point.h

很多二维 三维几何计算算法 C++ 类库

/* Copyright 2004
Stanford University

This file is part of the DSR PDB Library.

The DSR PDB Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The DSR PDB Library 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the DSR PDB Library; see the file LICENSE.LGPL.  If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */

#ifndef CGAL_DSR_PDB_POINT_H
#define CGAL_DSR_PDB_POINT_H
#include <CGAL/PDB/basic.h>
#include <iostream>

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/squared_distance_3.h>

CGAL_PDB_BEGIN_NAMESPACE
  // An alternative point class.
  typedef CGAL::Exact_predicates_inexact_constructions_kernel::Point_3 Point;
  typedef CGAL::Exact_predicates_inexact_constructions_kernel::Vector_3 Vector;

  struct Squared_distance{
    double operator()(const Point &a, const Point &b) const {
      return CGAL::squared_distance(a,b);
    }
  };

  //! Functor to compute the squared norm of a Vector
  struct Squared_norm{
    double operator()(const Vector &v) const {
      return v.x()*v.x()+v.y()*v.y()+ v.z()*v.z();
    }
  };

  //! Functor to compute the cross product of two vectors
  struct Cross_product{
    Vector operator()(const Vector &a, const Vector &b) const {
      double x = a.y() * b.z() - b.y() * a.z();
      double y = a.z() * b.x() - b.z() * a.x();
      double z = a.x() * b.y() - b.x() * a.y();

      return Vector(x,y,z);
    }
  };

  /*!
    This class represents a point in spherical coordinates. 
  */
  struct Spherical_point{
    //! Construct a spherical point from coordinates.
    Spherical_point(double r, double theta, double phi) {
      phi_=phi;
      theta_=theta;
      r_=r;
    }

    //! Construct a point from a vector.
    Spherical_point(const Vector &v) {
      double xy2=v.x()*v.x()+v.y()*v.y();
      double sd= std::sqrt(xy2+v.z()*v.z());
      r_=sd;
      theta_= std::atan2(v.y(), v.x());
      double xy=std::sqrt(xy2);
      phi_= std::atan2(v.z(), xy);
    }

    Spherical_point(){}

    //! The r component.
    double r() const {
      return r_;
    }


    //! The polar angle.
    double phi() const {
      return phi_;
    }

    //! The azimuthal angle in the x-y plane.
    double theta() const {
      return theta_;
    }

  private:
    double phi_, theta_, r_;

  };


  //! Construct a spherical point with a certain axis.
  /*!  \note This class is poorly designed having two completely
    separate usages just sharing internal code.
  */
  struct Construct_spherical_point{
    Construct_spherical_point(const Vector &xaxis,
			      const Vector &zaxis){
      make_axis(xaxis, zaxis);
      base_=Point(0,0,0);
    }
        
    Construct_spherical_point(const Point &p,
			      const Point &pop,
			      const Point &popop){
      base_=p;
      make_axis(p-pop, popop-pop);
    }
    
    //! Construct the spherical coordinates of a vector.
    Spherical_point operator()(const Vector &v) const {
      double vz= v*z_;
      double vx= v*x_;
      double vy= v*y_;
      return Spherical_point(vx, vy, vz);
    };

    //! Construct the spherical coordinates of a point relative to the base passed in the constructor.
    Spherical_point operator()(const Point &p) const {
      return operator()(p-base_);
    }

  private:
    void make_axis(const Vector &xaxis,
		   const Vector &zaxis){
      Squared_norm sn;
      z_= zaxis/sn(zaxis);
      Vector xmz= xaxis- (xaxis*z_)*z_;
      x_= xmz/sn(xmz);
      Cross_product cp;
      y_= cp(z_, x_);
    }

    Vector z_;
    Vector x_;
    Vector y_;
    Point base_;
  };
  
CGAL_PDB_END_NAMESPACE
#endif