point.h

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//
// Copyright (C) 2003-2006 Rational Discovery LLC
//
//   @@ All Rights Reserved  @@
//


#ifndef __RD_POINT_H__
#define __RD_POINT_H__
#include <iostream>
#include <cmath>
#include <vector>
#include <map>

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif


#include <RDGeneral/Invariant.h>
#include <Numerics/Vector.h>
#include <boost/smart_ptr.hpp>

namespace RDGeom {
  class Point3D;
  class Point2D;
  class Point;
  class PointND;
}


std::ostream & operator<<(std::ostream& target, const RDGeom::Point &pt);

RDGeom::Point3D operator+ (const RDGeom::Point3D& p1, const RDGeom::Point3D& p2);
RDGeom::Point3D operator- (const RDGeom::Point3D& p1, const RDGeom::Point3D& p2);
RDGeom::Point3D operator* (const RDGeom::Point3D& p1, const double v);
RDGeom::Point3D operator/ (const RDGeom::Point3D& p1, const double v);

RDGeom::Point2D operator+ (const RDGeom::Point2D& p1, const RDGeom::Point2D& p2);
RDGeom::Point2D operator- (const RDGeom::Point2D& p1, const RDGeom::Point2D& p2);
RDGeom::Point2D operator* (const RDGeom::Point2D& p1, const double v);
RDGeom::Point2D operator/ (const RDGeom::Point2D& p1, const double v);

RDGeom::PointND operator+ (const RDGeom::PointND& p1, const RDGeom::PointND& p2);
RDGeom::PointND operator- (const RDGeom::PointND& p1, const RDGeom::PointND& p2);
RDGeom::PointND operator* (const RDGeom::PointND& p1, const double v);
RDGeom::PointND operator/ (const RDGeom::PointND& p1, const double v);


namespace RDGeom {

  class Point {
    // this is the virtual base class, mandating certain functions
  public:
    virtual ~Point() {};
    
    virtual double operator[](unsigned int i) const = 0;
    virtual double& operator[](unsigned int i) = 0;

    virtual void normalize() = 0;
    virtual double length() const = 0;
    virtual double lengthSq() const = 0;
    virtual unsigned int dimension() const = 0;
  };
   
  //typedef class Point3D Point;
  class Point3D : public Point {

  public:
    double x,
      y,
      z;

    Point3D() : x(0.0), y(0.0), z(0.0) {};
    Point3D(double xv,double yv,double zv): x(xv),y(yv),z(zv) {};

    ~Point3D() {};

    Point3D(const Point3D &other) :
      x(other.x), y(other.y), z(other.z) {
    }

    inline unsigned int dimension() const {return 3;}

    inline double operator[](unsigned int i) const {
      PRECONDITION(i < 3, "Invalid index on Point3D");
      if (i == 0) {
        return x;
      } else if (i == 1) {
        return y;
      } else {
        return z;
      }
    }
        
    inline double& operator[](unsigned int i) {
      PRECONDITION(i < 3, "Invalid index on Point3D");
      if (i == 0) {
        return x;
      } else if (i == 1) {
        return y;
      } else {
        return z;
      }
    }

    Point3D&
      operator=(const Point3D &other)
    {
      x = other.x;y=other.y;z=other.z;
      return *this;
    };

    Point3D& operator+=(const Point3D &other) {
      x += other.x;
      y += other.y;
      z += other.z;
      return *this;
    };
 
    Point3D& operator-=(const Point3D &other) {
      x -= other.x;
      y -= other.y;
      z -= other.z;
      return *this;
    };
    
    Point3D& operator*=(double scale) {
      x *= scale;
      y *= scale;
      z *= scale;
      return *this;
    };  

    Point3D& operator/=(double scale) {
      x /= scale;
      y /= scale;
      z /= scale;
      return *this;
    };  

    Point3D operator-() const {
      Point3D res(x, y, z);
      res.x *= -1.0;
      res.y *= -1.0;
      res.z *= -1.0;
      return res;
    }

    void normalize() {
      double l = this->length();
      x /= l;
      y /= l;
      z /= l;
    };

    double length() const {
      double res = x*x+y*y+z*z;
      return sqrt(res);
    };

    double lengthSq() const {
      double res = pow(x,2) + pow(y,2) + pow(z,2);
      return res;
    };

    double dotProduct(const Point3D &other) const {
      double res = x*(other.x) + y*(other.y) + z*(other.z);
      return res;
    };

    /*! \brief determines the angle between a vector to this point
     *   from the origin and a vector to the other point.
     * 
     *  The angle is unsigned: the results of this call will always
     *   be between 0 and M_PI
     */
    double angleTo(const Point3D &other) const {
      Point3D t1,t2;
      t1 = *this;
      t2 = other;
      t1.normalize();
      t2.normalize();
      double dotProd = t1.dotProduct(t2);
      // watch for roundoff error:
      if(dotProd<-1.0) dotProd = -1.0;
      else if(dotProd>1.0) dotProd = 1.0;
      return acos(dotProd);
    }

    /*! \brief determines the signed angle between a vector to this point
     *   from the origin and a vector to the other point.
     * 
     *  The results of this call will be between 0 and M_2_PI
     */
    double signedAngleTo(const Point3D &other) const {
      double res=this->angleTo(other);
      // check the sign of the z component of the cross product:
      if((this->x*other.y-this->y*other.x)<-1e-6) res = 2.0*M_PI-res;
      return res;
    }

    /*! \brief Returns a normalized direction vector from this
     *   point to another.
     * 
     */
    Point3D directionVector(const Point3D &other) const {
      Point3D res;
      res.x = other.x - x;
      res.y = other.y - y;
      res.z = other.z - z;
      res.normalize();
      return res;
        
    }

    
    /*! \brief Cross product of this point with the another point
     * 
     * The order is important here
     *  The result is "this" cross with "other" not (other x this)
     */
    Point3D crossProduct(const Point3D &other) const {
      Point3D res;
      res.x = y*(other.z) - z*(other.y);
      res.y = -x*(other.z) + z*(other.x);
      res.z = x*(other.y) - y*(other.x);
      return res;
    };

    /*! \brief Get a unit perpendicular from this point (treating it as a vector):
     *
     */
    Point3D getPerpendicular() const {
      Point3D res(0.0,0.0,0.0);
      if(x){
        if(y){
          res.y = -1*x;
          res.x = y;
        } else if(z) {
          res.z = -1*x;
          res.x = z;
        } else {
          res.y = 1;
        }
      } else if(y){
        if(z){
          res.z = -1*y;
          res.y = z;
        } else {
          res.x = 1;
        }
      } else if(z){
        res.x = 1;
      }
      double l=res.length();
      POSTCONDITION(l>0.0,"zero perpendicular");
      res = res/l;
      return res;
    }
  };
  
  // given a  set of four pts in 3D compute the dihedral angle between the
  // plane of the first three points (pt1, pt2, pt3) and the plane of the 
  // last three points (pt2, pt3, pt4)
  // the computed angle is between 0 and PI
  double computeDihedralAngle(Point3D pt1, Point3D pt2, Point3D pt3, Point3D pt4);

  class Point2D : public Point {
  public:
    double x,
      y;

    Point2D() : x(0.0), y(0.0) {};
    Point2D(double xv,double yv): x(xv),y(yv) {};
    
    ~Point2D() {}; 

    Point2D(const Point2D &other) : x(other.x), y(other.y) {
    }

    inline unsigned int dimension() const {return 2;}

    inline double operator[](unsigned int i) const {
      PRECONDITION(i < 2, "Invalid index on Point2D");
      if (i == 0) {
        return x;
      } else { 
        return y;
      } 
    }

    inline double& operator[](unsigned int i) {
      PRECONDITION(i < 2, "Invalid index on Point2D");
      if (i == 0) {
        return x;
      } else { 
        return y;
      } 
    }

    Point2D&
      operator=(const Point2D &other)
    {
      x = other.x;y=other.y;
      return *this;
    };

    Point2D& operator+=(const Point2D &other) {
      x += other.x;
      y += other.y;
      return *this;
    };

    Point2D& operator-=(const Point2D &other) {
      x -= other.x;
      y -= other.y;
      return *this;
    };
    
    Point2D& operator*=(double scale){
      x *= scale;
      y *= scale;
      return *this;
    };

    Point2D& operator/=(double scale){
      x /= scale;
      y /= scale;
      return *this;
    };

    Point2D operator-() const {
      Point2D res(x, y);
      res.x *= -1.0;
      res.y *= -1.0;
      return res;
    }
      
    void normalize() {
      double ln = this->length();
      x /= ln;
      y /= ln;
    };

    void rotate90() {
      double temp = x;
      x = -y;
      y = temp;
    }

    double length() const {
      double res = pow(x,2) + pow(y,2);
      return sqrt(res);
    };

    double lengthSq() const {
      double res = x*x+y*y;
      return res;
    };

    double dotProduct(const Point2D &other) const {
      double res = x*(other.x) + y*(other.y);
      return res;
    };

    double angleTo(const Point2D &other) const {
      Point2D t1,t2;
      t1 = *this;
      t2 = other;
      t1.normalize();
      t2.normalize();
      double dotProd = t1.dotProduct(t2);
      // watch for roundoff error:
      if(dotProd<-1.0) dotProd = -1.0;
      else if(dotProd>1.0) dotProd = 1.0;
      return acos(dotProd);
    }

    double signedAngleTo(const Point2D &other) const {
      double res=this->angleTo(other);
      if((this->x*other.y-this->y*other.x)<-1e-6) res = 2.0*M_PI-res;
      return res;
    }

    Point2D directionVector(const Point2D &other) const {
      Point2D res;
      res.x = other.x - x;
      res.y = other.y - y;
      res.normalize();
      return res;
        
    }
    
  };
  
  class PointND : public Point {
  public:

    typedef boost::shared_ptr<RDNumeric::Vector<double> > VECT_SH_PTR;

    PointND(unsigned int dim){
      RDNumeric::Vector<double> *nvec = new RDNumeric::Vector<double>(dim, 0.0);
      dp_storage.reset(nvec);
    };

    PointND(const PointND &other) {
      RDNumeric::Vector<double> *nvec = new RDNumeric::Vector<double>(*other.getStorage());
      dp_storage.reset(nvec);
    }

#if 0
        template <typename T>
    PointND(const T &vals){
      RDNumeric::Vector<double> *nvec = new RDNumeric::Vector<double>(vals.size(), 0.0);
      dp_storage.reset(nvec);
      unsigned int idx=0;
      typename T::const_iterator it;
      for(it=vals.begin();
          it!=vals.end();
          ++it){
        nvec->setVal(idx,*it);
        ++idx;
      };
    };
#endif

    ~PointND() {}

    inline double operator[](unsigned int i) const {
      return dp_storage.get()->getVal(i);
    }

    inline double& operator[](unsigned int i) {
      return (*dp_storage.get())[i];
    }

    inline void normalize() {
      dp_storage.get()->normalize();
    }

    inline double length() const {
      return dp_storage.get()->normL2();
    }

    inline double lengthSq() const {
      return dp_storage.get()->normL2Sq();
    }
    
    unsigned int dimension() const {
      return dp_storage.get()->size();
    }
    
    PointND& operator=(const PointND &other) {
      RDNumeric::Vector<double> *nvec = new RDNumeric::Vector<double>(*other.getStorage());
      dp_storage.reset(nvec);
      return *this;
    }

    PointND& operator+=(const PointND &other) {
      (*dp_storage.get()) += (*other.getStorage());
      return *this;
    }
    
    PointND& operator-=(const PointND &other) {
      (*dp_storage.get()) -= (*other.getStorage());
      return *this;
    }

    PointND& operator*=(double scale) {
      (*dp_storage.get()) *= scale;
      return *this;
    }

    PointND& operator/=(double scale) {
      (*dp_storage.get()) /= scale;
      return *this;
    }
    
    PointND directionVector(const PointND &other) {
      PRECONDITION(this->dimension() == other.dimension(), "Point dimensions do not match");
      PointND np(other);
      np -= (*this);
      np.normalize();
      return np;
    }

    double dotProduct(const PointND &other) const {
      return dp_storage.get()->dotProduct(*other.getStorage());
    }
    
    double angleTo(const PointND &other) const {
      double dp = this->dotProduct(other);
      double n1 = this->length();
      double n2 = other.length();
      if ((n1 > 1.e-8) && (n2 > 1.e-8)) {
        dp /= (n1*n2);
      }
      if (dp < -1.0) dp = -1.0;
      else if (dp > 1.0) dp = 1.0;
      return acos(dp);
    }

  private:
    VECT_SH_PTR dp_storage;
    inline const RDNumeric::Vector<double> * getStorage() const {
      return dp_storage.get();
    }
  };

  typedef std::vector<RDGeom::Point *> PointPtrVect;
  typedef PointPtrVect::iterator PointPtrVect_I;
  typedef PointPtrVect::const_iterator PointPtrVect_CI;

  typedef std::vector<RDGeom::Point3D *> Point3DPtrVect;
  typedef std::vector<RDGeom::Point2D *> Point2DPtrVect;
  typedef Point3DPtrVect::iterator Point3DPtrVect_I;
  typedef Point3DPtrVect::const_iterator Point3DPtrVect_CI;
  typedef Point2DPtrVect::iterator Point2DPtrVect_I;
  typedef Point2DPtrVect::const_iterator Point2DPtrVect_CI;

  typedef std::vector<const RDGeom::Point3D *> Point3DConstPtrVect;
  typedef Point3DConstPtrVect::iterator Point3DConstPtrVect_I;
  typedef Point3DConstPtrVect::const_iterator Point3DConstPtrVect_CI;

  typedef std::vector<Point3D>                 POINT3D_VECT;
  typedef std::vector<Point3D>::iterator       POINT3D_VECT_I;
  typedef std::vector<Point3D>::const_iterator POINT3D_VECT_CI;

  typedef std::map<int, Point2D> INT_POINT2D_MAP;
  typedef INT_POINT2D_MAP::iterator INT_POINT2D_MAP_I;
  typedef INT_POINT2D_MAP::const_iterator INT_POINT2D_MAP_CI;
}




#endif

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