589 lines
15 KiB
C++
589 lines
15 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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/****************************************************************************
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History
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$Log: not supported by cvs2svn $
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Revision 1.14 2004/03/05 17:55:01 tarini
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errorino: upper case in Zero()
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Revision 1.13 2004/03/03 14:22:48 cignoni
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Yet against cr lf mismatch
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Revision 1.12 2004/02/23 23:42:26 cignoni
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Translated comments, removed unusued stuff. corrected linefeed/cr
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Revision 1.11 2004/02/19 16:12:28 cignoni
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cr lf mismatch 2
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Revision 1.10 2004/02/19 16:06:24 cignoni
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cr lf mismatch
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Revision 1.8 2004/02/19 15:13:40 cignoni
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corrected sqrt and added doxygen groups
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Revision 1.7 2004/02/17 02:08:47 cignoni
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Di prova...
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Revision 1.6 2004/02/15 23:35:47 cignoni
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Cambiato nome type template in accordo alla styleguide
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Revision 1.5 2004/02/10 01:07:15 cignoni
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Edited Comments and GPL license
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Revision 1.4 2004/02/09 13:48:02 cignoni
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Edited doxygen comments
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****************************************************************************/
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#ifndef __VCGLIB_POINT
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#define __VCGLIB_POINT
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#include <assert.h>
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#include <vcg/math/base.h>
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#include <vcg/space/space.h>
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namespace vcg {
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/** \addtogroup space */
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/*@{*/
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/**
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The templated class for representing a point in 3D space.
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The class is templated over the ScalarType class that is used to represent coordinates. All the usual
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operator overloading (* + - ...) is present.
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*/
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template <int N, class S>
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class Point : public Space<N,S>, Linear<Point>
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{
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public:
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typedef S ScalarType;
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typedef VoidType ParamType;
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typedef Point PointType;
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enum {Dimension=N};
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protected:
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/// The only data member. Hidden to user.
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S _v[N];
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public:
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//@{
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/** @name Standard Constructors and Initializers
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No casting operators have been introduced to avoid automatic unattended (and costly) conversion between different point types
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**/
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inline Point () { }
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inline Point ( const S nx, const S ny, const S nz, const S nw )
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{
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static_assert(N==4);
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_v[0] = nx;
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_v[1] = ny;
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_v[2] = nz;
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_v[3] = nw;
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}
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inline Point ( const S nx, const S ny, const S nz)
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{
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static_assert(N==3);
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_v[0] = nx;
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_v[1] = ny;
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_v[2] = nz;
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}
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inline Point ( const S nx, const S ny)
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{
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static_assert(N==2);
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_v[0] = nx;
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_v[1] = ny;
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}
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inline Point ( const S nv[N] )
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{
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_v[0] = nv[0];
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_v[1] = nv[1];
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if (N>2) _v[2] = nv[2];
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if (N>3) _v[3] = nv[3];
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}
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/// Padding function: give a default 0 value to all the elements that are not in the [0..2] range.
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/// Useful for managing in a consistent way object that could have point2 / point3 / point4
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inline S Ext( const int i ) const
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{
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if(i>=0 && i<=N) return _v[i];
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else return 0;
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}
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template <int N2, class S2>
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inline void Import( const Point<N2,S2> & b )
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{
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_v[0] = ScalarType(b[0]);
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_v[1] = ScalarType(b[1]);
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if (N>2) { if (N2>2) _v[2] = ScalarType(b[2]); else _v[2] = 0};
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if (N>3) { if (N2>3) _v[3] = ScalarType(b[3]); else _v[3] = 0};
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}
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static inline Point Construct( const PointType & b )
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{
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PointType p; p.Import(b);
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return p;
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}
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//@}
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//@{
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/** @name Data Access.
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access to data is done by overloading of [] or explicit naming of coords (x,y,z)**/
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inline S & operator [] ( const int i )
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{
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assert(i>=0 && i<N);
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return _v[i];
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}
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inline const S & operator [] ( const int i ) const
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{
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assert(i>=0 && i<3);
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return _v[i];
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}
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inline const S &X() const { return _v[0]; }
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inline const S &Y() const { return _v[1]; }
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inline const S &Z() const { static_assert(N>2); return _v[2]; }
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inline const S &W() const { static_assert(N>3); return _v[3]; }
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inline S &X() { return _v[0]; }
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inline S &Y() { return _v[1]; }
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inline S &Z() { static_assert(N>2); return _v[2]; }
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inline S &W() { static_assert(N>3); return _v[3]; }
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inline const S * V() const
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{
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return _v;
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}
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inline S & V( const int i )
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{
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assert(i>=0 && i<N);
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return _v[i];
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}
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inline const S & V( const int i ) const
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{
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assert(i>=0 && i<N);
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return _v[i];
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}
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//@}
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//@{
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/** @name Linearity for points
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**/
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/// sets a point to Zero
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inline void Zero()
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{
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_v[0] = 0;
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_v[1] = 0;
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if (N>2) _v[2] = 0;
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if (N>3) _v[3] = 0;
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}
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inline Point operator + ( Point const & p) const
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{
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if (N==2) return Point( _v[0]+p._v[0], _v[1]+p._v[1] );
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if (N==3) return Point( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2] );
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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] );
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}
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inline Point operator - ( Point const & p) const
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{
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if (N==2) return Point( _v[0]-p._v[0], _v[1]-p._v[1] );
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if (N==3) return Point( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2] );
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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] );
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}
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inline Point operator * ( const S s ) const
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{
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if (N==2) return Point( _v[0]*s, _v[1]*s );
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if (N==3) return Point( _v[0]*s, _v[1]*s, _v[2]*s );
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if (N==4) return Point( _v[0]*s, _v[1]*s, _v[2]*s, _v[3]*s );
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}
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inline Point operator / ( const S s ) const
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{
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if (N==2) return Point( _v[0]/s, _v[1]/s );
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if (N==3) return Point( _v[0]/s, _v[1]/s, _v[2]/s );
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if (N==4) return Point( _v[0]/s, _v[1]/s, _v[2]/s, _v[3]/s );
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}
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inline Point & operator += ( Point const & p)
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{
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_v[0] += p._v[0];
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_v[1] += p._v[1];
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if (N>2) _v[2] += p._v[2];
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if (N>3) _v[3] += p._v[3];
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return *this;
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}
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inline Point & operator -= ( Point const & p)
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{
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_v[0] -= p._v[0];
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_v[1] -= p._v[1];
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if (N>2) _v[2] -= p._v[2];
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if (N>3) _v[3] -= p._v[3];
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return *this;
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}
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inline Point & operator *= ( const S s )
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{
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_v[0] *= s;
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_v[1] *= s;
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if (N>2) _v[2] *= s;
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if (N>3) _v[3] *= s;
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return *this;
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}
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inline Point & operator /= ( const S s )
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{
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_v[0] /= s;
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_v[1] /= s;
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if (N>2) _v[2] /= s;
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if (N>3) _v[3] /= s;
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return *this;
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}
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inline Point operator - () const
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{
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if (N==2) return Point ( -_v[0], -_v[1] );
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if (N==3) return Point ( -_v[0], -_v[1], -_v[2] );
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if (N==4) return Point ( -_v[0], -_v[1], -_v[2] , -_v[3] );
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}
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//@}
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//@{
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/** @name Dot products
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**/
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/// Dot product
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inline S operator * ( Point const & p ) const
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{
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if (N==2) return ( _v[0]*p._v[0] + _v[1]*p._v[1] );
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if (N==3) return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] );
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if (N==4) return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] + _v[2]*p._v[2] );
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};
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/// slower version, more stable (double precision only)
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inline S StableDot ( const Point & p ) const
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{
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if (N==2) return _v[0]*p._v[0] + _v[1]*p._v[1];
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if (N==4) {
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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];
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int exp0,exp1,exp2,exp3;
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frexp( double(k0), &exp0 );frexp( double(k1), &exp1 );
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frexp( double(k2), &exp2 );frexp( double(k3), &exp3 );
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if (exp0>exp1) { math::Swap(k0,k1); math::Swap(exp0,exp1); }
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if (exp2>exp3) { math::Swap(k2,k3); math::Swap(exp2,exp3); }
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if (exp0>exp2) { math::Swap(k0,k2); math::Swap(exp0,exp2); }
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if (exp1>exp3) { math::Swap(k1,k3); math::Swap(exp1,exp3); }
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if (exp2>exp3) { math::Swap(k2,k3); math::Swap(exp2,exp3); }
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return ( (k0 + k1) + k2 ) +k3;
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};
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if (N==3) {
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T k0=_v[0]*p._v[0], k1=_v[1]*p._v[1], k2=_v[2]*p._v[2];
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int exp0,exp1,exp2;
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frexp( double(k0), &exp0 );
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frexp( double(k1), &exp1 );
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frexp( double(k2), &exp2 );
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if( exp0<exp1 ) {
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if(exp0<exp2) return (k1+k2)+k0;
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else return (k0+k1)+k2;
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} else {
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if(exp1<exp2) return (k0+k2)+k1;
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else return (k0+k1)+k2;
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}
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};
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}
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//@}
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//@{
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/** @name Cross products
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**/
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/// Cross product for 3D Point
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inline Point operator ^ ( Point const & p ) const
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{
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static_assert(N==3);
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return Point <S>
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(
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_v[1]*p._v[2] - _v[2]*p._v[1],
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_v[2]*p._v[0] - _v[0]*p._v[2],
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_v[0]*p._v[1] - _v[1]*p._v[0]
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);
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}
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/// Cross product for 2D Point
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/// if called from a 3D or 4D points, returns the z component of the cross prod.
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inline S operator % ( Point const & p ) const
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{
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return _v[0]*p._v[1] - _v[1]*p._v[0];
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}
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//@}
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//@{
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/** @name Norms
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**/
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// Euclidean norm
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inline S Norm() const
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{
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if (N==2) return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] );
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if (N==3) return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
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if (N==4) return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[4]*_v[4] );
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}
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// Squared Euclidean norm
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inline S SquaredNorm() const
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{
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if (N==2) return ( _v[0]*_v[0] + _v[1]*_v[1] );
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if (N==3) return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
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if (N==4) return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3] );
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}
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// Normalization (division by norm)
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inline Point & Normalize()
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{
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S n = Norm();
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if(n>0.0) (*this)/=n;
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return *this;
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}
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/// Homogeneous normalization (division by W)
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inline Point & HomoNormalize(){
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if (_v[3]!=0.0) { _v[0] /= _v[3]; _v[1] /= _v[3]; _v[2] /= _v[3]; _v[3]=1.0; }
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return *this;
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};
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//@}
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// Per component scaling
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inline Point & Scale( const Point & p )
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{
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_v[0] *= p._v[0];
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_v[1] *= p._v[1];
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if (N>2) _v[2] *= p._v[2];
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if (N>3) _v[3] *= p._v[3];
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return *this;
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}
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// Convert to polar coordinates
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void ToPolar( S & ro, S & tetha, S & fi ) const
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{
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ro = Norm();
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tetha = (S)atan2( _v[1], _v[0] );
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fi = (S)acos( _v[2]/ro );
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}
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//@{
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/** @name Comparison Operators.
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Lexicographical order.
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**/
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inline bool operator == ( Point const & p ) const
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{
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if (N==2) return _v[0]==p._v[0] && _v[1]==p._v[1];
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if (N==3) return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2];
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if (N==4) return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2] && _v[3]==p._v[3];
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}
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inline bool operator != ( Point const & p ) const
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{
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if (N==2) return _v[0]!=p._v[0] || _v[1]!=p._v[1] ;
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if (N==3) return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2];
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if (N==4) return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2] || _v[3]!=p._v[3];
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}
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inline bool operator < ( Point const & p ) const
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{
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return (_v[2]!=p._v[2])?(_v[2]<p._v[2]):
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(_v[1]!=p._v[1])?(_v[1]<p._v[1]):
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(_v[0]<p._v[0]);
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}
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inline bool operator > ( Point const & p ) const
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{
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return (_v[2]!=p._v[2])?(_v[2]>p._v[2]):
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(_v[1]!=p._v[1])?(_v[1]>p._v[1]):
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(_v[0]>p._v[0]);
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}
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inline bool operator <= ( Point const & p ) const
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{
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return (_v[2]!=p._v[2])?(_v[2]< p._v[2]):
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(_v[1]!=p._v[1])?(_v[1]< p._v[1]):
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(_v[0]<=p._v[0]);
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}
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inline bool operator >= ( Point const & p ) const
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{
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return (_v[2]!=p._v[2])?(_v[2]> p._v[2]):
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(_v[1]!=p._v[1])?(_v[1]> p._v[1]):
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(_v[0]>=p._v[0]);
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}
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inline PointType LocalToGlobal(ParamType p) const{
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return *this;
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};
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//@}
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}; // end class definition
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template <class S>
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inline S Angle( Point<3,S> const & p1, Point<3,S> const & p2 )
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{
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S w = p1.Norm()*p2.Norm();
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if(w==0) return -1;
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S t = (p1*p2)/w;
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if(t>1) t = 1;
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else if(t<-1) t = -1;
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return (S) acos(t);
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}
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// versione uguale alla precedente ma che assume che i due vettori sono unitari
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template <class S>
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inline S AngleN( Point<3,S> const & p1, Point<3,S> const & p2 )
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{
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S w = p1*p2;
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if(w>1)
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w = 1;
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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
|
|
|