883 lines
26 KiB
C++
883 lines
26 KiB
C++
/****************************************************************************
|
|
* 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 1.4 2004/04/29 10:47:06 ganovelli
|
|
some siyntax error corrected
|
|
|
|
Revision 1.3 2004/04/05 12:36:43 tarini
|
|
unified version: PointBase version, with no guards "(N==3)"
|
|
|
|
|
|
|
|
Revision 1.1 2004/03/16 03:07:38 tarini
|
|
"dimensionally unified" version: first commit
|
|
|
|
****************************************************************************/
|
|
|
|
#ifndef __VCGLIB_POINT
|
|
#define __VCGLIB_POINT
|
|
|
|
#include <assert.h>
|
|
#include <vcg/math/base.h>
|
|
#include <vcg/space/space.h>
|
|
|
|
namespace vcg {
|
|
|
|
|
|
|
|
|
|
template <int N, class S>
|
|
class Point;
|
|
|
|
/** \addtogroup space */
|
|
/*@{*/
|
|
/**
|
|
The templated class for representing a point in R^N space.
|
|
The class is templated over the ScalarType class that is used to represent coordinates.
|
|
PointBase provides the interface and the common operators for points
|
|
of any dimensionality.
|
|
*/
|
|
|
|
template <int N, class S>
|
|
class PointBase
|
|
{
|
|
public:
|
|
typedef S ScalarType;
|
|
typedef VoidType ParamType;
|
|
typedef Point<N,S> 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 PointType types
|
|
**/
|
|
|
|
inline PointBase () { };
|
|
// inline PointBase ( const S nv[N] );
|
|
|
|
/// 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;
|
|
}
|
|
|
|
/// importer for points with different scalar type and-or dimensionality
|
|
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;};
|
|
}
|
|
|
|
/// constructor for points with different scalar type and-or dimensionality
|
|
template <int N2, class S2>
|
|
static inline PointType Construct( const Point<N2,S2> & b )
|
|
{
|
|
PointType p; p.Import(b);
|
|
return p;
|
|
}
|
|
|
|
/// importer for homogeneous points
|
|
template <class S2>
|
|
inline void ImportHomo( const Point<N-1,S2> & b )
|
|
{
|
|
_v[0] = ScalarType(b[0]);
|
|
_v[1] = ScalarType(b[1]);
|
|
if (N>2) { _v[2] = ScalarType(_v[2]); };
|
|
_v[N-1] = 1.0;
|
|
}
|
|
|
|
/// constructor for homogeneus point.
|
|
template <int N2, class S2>
|
|
static inline PointType Construct( const Point<N-1,S2> & b )
|
|
{
|
|
PointType p; p.ImportHomo(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<N);
|
|
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]; }
|
|
/// W is in any case the last coordinate.
|
|
/// (in a 2D point, W() == Y(). In a 3D point, W()==Z()
|
|
/// in a 4D point, W() is a separate component)
|
|
inline const S &W() const { return _v[N-1]; }
|
|
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() { return _v[N-1]; }
|
|
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 PointType to Zero
|
|
inline void Zero();
|
|
inline PointType operator + ( PointType const & p) const;
|
|
inline PointType operator - ( PointType const & p) const;
|
|
inline PointType operator * ( const S s ) const;
|
|
inline PointType operator / ( const S s ) const;
|
|
inline PointType & operator += ( PointType const & p);
|
|
inline PointType & operator -= ( PointType const & p);
|
|
inline PointType & operator *= ( const S s );
|
|
inline PointType & operator /= ( const S s );
|
|
inline PointType operator - () const;
|
|
//@}
|
|
//@{
|
|
|
|
/** @name Dot products (cross product "%" is defined olny for 3D points)
|
|
**/
|
|
/// Dot product
|
|
inline S operator * ( PointType const & p ) const;
|
|
|
|
/// slower version, more stable (double precision only)
|
|
inline S StableDot ( const PointType & p ) const;
|
|
|
|
//@}
|
|
|
|
//@{
|
|
|
|
/** @name Norms
|
|
**/
|
|
|
|
/// Euclidean norm
|
|
inline S Norm() const;
|
|
/// Euclidean norm, static version
|
|
template <class PT> static S Norm(const PT &p );
|
|
/// Squared Euclidean norm
|
|
inline S SquaredNorm() const;
|
|
/// Squared Euclidean norm, static version
|
|
template <class PT> static S SquaredNorm(const PT &p );
|
|
/// Normalization (division by norm)
|
|
inline PointType & Normalize();
|
|
/// Normalization (division by norm), static version
|
|
template <class PT> static PointType & Normalize(const PT &p);
|
|
/// Homogeneous normalization (division by W)
|
|
inline PointType & HomoNormalize();
|
|
|
|
/// norm infinity: largest absolute value of compoenet
|
|
inline S NormInfinity() const;
|
|
/// norm 1: sum of absolute values of components
|
|
inline S NormOne() const;
|
|
|
|
//@}
|
|
/// Signed area operator
|
|
/// a % b returns the signed area of the parallelogram inside a and b
|
|
inline S operator % ( PointType const & p ) const;
|
|
|
|
/// the sum of the components
|
|
inline S Sum() const;
|
|
/// returns the biggest component
|
|
inline S Max() const;
|
|
/// returns the smallest component
|
|
inline S Min() const;
|
|
/// returns the index of the biggest component
|
|
inline int MaxI() const;
|
|
/// returns the index of the smallest component
|
|
inline int MinI() const;
|
|
|
|
|
|
/// Per component scaling
|
|
inline PointType & Scale( const PointType & p );
|
|
|
|
|
|
/// 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.
|
|
Lexicographic order.
|
|
**/
|
|
|
|
inline bool operator == ( PointType const & p ) const;
|
|
inline bool operator != ( PointType const & p ) const;
|
|
inline bool operator < ( PointType const & p ) const;
|
|
inline bool operator > ( PointType const & p ) const;
|
|
inline bool operator <= ( PointType const & p ) const;
|
|
inline bool operator >= ( PointType const & p ) const;
|
|
//@}
|
|
|
|
//@{
|
|
|
|
/** @name
|
|
Glocal to Local and viceversa
|
|
(provided for uniformity with other spatial classes. trivial for points)
|
|
**/
|
|
|
|
inline PointType LocalToGlobal(ParamType p) const{
|
|
return *this; }
|
|
|
|
inline ParamType GlobalToLocal(PointType p) const{
|
|
ParamType p(); return p; }
|
|
//@}
|
|
|
|
}; // end class definition
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
template <class S>
|
|
class Point<2, S> : public PointBase<2,S> {
|
|
public:
|
|
typedef S ScalarType;
|
|
typedef Point<2,S> PointType;
|
|
|
|
//@{
|
|
/** @name Special members for 2D points. **/
|
|
|
|
/// default
|
|
inline Point (){}
|
|
|
|
/// yx constructor
|
|
inline Point ( const S a, const S b){
|
|
_v[0]=a; _v[1]=b; };
|
|
|
|
/// unary orthogonal operator (2D equivalent of cross product)
|
|
/// returns orthogonal vector (90 deg left)
|
|
inline Point operator ~ () const {
|
|
return Point ( -_v[2], _v[1] );
|
|
}
|
|
|
|
/// returns the angle with X axis (radiants, in [-PI, +PI] )
|
|
inline ScalarType &Angle(){
|
|
return math::Atan2(_v[1],_v[0]);}
|
|
|
|
/// transform the point in cartesian coords into polar coords
|
|
inline Point & ToPolar(){
|
|
ScalarType t = Angle();
|
|
_v[0] = Norm();
|
|
_v[1] = t;
|
|
return *this;}
|
|
|
|
/// transform the point in polar coords into cartesian coords
|
|
inline Point & ToCartesian() {
|
|
ScalarType l = _v[0];
|
|
_v[0] = (ScalarType)(l*math::Cos(_v[1]));
|
|
_v[1] = (ScalarType)(l*math::Sin(_v[1]));
|
|
return *this;}
|
|
|
|
/// rotates the point of an angle (radiants, counterclockwise)
|
|
inline Point & Rotate( const ScalarType rad ){
|
|
ScalarType t = _v[0];
|
|
ScalarType s = math::Sin(rad);
|
|
ScalarType c = math::Cos(rad);
|
|
_v[0] = _v[0]*c - _v[1]*s;
|
|
_v[1] = t *s + _v[1]*c;
|
|
return *this;}
|
|
|
|
//@}
|
|
|
|
//@{
|
|
/** @name Implementation of standard functions for 3D points **/
|
|
|
|
inline void Zero(){
|
|
_v[0]=0; _v[1]=0; };
|
|
|
|
inline Point ( const S nv[2] ){
|
|
_v[0]=nv[0]; _v[1]=nv[1]; };
|
|
|
|
inline Point operator + ( Point const & p) const {
|
|
return Point( _v[0]+p._v[0], _v[1]+p._v[1]); }
|
|
|
|
inline Point operator - ( Point const & p) const {
|
|
return Point( _v[0]-p._v[0], _v[1]-p._v[1]); }
|
|
|
|
inline Point operator * ( const S s ) const {
|
|
return Point( _v[0]*s, _v[1]*s ); }
|
|
|
|
inline Point operator / ( const S s ) const {
|
|
S t=1.0/s;
|
|
return Point( _v[0]*t, _v[1]*t ); }
|
|
|
|
inline Point operator - () const {
|
|
return Point ( -_v[0], -_v[1] ); }
|
|
|
|
inline Point & operator += ( Point const & p ) {
|
|
_v[0] += p._v[0]; _v[1] += p._v[1]; return *this; }
|
|
|
|
inline Point & operator -= ( Point const & p ) {
|
|
_v[0] -= p._v[0]; _v[1] -= p._v[1]; return *this; }
|
|
|
|
inline Point & operator *= ( const S s ) {
|
|
_v[0] *= s; _v[1] *= s; return *this; }
|
|
|
|
inline Point & operator /= ( const S s ) {
|
|
S t=1.0/s; _v[0] *= t; _v[1] *= t; return *this; }
|
|
|
|
inline S Norm() const {
|
|
return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] );}
|
|
|
|
template <class PT> static S Norm(const PT &p ) {
|
|
return math::Sqrt( p.V(0)*p.V(0) + p.V(1)*p.V(1) );}
|
|
|
|
inline S SquaredNorm() const {
|
|
return ( _v[0]*_v[0] + _v[1]*_v[1] );}
|
|
|
|
template <class PT> static S SquaredNorm(const PT &p ) {
|
|
return ( p.V(0)*p.V(0) + p.V(1)*p.V(1) );}
|
|
|
|
inline S operator * ( Point const & p ) const {
|
|
return ( _v[0]*p._v[0] + _v[1]*p._v[1]) ; }
|
|
|
|
inline bool operator == ( Point const & p ) const {
|
|
return _v[0]==p._v[0] && _v[1]==p._v[1] ;}
|
|
|
|
inline bool operator != ( Point const & p ) const {
|
|
return _v[0]!=p._v[0] || _v[1]!=p._v[1] ;}
|
|
|
|
inline bool operator < ( Point const & p ) const{
|
|
return (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<p._v[0]); }
|
|
|
|
inline bool operator > ( Point const & p ) const {
|
|
return (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>p._v[0]); }
|
|
|
|
inline bool operator <= ( Point const & p ) {
|
|
return (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<=p._v[0]); }
|
|
|
|
inline bool operator >= ( Point const & p ) const {
|
|
return (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>=p._v[0]); }
|
|
|
|
inline Point & Normalize() {
|
|
PointType n = Norm(); if(n!=0.0) { n=1.0/n; _v[0]*=n; _v[1]*=n;} return *this;};
|
|
|
|
template <class PT> Point & Normalize(const PT &p){
|
|
PointType n = Norm(); if(n!=0.0) { n=1.0/n; V(0)*=n; V(1)*=n; }
|
|
return *this;};
|
|
|
|
inline Point & HomoNormalize(){
|
|
if (_v[2]!=0.0) { _v[0] /= W(); W()=1.0; } return *this;};
|
|
|
|
inline S NormInfinity() const {
|
|
return math::Max( math::Abs(_v[0]), math::Abs(_v[1]) ); }
|
|
|
|
inline S NormOne() const {
|
|
return math::Abs(_v[0])+ math::Abs(_v[1]);}
|
|
|
|
inline S operator % ( Point const & p ) const {
|
|
return _v[0] * p._v[1] - _v[1] * p._v[0]; }
|
|
|
|
inline S Sum() const {
|
|
return _v[0]+_v[1];}
|
|
|
|
inline S Max() const {
|
|
return math::Max( _v[0], _v[1] ); }
|
|
|
|
inline S Min() const {
|
|
return math::Min( _v[0], _v[1] ); }
|
|
|
|
inline int MaxI() const {
|
|
return (_v[0] < _v[1]) ? 1:0; };
|
|
|
|
inline int MinI() const {
|
|
return (_v[0] > _v[1]) ? 1:0; };
|
|
|
|
inline PointType & Scale( const PointType & p ) {
|
|
_v[0] *= p._v[0]; _v[1] *= p._v[1]; return *this; }
|
|
|
|
inline S StableDot ( const PointType & p ) const {
|
|
return _v[0]*p._v[0] +_v[1]*p._v[1]; }
|
|
//@}
|
|
|
|
};
|
|
|
|
template <class S>
|
|
class Point<3,S> : public PointBase<3,S> {
|
|
public:
|
|
typedef S ScalarType;
|
|
typedef Point<3,S> PointType;
|
|
|
|
//@{
|
|
/** @name Special members for 3D points. **/
|
|
|
|
/// default
|
|
inline Point ():PointBase<3,S>(){}
|
|
/// yxz constructor
|
|
inline Point ( const S a, const S b, const S c){
|
|
_v[0]=a; _v[1]=b; _v[2]=c; };
|
|
|
|
/// Cross product for 3D points
|
|
inline PointType operator ^ ( PointType const & p ) const {
|
|
return Point (
|
|
_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] );
|
|
}
|
|
//@}
|
|
|
|
//@{
|
|
/** @name Implementation of standard functions for 3D points **/
|
|
|
|
inline void Zero(){
|
|
_v[0]=0; _v[1]=0; _v[2]=0; };
|
|
|
|
inline Point ( const S nv[3] ){
|
|
_v[0]=nv[0]; _v[1]=nv[1]; _v[2]=nv[2]; };
|
|
|
|
inline Point operator + ( Point const & p) const{
|
|
return Point( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2]); }
|
|
|
|
inline Point operator - ( Point const & p) const {
|
|
return Point( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2]); }
|
|
|
|
inline Point operator * ( const S s ) const {
|
|
return Point( _v[0]*s, _v[1]*s , _v[2]*s ); }
|
|
|
|
inline Point operator / ( const S s ) const {
|
|
S t=1.0/s;
|
|
return Point( _v[0]*t, _v[1]*t , _v[2]*t ); }
|
|
|
|
inline Point operator - () const {
|
|
return Point ( -_v[0], -_v[1] , -_v[2] ); }
|
|
|
|
inline Point & operator += ( Point const & p ) {
|
|
_v[0] += p._v[0]; _v[1] += p._v[1]; _v[2] += p._v[2]; return *this; }
|
|
|
|
inline Point & operator -= ( Point const & p ) {
|
|
_v[0] -= p._v[0]; _v[1] -= p._v[1]; _v[2] -= p._v[2]; return *this; }
|
|
|
|
inline Point & operator *= ( const S s ) {
|
|
_v[0] *= s; _v[1] *= s; _v[2] *= s; return *this; }
|
|
|
|
inline Point & operator /= ( const S s ) {
|
|
S t=1.0/s; _v[0] *= t; _v[1] *= t; _v[2] *= t; return *this; }
|
|
|
|
inline S Norm() const {
|
|
return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );}
|
|
|
|
template <class PT> static S Norm(const PT &p ) {
|
|
return math::Sqrt( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2) );}
|
|
|
|
inline S SquaredNorm() const {
|
|
return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );}
|
|
|
|
template <class PT> static S SquaredNorm(const PT &p ) {
|
|
return ( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2) );}
|
|
|
|
inline S operator * ( PointType const & p ) const {
|
|
return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2]) ; }
|
|
|
|
inline bool operator == ( PointType const & p ) const {
|
|
return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2] ;}
|
|
|
|
inline bool operator != ( PointType const & p ) const {
|
|
return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2] ;}
|
|
|
|
inline bool operator < ( PointType 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 > ( PointType 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 <= ( PointType const & p ) {
|
|
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 >= ( PointType 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 & Normalize() {
|
|
S n = Norm();
|
|
if(n!=0.0) {
|
|
n=S(1.0)/n;
|
|
_v[0]*=n; _v[1]*=n; _v[2]*=n; }
|
|
return *this;};
|
|
|
|
template <class PT> PointType & Normalize(const PT &p){
|
|
S n = Norm(); if(n!=0.0) { n=1.0/n; V(0)*=n; V(1)*=n; V(2)*=n; }
|
|
return *this;};
|
|
|
|
inline PointType & HomoNormalize(){
|
|
if (_v[2]!=0.0) { _v[0] /= W(); _v[1] /= W(); W()=1.0; }
|
|
return *this;};
|
|
|
|
inline S NormInfinity() const {
|
|
return math::Max( math::Max( math::Abs(_v[0]), math::Abs(_v[1]) ),
|
|
math::Abs(_v[3]) ); }
|
|
|
|
inline S NormOne() const {
|
|
return math::Abs(_v[0])+ math::Abs(_v[1])+math::Max(math::Abs(_v[2]));}
|
|
|
|
inline S operator % ( PointType const & p ) const {
|
|
S t = (*this)*p; /* Area, general formula */
|
|
return math::Sqrt( SquaredNorm() * p.SquaredNorm() - (t*t) );};
|
|
|
|
inline S Sum() const {
|
|
return _v[0]+_v[1]+_v[2];}
|
|
|
|
inline S Max() const {
|
|
return math::Max( math::Max( _v[0], _v[1] ), _v[2] ); }
|
|
|
|
inline S Min() const {
|
|
return math::Min( math::Min( _v[0], _v[1] ), _v[2] ); }
|
|
|
|
inline int MaxI() const {
|
|
int i= (_v[0] < _v[1]) ? 1:0; if (_v[i] < _v[2]) i=2; return i;};
|
|
|
|
inline int MinI() const {
|
|
int i= (_v[0] > _v[1]) ? 1:0; if (_v[i] > _v[2]) i=2; return i;};
|
|
|
|
inline PointType & Scale( const PointType & p ) {
|
|
_v[0] *= p._v[0]; _v[1] *= p._v[1]; _v[2] *= p._v[2]; return *this; }
|
|
|
|
inline S StableDot ( const PointType & p ) const {
|
|
PointType 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;
|
|
}
|
|
//@}
|
|
|
|
};
|
|
|
|
template <class S>
|
|
class Point<4, S> : public PointBase<4,S> {
|
|
public:
|
|
typedef S ScalarType;
|
|
typedef Point<4,S> PointType;
|
|
//@{
|
|
/** @name Special members for 4D points. **/
|
|
/// default
|
|
inline Point (){}
|
|
|
|
/// xyzw constructor
|
|
//@}
|
|
inline Point ( const S a, const S b, const S c, const S d){
|
|
_v[0]=a; _v[1]=b; _v[2]=c; _v[3]=d; };
|
|
//@{
|
|
/** @name Implementation of standard functions for 3D points **/
|
|
|
|
inline void Zero(){
|
|
_v[0]=0; _v[1]=0; _v[2]=0; _v[3]=0; };
|
|
|
|
inline Point ( const S nv[4] ){
|
|
_v[0]=nv[0]; _v[1]=nv[1]; _v[2]=nv[2]; _v[3]=nv[3]; };
|
|
|
|
inline Point operator + ( Point const & p) const {
|
|
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 {
|
|
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 {
|
|
return Point( _v[0]*s, _v[1]*s , _v[2]*s , _v[3]*s ); }
|
|
|
|
inline PointType operator ^ ( PointType const & p ) const {
|
|
assert(0);
|
|
return *this;
|
|
}
|
|
|
|
inline Point operator / ( const S s ) const {
|
|
S t=1.0/s;
|
|
return Point( _v[0]*t, _v[1]*t , _v[2]*t , _v[3]*t ); }
|
|
|
|
inline Point operator - () const {
|
|
return Point ( -_v[0], -_v[1] , -_v[2] , -_v[3] ); }
|
|
|
|
inline Point & operator += ( Point const & p ) {
|
|
_v[0] += p._v[0]; _v[1] += p._v[1]; _v[2] += p._v[2]; _v[3] += p._v[3]; return *this; }
|
|
|
|
inline Point & operator -= ( Point const & p ) {
|
|
_v[0] -= p._v[0]; _v[1] -= p._v[1]; _v[2] -= p._v[2]; _v[3] -= p._v[3]; return *this; }
|
|
|
|
inline Point & operator *= ( const S s ) {
|
|
_v[0] *= s; _v[1] *= s; _v[2] *= s; _v[3] *= s; return *this; }
|
|
|
|
inline Point & operator /= ( const S s ) {
|
|
S t=1.0/s; _v[0] *= t; _v[1] *= t; _v[2] *= t; _v[3] *= t; return *this; }
|
|
|
|
inline S Norm() const {
|
|
return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3] );}
|
|
|
|
template <class PT> static S Norm(const PT &p ) {
|
|
return math::Sqrt( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2) + p.V(3)*p.V(3) );}
|
|
|
|
inline S SquaredNorm() const {
|
|
return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3] );}
|
|
|
|
template <class PT> static S SquaredNorm(const PT &p ) {
|
|
return ( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2) + p.V(3)*p.V(3) );}
|
|
|
|
inline S operator * ( PointType const & p ) const {
|
|
return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] + _v[3]*p._v[3] ); }
|
|
|
|
inline bool operator == ( PointType const & p ) const {
|
|
return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2] && _v[3]==p._v[3];}
|
|
|
|
inline bool operator != ( PointType const & p ) const {
|
|
return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2] || _v[3]!=p._v[3];}
|
|
|
|
inline bool operator < ( PointType const & p ) const{
|
|
return (_v[3]!=p._v[3])?(_v[3]< p._v[3]) : (_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 > ( PointType const & p ) const {
|
|
return (_v[3]!=p._v[3])?(_v[3]> p._v[3]) : (_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 <= ( PointType const & p ) {
|
|
return (_v[3]!=p._v[3])?(_v[3]< p._v[3]) : (_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 >= ( PointType const & p ) const {
|
|
return (_v[3]!=p._v[3])?(_v[3]> p._v[3]) : (_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 & Normalize() {
|
|
PointType n = Norm(); if(n!=0.0) { n=1.0/n; _v[0]*=n; _v[1]*=n; _v[2]*=n; _v[3]*=n; }
|
|
return *this;};
|
|
|
|
template <class PT> PointType & Normalize(const PT &p){
|
|
PointType n = Norm(); if(n!=0.0) { n=1.0/n; V(0)*=n; V(1)*=n; V(2)*=n; V(3)*=n; }
|
|
return *this;};
|
|
|
|
inline PointType & HomoNormalize(){
|
|
if (_v[3]!=0.0) { _v[0] /= W(); _v[1] /= W(); _v[2] /= W(); W()=1.0; }
|
|
return *this;};
|
|
|
|
inline S NormInfinity() const {
|
|
return math::Max( math::Max( math::Abs(_v[0]), math::Abs(_v[1]) ),
|
|
math::Max( math::Abs(_v[2]), math::Abs(_v[3]) ) ); }
|
|
|
|
inline S NormOne() const {
|
|
return math::Abs(_v[0])+ math::Abs(_v[1])+math::Max(math::Abs(_v[2]),math::Abs(_v[3]));}
|
|
|
|
inline S operator % ( PointType const & p ) const {
|
|
S t = (*this)*p; /* Area, general formula */
|
|
return math::Sqrt( SquaredNorm() * p.SquaredNorm() - (t*t) );};
|
|
|
|
inline S Sum() const {
|
|
return _v[0]+_v[1]+_v[2]+_v[3];}
|
|
|
|
inline S Max() const {
|
|
return math::Max( math::Max( _v[0], _v[1] ), math::Max( _v[2], _v[3] )); }
|
|
|
|
inline S Min() const {
|
|
return math::Min( math::Min( _v[0], _v[1] ), math::Min( _v[2], _v[3] )); }
|
|
|
|
inline int MaxI() const {
|
|
int i= (_v[0] < _v[1]) ? 1:0; if (_v[i] < _v[2]) i=2; if (_v[i] < _v[3]) i=3;
|
|
return i;};
|
|
|
|
inline int MinI() const {
|
|
int i= (_v[0] > _v[1]) ? 1:0; if (_v[i] > _v[2]) i=2; if (_v[i] > _v[3]) i=3;
|
|
return i;};
|
|
|
|
inline PointType & Scale( const PointType & p ) {
|
|
_v[0] *= p._v[0]; _v[1] *= p._v[1]; _v[2] *= p._v[2]; _v[3] *= p._v[3]; return *this; }
|
|
|
|
inline S StableDot ( const PointType & p ) const {
|
|
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; }
|
|
|
|
//@}
|
|
};
|
|
|
|
|
|
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 siano 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();
|
|
}
|
|
|
|
|
|
template <typename S>
|
|
struct Point2:public Point<2,S>{
|
|
inline Point2(){};
|
|
inline Point2(Point<2,S> const & p):Point<2,S>(p){} ;
|
|
inline Point2( const S a, const S b):Point<2,S>(a,b){};
|
|
};
|
|
|
|
template <typename S>
|
|
struct Point3:public Point<3,S> {
|
|
inline Point3(){};
|
|
inline Point3(Point<3,S> const & p):Point<3,S> (p){}
|
|
inline Point3( const S a, const S b, const S c):Point<3,S> (a,b,c){};
|
|
};
|
|
|
|
|
|
template <typename S>
|
|
struct Point4:public Point<4,S>{
|
|
inline Point4(){};
|
|
inline Point4(Point<4,S> const & p):Point<4,S>(p){}
|
|
inline Point4( const S a, const S b, const S c, const S d):Point<4,S>(a,b,c,d){};
|
|
};
|
|
|
|
typedef Point2<short> Point2s;
|
|
typedef Point2<int> Point2i;
|
|
typedef Point2<float> Point2f;
|
|
typedef Point2<double> Point2d;
|
|
typedef Point2<short> Vector2s;
|
|
typedef Point2<int> Vector2i;
|
|
typedef Point2<float> Vector2f;
|
|
typedef Point2<double> Vector2d;
|
|
|
|
typedef Point3<short> Point3s;
|
|
typedef Point3<int> Point3i;
|
|
typedef Point3<float> Point3f;
|
|
typedef Point3<double> Point3d;
|
|
typedef Point3<short> Vector3s;
|
|
typedef Point3<int> Vector3i;
|
|
typedef Point3<float> Vector3f;
|
|
typedef Point3<double> Vector3d;
|
|
|
|
|
|
typedef Point4<short> Point4s;
|
|
typedef Point4<int> Point4i;
|
|
typedef Point4<float> Point4f;
|
|
typedef Point4<double> Point4d;
|
|
typedef Point4<short> Vector4s;
|
|
typedef Point4<int> Vector4i;
|
|
typedef Point4<float> Vector4f;
|
|
typedef Point4<double> Vector4d;
|
|
|
|
/*@}*/
|
|
|
|
|
|
|
|
|
|
} // end namespace
|
|
#endif
|
|
|