613 lines
18 KiB
C++
613 lines
18 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 1.26 2006/11/13 13:03:45 ponchio
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Added GetBBox in Point3 (declaration) the body of the function is in box3.h
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Revision 1.25 2006/10/13 12:59:24 cignoni
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Added **explicit** constructor from three coords of a different scalartype
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Revision 1.24 2006/09/28 13:37:35 m_di_benedetto
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added non const * V()
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Revision 1.23 2005/11/09 16:11:55 cignoni
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Added Abs and LowClampToZero
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Revision 1.22 2005/09/14 14:09:21 m_di_benedetto
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Added specialized Convert() for the same scalar type.
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Revision 1.21 2005/05/06 14:45:33 spinelli
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cambiato parentesi nel costruttore di GetUV per rendere compatibile tale costruttore con MVC e borland
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Revision 1.20 2005/04/27 16:05:19 callieri
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line 466, added parentesis on default value creator getUV [borland]
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Revision 1.19 2004/11/09 15:49:07 ganovelli
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added GetUV
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Revision 1.18 2004/10/13 12:45:51 cignoni
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Better Doxygen documentation
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Revision 1.17 2004/09/10 14:01:40 cignoni
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Added polar to cartesian
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Revision 1.16 2004/03/21 17:14:56 ponchio
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Added a math::
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Revision 1.15 2004/03/07 22:45:32 cignoni
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Moved quality and normal functions to the triangle class.
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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_POINT3
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#define __VCGLIB_POINT3
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#include <assert.h>
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#include <algorithm>
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#include <vcg/math/base.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 <class T> class Box3;
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template <class P3ScalarType> class Point3
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{
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protected:
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/// The only data member. Hidden to user.
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P3ScalarType _v[3];
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public:
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typedef P3ScalarType ScalarType;
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enum {Dimension = 3};
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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 Point3 () { }
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inline Point3 ( const P3ScalarType nx, const P3ScalarType ny, const P3ScalarType nz )
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{
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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 Point3 ( Point3 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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_v[2]= p._v[2];
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}
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inline Point3 ( const P3ScalarType nv[3] )
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{
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_v[0] = nv[0];
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_v[1] = nv[1];
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_v[2] = nv[2];
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}
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inline Point3 & operator =( Point3 const & p )
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{
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_v[0]= p._v[0]; _v[1]= p._v[1]; _v[2]= p._v[2];
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return *this;
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}
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inline void SetZero()
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{
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_v[0] = 0;
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_v[1] = 0;
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_v[2] = 0;
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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 P3ScalarType Ext( const int i ) const
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{
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if(i>=0 && i<=2) return _v[i];
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else return 0;
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}
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template <class Q>
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inline void Import( const Point3<Q> & b )
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{
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_v[0] = P3ScalarType(b[0]);
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_v[1] = P3ScalarType(b[1]);
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_v[2] = P3ScalarType(b[2]);
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}
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template <class EigenVector>
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inline void FromEigenVector( const EigenVector & b )
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{
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_v[0] = P3ScalarType(b[0]);
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_v[1] = P3ScalarType(b[1]);
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_v[2] = P3ScalarType(b[2]);
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}
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template <class EigenVector>
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inline void ToEigenVector( EigenVector & b ) const
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{
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b[0]=_v[0] ;
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b[1]=_v[1] ;
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b[2]=_v[2] ;
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}
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template <class Q>
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static inline Point3 Construct( const Point3<Q> & b )
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{
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return Point3(P3ScalarType(b[0]),P3ScalarType(b[1]),P3ScalarType(b[2]));
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}
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template <class Q>
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static inline Point3 Construct( const Q & P0, const Q & P1, const Q & P2)
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{
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return Point3(P3ScalarType(P0),P3ScalarType(P1),P3ScalarType(P2));
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}
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static inline Point3 Construct( const Point3<ScalarType> & b )
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{
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return b;
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}
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static inline Point3 Zero(void)
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{
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return Point3(0,0,0);
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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 P3ScalarType & operator [] ( const int i )
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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 P3ScalarType & 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 P3ScalarType &X() const { return _v[0]; }
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inline const P3ScalarType &Y() const { return _v[1]; }
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inline const P3ScalarType &Z() const { return _v[2]; }
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inline P3ScalarType &X() { return _v[0]; }
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inline P3ScalarType &Y() { return _v[1]; }
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inline P3ScalarType &Z() { return _v[2]; }
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inline const P3ScalarType * V() const
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{
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return _v;
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}
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inline P3ScalarType * V()
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{
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return _v;
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}
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inline P3ScalarType & V( const int i )
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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 P3ScalarType & V( 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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//@}
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//@{
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/** @name Classical overloading of operators
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Note
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**/
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inline Point3 operator + ( Point3 const & p) const
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{
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return Point3<P3ScalarType>( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2] );
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}
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inline Point3 operator - ( Point3 const & p) const
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{
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return Point3<P3ScalarType>( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2] );
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}
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inline Point3 operator * ( const P3ScalarType s ) const
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{
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return Point3<P3ScalarType>( _v[0]*s, _v[1]*s, _v[2]*s );
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}
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inline Point3 operator / ( const P3ScalarType s ) const
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{
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return Point3<P3ScalarType>( _v[0]/s, _v[1]/s, _v[2]/s );
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}
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/// Dot product
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inline P3ScalarType operator * ( Point3 const & p ) const
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{
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return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] );
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}
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inline P3ScalarType dot( const Point3 & p ) const { return (*this) * p; }
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/// Cross product
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inline Point3 operator ^ ( Point3 const & p ) const
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{
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return Point3 <P3ScalarType>
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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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inline Point3 & operator += ( Point3 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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_v[2] += p._v[2];
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return *this;
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}
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inline Point3 & operator -= ( Point3 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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_v[2] -= p._v[2];
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return *this;
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}
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inline Point3 & operator *= ( const P3ScalarType s )
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{
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_v[0] *= s;
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_v[1] *= s;
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_v[2] *= s;
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return *this;
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}
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inline Point3 & operator /= ( const P3ScalarType s )
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{
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_v[0] /= s;
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_v[1] /= s;
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_v[2] /= s;
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return *this;
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}
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// Norme
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inline P3ScalarType Norm() const
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{
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return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
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}
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inline P3ScalarType SquaredNorm() const
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{
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return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
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}
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// Scalatura differenziata
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inline Point3 & Scale( const P3ScalarType sx, const P3ScalarType sy, const P3ScalarType sz )
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{
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_v[0] *= sx;
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_v[1] *= sy;
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_v[2] *= sz;
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return *this;
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}
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inline Point3 & Scale( const Point3 & 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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_v[2] *= p._v[2];
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return *this;
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}
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// Normalizzazione
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inline Point3 & Normalize()
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{
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P3ScalarType n = P3ScalarType(math::Sqrt(_v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2]));
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if (n > P3ScalarType(0)) { _v[0] /= n; _v[1] /= n; _v[2] /= n; }
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return *this;
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}
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// for compatibility with eigen port
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inline Point3 & normalized() { return Normalize(); }
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/**
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* Convert to polar coordinates from cartesian coordinates.
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*
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* Theta is the azimuth angle and ranges between [0, 2PI) degrees.
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* Phi is the elevation angle (not the polar angle) and ranges between [-PI/2, PI/2] degrees.
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*
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* /note Note that instead of the classical polar angle, which ranges between
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* 0 and PI degrees we opt for the elevation angle to obtain a more
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* intuitive spherical coordinate system.
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*/
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void ToPolarRad(P3ScalarType &ro, P3ScalarType &theta, P3ScalarType &phi) const
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{
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ro = Norm();
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theta = (P3ScalarType)atan2(_v[2], _v[0]);
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phi = (P3ScalarType)asin(_v[1]/ro);
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}
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/**
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* Convert from polar coordinates to cartesian coordinates.
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*
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* Theta is the azimuth angle and ranges between [0, 2PI) radians.
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* Phi is the elevation angle (not the polar angle) and ranges between [-PI/2, PI/2] radians.
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*
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* \note Note that instead of the classical polar angle, which ranges between
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* 0 and PI degrees, we opt for the elevation angle to obtain a more
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* intuitive spherical coordinate system.
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*/
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void FromPolarRad(const P3ScalarType &ro, const P3ScalarType &theta, const P3ScalarType &phi)
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{
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_v[0]= ro*cos(theta)*cos(phi);
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_v[1]= ro*sin(phi);
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_v[2]= ro*sin(theta)*cos(phi);
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}
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Box3<P3ScalarType> GetBBox(Box3<P3ScalarType> &bb) const;
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//@}
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//@{
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size_t MaxCoeffId() const
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{
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if (_v[0]>_v[1])
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return _v[0]>_v[2] ? 0 : 2;
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else
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return _v[1]>_v[2] ? 1 : 2;
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}
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/** @name Comparison Operators.
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Note that the reverse z prioritized ordering, useful in many situations.
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**/
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inline bool operator == ( Point3 const & p ) const
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{
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return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2];
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}
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inline bool operator != ( Point3 const & p ) const
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{
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return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2];
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}
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inline bool operator < ( Point3 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 > ( Point3 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 <= ( Point3 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 >= ( Point3 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 Point3 operator - () const
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{
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return Point3<P3ScalarType> ( -_v[0], -_v[1], -_v[2] );
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}
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//@}
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}; // end class definition
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template <class P3ScalarType>
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inline P3ScalarType Angle( Point3<P3ScalarType> const & p1, Point3<P3ScalarType> const & p2 )
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{
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P3ScalarType w = p1.Norm()*p2.Norm();
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if(w==0) return -1;
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P3ScalarType 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 (P3ScalarType) 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 P3ScalarType>
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inline P3ScalarType AngleN( Point3<P3ScalarType> const & p1, Point3<P3ScalarType> const & p2 )
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{
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P3ScalarType w = p1*p2;
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if(w>1)
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w = 1;
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else if(w<-1)
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w=-1;
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return (P3ScalarType) acos(w);
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}
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template <class P3ScalarType>
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inline P3ScalarType Norm( Point3<P3ScalarType> const & p )
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{
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return p.Norm();
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}
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template <class P3ScalarType>
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inline P3ScalarType SquaredNorm( Point3<P3ScalarType> const & p )
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{
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return p.SquaredNorm();
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}
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template <class P3ScalarType>
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inline Point3<P3ScalarType> & Normalize( Point3<P3ScalarType> & p )
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{
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p.Normalize();
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return p;
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}
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template <class P3ScalarType>
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inline P3ScalarType Distance( Point3<P3ScalarType> const & p1,Point3<P3ScalarType> const & p2 )
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{
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return (p1-p2).Norm();
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}
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template <class P3ScalarType>
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inline P3ScalarType SquaredDistance( Point3<P3ScalarType> const & p1,Point3<P3ScalarType> const & p2 )
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{
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return (p1-p2).SquaredNorm();
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}
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template <class P3ScalarType>
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P3ScalarType ApproximateGeodesicDistance(const Point3<P3ScalarType>& p0, const Point3<P3ScalarType>& n0,
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const Point3<P3ScalarType>& p1, const Point3<P3ScalarType>& n1)
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{
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Point3<P3ScalarType> V(p0-p1);
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V.Normalize();
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const P3ScalarType C0 = V*n0;
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const P3ScalarType C1 = V*n1;
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const P3ScalarType De = Distance(p0,p1);
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if(fabs(C0-C1)<0.0001) return De/sqrt(1-C0*C1);
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const P3ScalarType Dg = ((asin(C0) - asin(C1))/(C0-C1));
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return Dg*De;
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}
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|
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// Dot product preciso numericamente (solo double!!)
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// Implementazione: si sommano i prodotti per ordine di esponente
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// (prima le piu' grandi)
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template<class P3ScalarType>
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double stable_dot ( Point3<P3ScalarType> const & p0, Point3<P3ScalarType> const & p1 )
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{
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P3ScalarType k0 = p0._v[0]*p1._v[0];
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P3ScalarType k1 = p0._v[1]*p1._v[1];
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P3ScalarType k2 = p0._v[2]*p1._v[2];
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|
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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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|
|
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if( exp0<exp1 )
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|
{
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if(exp0<exp2)
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return (k1+k2)+k0;
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else
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return (k0+k1)+k2;
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}
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else
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{
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if(exp1<exp2)
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return(k0+k2)+k1;
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else
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return (k0+k1)+k2;
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}
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}
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/// Point(p) Edge(v1-v2) dist, q is the point in v1-v2 with min dist
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|
template<class P3ScalarType>
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|
P3ScalarType PSDist( const Point3<P3ScalarType> & p,
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|
const Point3<P3ScalarType> & v1,
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|
const Point3<P3ScalarType> & v2,
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|
Point3<P3ScalarType> & q )
|
|
{
|
|
Point3<P3ScalarType> e = v2-v1;
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|
P3ScalarType t = ((p-v1)*e)/e.SquaredNorm();
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|
if(t<0) t = 0;
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|
else if(t>1) t = 1;
|
|
q = v1+e*t;
|
|
return Distance(p,q);
|
|
}
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|
|
|
|
|
template <class P3ScalarType>
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|
void GetUV( Point3<P3ScalarType> &n,Point3<P3ScalarType> &u, Point3<P3ScalarType> &v, Point3<P3ScalarType> up=(Point3<P3ScalarType>(0,1,0)) )
|
|
{
|
|
n.Normalize();
|
|
const double LocEps=double(1e-7);
|
|
u=n^up;
|
|
double len = u.Norm();
|
|
if(len < LocEps)
|
|
{
|
|
if(fabs(n[0])<fabs(n[1])){
|
|
if(fabs(n[0])<fabs(n[2])) up=Point3<P3ScalarType>(1,0,0); // x is the min
|
|
else up=Point3<P3ScalarType>(0,0,1); // z is the min
|
|
}else {
|
|
if(fabs(n[1])<fabs(n[2])) up=Point3<P3ScalarType>(0,1,0); // y is the min
|
|
else up=Point3<P3ScalarType>(0,0,1); // z is the min
|
|
}
|
|
u=n^up;
|
|
}
|
|
u.Normalize();
|
|
v=n^u;
|
|
v.Normalize();
|
|
}
|
|
|
|
|
|
template <class SCALARTYPE>
|
|
inline Point3<SCALARTYPE> Abs(const Point3<SCALARTYPE> & p) {
|
|
return (Point3<SCALARTYPE>(math::Abs(p[0]), math::Abs(p[1]), math::Abs(p[2])));
|
|
}
|
|
// probably a more uniform naming should be defined...
|
|
template <class SCALARTYPE>
|
|
inline Point3<SCALARTYPE> LowClampToZero(const Point3<SCALARTYPE> & p) {
|
|
return (Point3<SCALARTYPE>(std::max(p[0], (SCALARTYPE)0), std::max(p[1], (SCALARTYPE)0), std::max(p[2], (SCALARTYPE)0)));
|
|
}
|
|
|
|
typedef Point3<short> Point3s;
|
|
typedef Point3<int> Point3i;
|
|
typedef Point3<float> Point3f;
|
|
typedef Point3<double> Point3d;
|
|
|
|
/*@}*/
|
|
|
|
} // end namespace
|
|
|
|
#endif
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|
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