e61c
2 changed files with 979 additions and 0 deletions
vcg/space

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/****************************************************************************
* 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. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
Revision 1.5 2004/03/05 17:51:28 tarini
Errorino "ScalarType" -> "S"
Revision 1.4 2004/03/03 14:32:13 cignoni
Yet another cr lf mismatch
Revision 1.3 2004/02/23 23:44:21 cignoni
cr lf mismatch
Revision 1.2 2004/02/19 15:40:56 cignoni
Added doxygen groups
Revision 1.1 2004/02/13 02:16:22 cignoni
First working release.
****************************************************************************/
#ifndef __VCGLIB_BOX
#define __VCGLIB_BOX
#include <vcg/space/point.h>
#include <vcg/space/space.h>
#include <vcg/math/linear.h>
namespace vcg {
/** \addtogroup space */
/*@{*/
/**
Templated class for 3D boxes.
This is the class for definition of a axis aligned box in 2D or 3D space.
Typically used as bounding boxes.
It is stored just as two Points (at the opposite vertices).
@param S (template parameter) Specifies the type of scalar used to represent coords.
*/
template <int N, class S>
class Box : public Space<N,S> , Linear<Box>
{
public:
typedef S ScalarType;
typedef Point<N,S> ParamType;
typedef Point<N,S> PointType;
enum {Dimension=N};
/// The scalar type
protected:
/// _min coordinate point
Point<3,S> _min;
/// _max coordinate point
Point<3,S> _max;
public:
inline const PointType &Max() const { return _max; }
inline PointType &Max() { return _max; }
inline const PointType &Min() const { return _min; }
inline PointType &Min() { return _min; }
/// The box constructor
inline Box() {
_min.X()= 1;_max.X()= -1;
_min.Y()= 1;_max.Y()= -1;
if (N>2) {_min.Z()= 1;_max.Z()= -1;}
}
/// Min Max constructor
inline Box( const PointType & mi, const PointType & ma ) { _min = mi; _max = ma; }
/// The box distructor
inline ~Box() { }
/// Operator to compare two boxes
inline bool operator == ( Box const & p ) const
{
return _min==p._min && _max==p._max;
}
/// Operator to dispare two boxes
inline bool operator != ( Box const & p ) const
{
return _min!=p._min || _max!=p._max;
}
/** Infaltes the box of a percentage..
@param s Scalar value. E.g if s=0.1 the box enlarges of 10% in every direction
if S==0.5 box doubles (+50% in every direction)
if S < 0 box shrinks
if S==0.5 box reduces to a point
*/
void Inflate( const S s )
{
Inflate( (_max-_min)*s );
}
/** Enlarges the box dimensions by k in every direction, with k = bbox.diag*s
*/
void InflateFix( const S s )
{
S k = Diag()*s;
if (N==2) Inflate( PointType (k,k));
if (N==3) Inflate( PointType (k,k,k));
}
/** Enlarges the box dimensions by a fixed delta.
@param delta Point in D space. If delta > 0 box enlarges. If delta < 0 box reduces.
*/
void Inflate( const PointType & delta )
{
_min -= delta;
_max += delta;
}
/// Initializing the box
void Set( const PointType & p )
{
_min = _max = p;
}
/// Set the box to a null value
void SetNull()
{
_min.X()= 1; _max.X()= -1;
_min.Y()= 1; _max.Y()= -1;
_min.Z()= 1; _max.Z()= -1;
}
/** Add two boxex:
Returns minimal box that contains both operands.
@param b The box to add
*/
void Add( Box const & b )
{
if(IsNull()) *this=b;
else
Add(_min); Add(_max);
}
/** Add a point to a box.
The box is modified is the added point is aoutside it.
@param p The point to add
*/
void Add( const PointType & p )
{
if(IsNull()) Set(p);
else
{
if(_min.X() > p.X()) _min.X() = p.X();
else if(_max.X() < p.X()) _max.X() = p.X();
if(_min.Y() > p.Y()) _min.Y() = p.Y();
else if(_max.Y() < p.Y()) _max.Y() = p.Y();
if (N>2) {
if(_min.Z() > p.Z()) _min.Z() = p.Z();
else if(_max.Z() < p.Z()) _max.Z() = p.Z();
};
}
}
/** Coputes intersection of Boxes: the minimal box containing both operands.
@param b The other operand
*/
void Intersect( const Box & b )
{
if(_min.X() < b._min.X()) _min.X() = b._min.X();
if(_min.Y() < b._min.Y()) _min.Y() = b._min.Y();
if (N>2) if(_min.Z() < b._min.Z()) _min.Z() = b._min.Z();
if(_max.X() > b._max.X()) _max.X() = b._max.X();
if(_max.Y() > b._max.Y()) _max.Y() = b._max.Y();
if (N>2) if(_max.Z() > b._max.Z()) _max.Z() = b._max.Z();
if(_min.X()>_max.X() || _min.Y()>_max.Y() ) SetNull();
else if (N>2) if (_min.Z()>_max.Z()) SetNull();
}
/** Traslalate the box.
@param p: the translation vector
*/
void Translate( const PointType & p )
{
_min += p;
_max += p;
}
/** Check wheter a point is inside box.
@param p The point
@returns True if inside, false otherwise
*/
bool IsIn( PointType const & p ) const
{
if (N==2) return (
_min.X() <= p.X() && p.X() <= _max.X() &&
_min.Y() <= p.Y() && p.Y() <= _max.Y()
);
if (N==3) return (
_min.X() <= p.X() && p.X() <= _max.X() &&
_min.Y() <= p.Y() && p.Y() <= _max.Y() &&
_min.Z() <= p.Z() && p.Z() <= _max.Z()
);
}
/** Check wheter a point is inside box, open at left and closed at right [min..max)
@param p The point 3D
@returns True if inside, false otherwise
*/
bool IsInEx( PointType const & p ) const
{
if (N==2) return (
_min.X() <= p.X() && p.X() < _max.X() &&
_min.Y() <= p.Y() && p.Y() < _max.Y()
);
if (N==3) return (
_min.X() <= p.X() && p.X() < _max.X() &&
_min.Y() <= p.Y() && p.Y() < _max.Y() &&
_min.Z() <= p.Z() && p.Z() < _max.Z()
);
}
/**
TODO: Move TO COLLIDE!!!
Verifica se due box collidono cioe' se hanno una intersezione non vuota. Per esempio
due box adiacenti non collidono.
@param b A box
@return True se collidoo, false altrimenti
*/
bool Collide(Box const &b)
{
return b._min.X()<_max.X() && b._max.X()>_min.X() &&
b._min.Y()<_max.Y() && b._max.Y()>_min.Y() &&
b._min.Z()<_max.Z() && b._max.Z()>_min.Z() ;
}
/** Controlla se il box e' nullo.
@return True se il box e' nullo, false altrimenti
*/
bool IsNull() const { return _min.X()>_max.X() || _min.Y()>_max.Y() || _min.Z()>_max.Z(); }
/** Controlla se il box e' vuoto.
@return True se il box e' vuoto, false altrimenti
*/
bool IsEmpty() const { return _min==_max; }
/// Restituisce la lunghezza della diagonale del box.
S Diag() const
{
return Distance(_min,_max);
}
/// Calcola il quadrato della diagonale del box.
S SquaredDiag() const
{
return SquaredDistance(_min,_max);
}
/// Calcola il centro del box.
PointType Center() const
{
return (_min+_max)/2;
}
/// Returns global coords of a local point expressed in [0..1]^3
PointType LocalToGlobal(PointType const & p) const{
return PointType(
_min[0] + p[0]*(_max[0]-_min[0]),
_min[1] + p[1]*(_max[1]-_min[1]),
_min[2] + p[2]*(_max[2]-_min[2]));
}
/// Returns local coords expressed in [0..1]^3 of a point in 3D
PointType GlobalToLocal(PointType const & p) const{
return PointType(
(p[0]-_min[0])/(_max[0]-_min[0]),
(p[1]-_min[1])/(_max[1]-_min[1]),
(p[2]-_min[2])/(_max[2]-_min[2])
);
}
/// Computes the Volume for the box.
inline S Volume() const
{
if (N==2) return (_max.X()-_min.X())*(_max.Y()-_min.Y());
if (N==3) return (_max.X()-_min.X())*(_max.Y()-_min.Y())*(_max.Z()-_min.Z());
}
/// Area() and Volume() are sinonims (a
inline S Area() const {
return Volume();
};
/// Compute box size.
PointType Size() const
{
return (_max-_min);
}
/// Compute box size X.
inline S SizeX() const { return _max.X()-_min.X();}
/// Compute box size Y.
inline S SizeY() const { return _max.Y()-_min.Y();}
/// Compute box size Z.
inline S SizeZ() const { static_assert(N>2); return _max.Z()-_min.Z();}
/** @name Linearity for boxes
**/
/// sets a point to Zero
inline void Zero()
{
_min.Zero();
_max.Zero();
}
inline Box operator + ( Box const & p) const
{
return Box(_min+p._min,_max+p._max);
}
inline Box operator - ( Box const & p) const
{
return Box(_min-p._min,_max-p._max);
}
inline Box operator * ( const S s ) const
{
return Box(_min*s,_max*s);
}
inline Box operator / ( const S s ) const
{
S inv=S(1.0)/s;
return Box(_min*inv,_max*inv);
}
inline Box & operator += ( Box const & p)
{
_min+=p._min; _max+=p._max; return *this;
}
inline Box & operator -= ( Box const & p)
{
_min-=p._min; _max-=p._max; return *this;
}
inline Box & operator *= ( const S s )
{
_min*=s; _max*=s; return *this;
}
inline Box & operator /= ( const S s )
{
S inv=S(1.0)/s;
_min*=s; _max*=s; return *this;
return *this;
}
inline Box operator - () const
{
return Box(-_min,-_max);
}
//@}
//@{
/** @name Iporters (for boxes in different spaces and with different scalar types)
**/
/// imports the box
template <int N0, class S0>
inline void Import( const Box<N0,S0> & b )
{ _max.Import( b._max );_min.Import( b._min );
}
template <int N0, class S0>
/// constructs a new ray importing it from an existing one
static Box Construct( const Box<N0,S0> & b )
{
return Box(PointType::Construct(b._min),PointType::Construct(b._max));
}
}; // end class definition
typedef Box<3,short> Box3s;
typedef Box<3,int> Box3i;
typedef Box<3,float> Box3f;
typedef Box<3,double> Box3d;
typedef Box<2,short> Box2s;
typedef Box<2,int> Box2i;
typedef Box<2,float> Box2f;
typedef Box<2,double> Box2d;
/*@}*/
} // end namespace
#endif

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/****************************************************************************
* 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. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
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_POINT
#define __VCGLIB_POINT
#include <assert.h>
#include <vcg/math/base.h>
#include <vcg/space/space.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 <int N, class S>
class Point : public Space<N,S>, Linear<Point>
{
public:
typedef S ScalarType;
typedef VoidType ParamType;
typedef Point PointType;
enum {Dimension=N};
protected:
/// The only data member. Hidden to user.
S _v[N];
public:
//@{
/** @name Standard Constructors and Initializers
No casting operators have been introduced to avoid automatic unattended (and costly) conversion between different point types
**/
inline Point () { }
inline Point ( const S nx, const S ny, const S nz, const S nw )
{
static_assert(N==4);
_v[0] = nx;
_v[1] = ny;
_v[2] = nz;
_v[3] = nw;
}
inline Point ( const S nx, const S ny, const S nz)
{
static_assert(N==3);
_v[0] = nx;
_v[1] = ny;
_v[2] = nz;
}
inline Point ( const S nx, const S ny)
{
static_assert(N==2);
_v[0] = nx;
_v[1] = ny;
}
inline Point ( const S nv[N] )
{
_v[0] = nv[0];
_v[1] = nv[1];
if (N>2) _v[2] = nv[2];
if (N>3) _v[3] = nv[3];
}
/// 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 S Ext( const int i ) const
{
if(i>=0 && i<=N) return _v[i];
else return 0;
}
template <int N2, class S2>
inline void Import( const Point<N2,S2> & b )
{
_v[0] = ScalarType(b[0]);
_v[1] = ScalarType(b[1]);
if (N>2) { if (N2>2) _v[2] = ScalarType(b[2]); else _v[2] = 0};
if (N>3) { if (N2>3) _v[3] = ScalarType(b[3]); else _v[3] = 0};
}
static inline Point Construct( const PointType & b )
{
PointType p; p.Import(b);
return p;
}
//@}
//@{
/** @name Data Access.
access to data is done by overloading of [] or explicit naming of coords (x,y,z)**/
inline S & operator [] ( const int i )
{
assert(i>=0 && i<N);
return _v[i];
}
inline const S & operator [] ( const int i ) const
{
assert(i>=0 && i<3);
return _v[i];
}
inline const S &X() const { return _v[0]; }
inline const S &Y() const { return _v[1]; }
inline const S &Z() const { static_assert(N>2); return _v[2]; }
inline const S &W() const { static_assert(N>3); return _v[3]; }
inline S &X() { return _v[0]; }
inline S &Y() { return _v[1]; }
inline S &Z() { static_assert(N>2); return _v[2]; }
inline S &W() { static_assert(N>3); return _v[3]; }
inline const S * V() const
{
return _v;
}
inline S & V( const int i )
{
assert(i>=0 && i<N);
return _v[i];
}
inline const S & V( const int i ) const
{
assert(i>=0 && i<N);
return _v[i];
}
//@}
//@{
/** @name Linearity for points
**/
/// sets a point to Zero
inline void Zero()
{
_v[0] = 0;
_v[1] = 0;
if (N>2) _v[2] = 0;
if (N>3) _v[3] = 0;
}
inline Point operator + ( Point const & p) const
{
if (N==2) return Point( _v[0]+p._v[0], _v[1]+p._v[1] );
if (N==3) return Point( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2] );
if (N==4) return Point( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2], _v[3]+p._v[3] );
}
inline Point operator - ( Point const & p) const
{
if (N==2) return Point( _v[0]-p._v[0], _v[1]-p._v[1] );
if (N==3) return Point( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2] );
if (N==4) return Point( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2], _v[3]-p._v[3] );
}
inline Point operator * ( const S s ) const
{
if (N==2) return Point( _v[0]*s, _v[1]*s );
if (N==3) return Point( _v[0]*s, _v[1]*s, _v[2]*s );
if (N==4) return Point( _v[0]*s, _v[1]*s, _v[2]*s, _v[3]*s );
}
inline Point operator / ( const S s ) const
{
if (N==2) return Point( _v[0]/s, _v[1]/s );
if (N==3) return Point( _v[0]/s, _v[1]/s, _v[2]/s );
if (N==4) return Point( _v[0]/s, _v[1]/s, _v[2]/s, _v[3]/s );
}
inline Point & operator += ( Point const & p)
{
_v[0] += p._v[0];
_v[1] += p._v[1];
if (N>2) _v[2] += p._v[2];
if (N>3) _v[3] += p._v[3];
return *this;
}
inline Point & operator -= ( Point const & p)
{
_v[0] -= p._v[0];
_v[1] -= p._v[1];
if (N>2) _v[2] -= p._v[2];
if (N>3) _v[3] -= p._v[3];
return *this;
}
inline Point & operator *= ( const S s )
{
_v[0] *= s;
_v[1] *= s;
if (N>2) _v[2] *= s;
if (N>3) _v[3] *= s;
return *this;
}
inline Point & operator /= ( const S s )
{
_v[0] /= s;
_v[1] /= s;
if (N>2) _v[2] /= s;
if (N>3) _v[3] /= s;
return *this;
}
inline Point operator - () const
{
if (N==2) return Point ( -_v[0], -_v[1] );
if (N==3) return Point ( -_v[0], -_v[1], -_v[2] );
if (N==4) return Point ( -_v[0], -_v[1], -_v[2] , -_v[3] );
}
//@}
//@{
/** @name Dot products
**/
/// Dot product
inline S operator * ( Point const & p ) const
{
if (N==2) return ( _v[0]*p._v[0] + _v[1]*p._v[1] );
if (N==3) return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] );
if (N==4) return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] + _v[2]*p._v[2] );
};
/// slower version, more stable (double precision only)
inline S StableDot ( const Point & p ) const
{
if (N==2) return _v[0]*p._v[0] + _v[1]*p._v[1];
if (N==4) {
S k0=_v[0]*p._v[0], k1=_v[1]*p._v[1], k2=_v[2]*p._v[2], k3=_v[3]*p._v[3];
int exp0,exp1,exp2,exp3;
frexp( double(k0), &exp0 );frexp( double(k1), &exp1 );
frexp( double(k2), &exp2 );frexp( double(k3), &exp3 );
if (exp0>exp1) { math::Swap(k0,k1); math::Swap(exp0,exp1); }
if (exp2>exp3) { math::Swap(k2,k3); math::Swap(exp2,exp3); }
if (exp0>exp2) { math::Swap(k0,k2); math::Swap(exp0,exp2); }
if (exp1>exp3) { math::Swap(k1,k3); math::Swap(exp1,exp3); }
if (exp2>exp3) { math::Swap(k2,k3); math::Swap(exp2,exp3); }
return ( (k0 + k1) + k2 ) +k3;
};
if (N==3) {
T k0=_v[0]*p._v[0], k1=_v[1]*p._v[1], k2=_v[2]*p._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;
}
};
}
//@}
//@{
/** @name Cross products
**/
/// Cross product for 3D Point
inline Point operator ^ ( Point const & p ) const
{
static_assert(N==3);
return Point <S>
(
_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]
);
}
/// Cross product for 2D Point
/// if called from a 3D or 4D points, returns the z component of the cross prod.
inline S operator % ( Point const & p ) const
{
return _v[0]*p._v[1] - _v[1]*p._v[0];
}
//@}
//@{
/** @name Norms
**/
// Euclidean norm
inline S Norm() const
{
if (N==2) return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] );
if (N==3) return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
if (N==4) return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[4]*_v[4] );
}
// Squared Euclidean norm
inline S SquaredNorm() const
{
if (N==2) return ( _v[0]*_v[0] + _v[1]*_v[1] );
if (N==3) return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
if (N==4) return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3] );
}
// Normalization (division by norm)
inline Point & Normalize()
{
S n = Norm();
if(n>0.0) (*this)/=n;
return *this;
}
/// Homogeneous normalization (division by W)
inline Point & HomoNormalize(){
if (_v[3]!=0.0) { _v[0] /= _v[3]; _v[1] /= _v[3]; _v[2] /= _v[3]; _v[3]=1.0; }
return *this;
};
//@}
// Per component scaling
inline Point & Scale( const Point & p )
{
_v[0] *= p._v[0];
_v[1] *= p._v[1];
if (N>2) _v[2] *= p._v[2];
if (N>3) _v[3] *= p._v[3];
return *this;
}
// Convert to polar coordinates
void ToPolar( S & ro, S & tetha, S & fi ) const
{
ro = Norm();
tetha = (S)atan2( _v[1], _v[0] );
fi = (S)acos( _v[2]/ro );
}
//@{
/** @name Comparison Operators.
Lexicographical order.
**/
inline bool operator == ( Point const & p ) const
{
if (N==2) return _v[0]==p._v[0] && _v[1]==p._v[1];
if (N==3) return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2];
if (N==4) return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2] && _v[3]==p._v[3];
}
inline bool operator != ( Point const & p ) const
{
if (N==2) return _v[0]!=p._v[0] || _v[1]!=p._v[1] ;
if (N==3) return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2];
if (N==4) return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2] || _v[3]!=p._v[3];
}
inline bool operator < ( Point 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 > ( Point 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 <= ( Point 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 >= ( Point 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 PointType LocalToGlobal(ParamType p) const{
return *this;
};
//@}
}; // end class definition
template <class S>
inline S Angle( Point<3,S> const & p1, Point<3,S> const & p2 )
{
S w = p1.Norm()*p2.Norm();
if(w==0) return -1;
S t = (p1*p2)/w;
if(t>1) t = 1;
else if(t<-1) t = -1;
return (S) acos(t);
}
// versione uguale alla precedente ma che assume che i due vettori sono unitari
template <class S>
inline S AngleN( Point<3,S> const & p1, Point<3,S> const & p2 )
{
S w = p1*p2;
if(w>1)
w = 1;
else if(w<-1)
w=-1;
return (S) acos(w);
}
template <int N,class S>
inline S Norm( Point<N,S> const & p )
{
return p.Norm();
}
template <int N,class S>
inline S SquaredNorm( Point<N,S> const & p )
{
return p.SquaredNorm();
}
template <int N,class S>
inline Point<N,S> & Normalize( Point<N,S> & p )
{
p.Normalize();
return p;
}
template <int N, class S>
inline S Distance( Point<N,S> const & p1,Point<N,S> const & p2 )
{
return (p1-p2).Norm();
}
template <int N, class S>
inline S SquaredDistance( Point<N,S> const & p1,Point<N,S> 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 S>
double StableDot ( Point<3,S> const & p0, Point<3,S> const & p1 )
{
}
/// Computes a shape quality measure of the triangle composed by points p0,p1,p2
/// It Returns 2*AreaTri/(MaxEdge^2),
/// the range is range [0.0, 0.866]
/// e.g. Equilateral triangle sqrt(3)/2, halfsquare: 1/2, ... up to a line that has zero quality.
template<class S>
S Quality( Point<3,S> const &p0, Point<3,S> const & p1, Point<3,S> const & p2)
{
PointType<S> d10=p1-p0;
PointType<S> d20=p2-p0;
PointType<S> d12=p1-p2;
PointType<S> x = d10^d20;
S a = Norm( x );
if(a==0) return 0; // Area zero triangles have surely quality==0;
S b = SquaredNorm( d10 );
S t = b;
t = SquaredNorm( d20 ); if ( b<t ) b = t;
t = SquaredNorm( d12 ); if ( b<t ) b = t;
assert(b!=0.0);
return a/b;
}
/// Returns the normal to the plane passing through p0,p1,p2
template<class S>
Point<3,S> Normal(const Point<3,S> & p0, const Point<3,S> & p1, const Point<3,S> & p2)
{
return ((p1 - p0) ^ (p2 - p0));
}
/// Like the above, it returns the normal to the plane passing through p0,p1,p2, but normalized.
template<class S>
Point<3,S> NormalizedNormal(const Point<3,S> & p0, const Point<3,S> & p1, const Point<3,S> & p2)
{
return ((p1 - p0) ^ (p2 - p0)).Normalize();
}
/// Point(p) Edge(v1-v2) dist, q is the point in v1-v2 with min dist
template<class S>
S PSDist( const Point<3,S> & p,
const Point<3,S> & v1,
const Point<3,S> & v2,
Point<3,S> & q )
{
Point<3,S> e = v2-v1;
S 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 S>
inline Point<2,S>::Point ( const S nx, const S ny )
{_v[0]=nx;_v[1]=ny;};*/
/*template <class S>
inline Point<4,S>::Point ( const S nx, const S ny , const S nz , const S nw )
{_v[0]=nx;_v[1]=ny;_v[2]=nz;_v[3]=nw;};*/
/*template < class S>
Point<3,S> Point<3,S>::operator * ( const S s ) const
{
return Point<3,S>( _v[0]*s, _v[1]*s , _v[2]*s );
}*/
//template < class S>
/*Point<3,double> Point<2,double>::operator * ( const double s ) const
{
return Point<2,double>( _v[0]*s, _v[1]*s );
}*/
typedef Point<3,short> Point3s;
typedef Point<3,int> Point3i;
typedef Point<3,float> Point3f;
typedef Point<3,double> Point3d;
/*@}*/
} // end namespace
#endif