opennurbs_point.h

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/* $NoKeywords: $ */
/*
//
// Copyright (c) 1993-2007 Robert McNeel & Associates. All rights reserved.
// Rhinoceros is a registered trademark of Robert McNeel & Assoicates.
//
// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.
// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF
// MERCHANTABILITY ARE HEREBY DISCLAIMED.
//                              
// For complete openNURBS copyright information see <http://www.opennurbs.org>.
//
*/
 
//
//   defines double precision point, vector, and array classes
//
#if !defined(ON_POINT_INC_)
#define ON_POINT_INC_
 
class ON_BoundingBox;
class ON_Xform;
class ON_Line;
class ON_Plane;
 
class ON_2dPoint;
class ON_3dPoint;
class ON_4dPoint;
 
class ON_2dVector;
class ON_3dVector;
 
class ON_2fVector;
class ON_3fVector;
 
class ON_Interval;
 
//
//   ON_Interval
//
class ON_CLASS ON_Interval
{
public:
 
  static const ON_Interval EmptyInterval; // (ON_UNSET_VALUE,ON_UNSET_VALUE)
 
  // The default constructor creates an empty interval (ON_UNSET_VALUE,ON_UNSET_VALUE)
  ON_Interval();
 
  ON_Interval(double t0,double t1);
 
  ~ON_Interval();
 
  bool operator!=(const ON_Interval&) const;
  bool operator==(const ON_Interval&) const;
 
  // Interval = [m_t[0], m_t[1]]
  double m_t[2];
 
  /*
  Description:
    Sets interval to (ON_UNSET_VALUE,ON_UNSET_VALUE)
  See Also:
    ON_Interval::Set
  */
  void Destroy();
 
  /*
  Description:
    Sets interval to [t0,t1]
  Parameters:
    t0 - [in]
    t1 - [in]
  See Also:
    ON_Interval::ON_Interval( double, double )
  */
  void Set(
    double t0, 
    double t1
    );
 
  /*
  Description:
    Convert normalized parameter to interval value, or pair of values.
  Parameters:
    normalized_parameter - [in] 
  Returns:
    Interval parameter
    min*(1.0-normalized_parameter) + max*normalized_parameter
  See Also:
    ON_Interval::NormalizedParameterAt
  */
  double ParameterAt (
    double normalized_parameter
    ) const; 
  ON_Interval ParameterAt (
    ON_Interval normalized_interval
    ) const; 
  
  /*
  Description:
    Convert interval value, or pair of values, to normalized parameter.
  Parameters:
    interval_parameter - [in] value in interval
  Returns:
    Normalized parameter x so that 
    min*(1.0-x) + max*x = interval_parameter.
  See Also:
    ON_Interval::ParameterAt
  */
  double NormalizedParameterAt (
    double interval_parameter
    ) const;
  ON_Interval NormalizedParameterAt (
    ON_Interval interval_parameter
    ) const;
 
  double& operator[](int); // returns (index<=0) ? m_t[0] : m_t[1]
  double operator[](int) const; // returns (index<=0) ? m_t[0] : m_t[1]
 
  double Min() const; // returns smaller of m_t[0] and m_t[1]
  double Max() const; // returns larger of m_t[0] and m_t[1]
  double Mid() const; // returns 0.5*(m_t[0] + m_t[1])
  double Length() const;
 
  bool IsIncreasing() const; // returns true if m_t[0] < m_t[1]
  bool IsDecreasing() const; // returns true if m_t[0] > m_t[0];
  bool IsInterval() const;   // returns truc if m_t[0] != m_t[1]
  bool IsSingleton() const;  // returns true if m_t[0] == m_t[1] != ON_UNSET_VALUE
  bool IsEmptyInterval() const;   // returns true if m_t[0] == m_t[1] == ON_UNSET_VALUE
  bool IsValid() const;      // returns ON_IsValid(m_t[0]) && ON_IsValid(m_t[1])
 
  // OBSOLETE - Use IsEmptyInterval()
  bool IsEmptySet() const;   // returns true if m_t[0] == m_t[1] == ON_UNSET_VALUE
 
        bool MakeIncreasing();          // returns true if resulting interval IsIncreasing() 
 
  /*
  Returns:
    @untitled table
     0      this is idential to other
    -1      this[0] < other[0]
    +1      this[0] > other[0]
    -1      this[0] == other[0] and this[1] < other[1]
    +1      this[0] == other[0] and this[1] > other[1]
  */
  int Compare( const ON_Interval& other ) const;
 
  /* 
  Description:
    Test a value t to see if it is inside the interval.
  Parameters:
    t - [in] value to test
    bTestOpenInterval - [in] 
        If false, t is tested to see if it satisfies min <= t <= max.
        If true, t is tested to see if it satisfies min < t < max.
  Returns:
    true if t is in the interval and false if t is not
    in the interval.
  */
  bool Includes(
    double t,
    bool bTestOpenInterval = false
    ) const;
 
  /* 
  Description:
    Test an interval to see if it is contained in this interval.
  Parameters:
    other - [in] interval to test
    bProperSubSet - [in] if true, then the test is for a proper subinterval.
  Returns:
    If bProperSubSet is false, then the result is true when
    this->Min() <= other.Min() and other.Max() <= this->Max().
    If bProperSubSet is true, then the result is true when
    this->Min() <= other.Min() and other.Max() <= this->Max()
    and at least one of the inequalites is strict.
  */
  bool Includes( 
    const ON_Interval& other,
    bool bProperSubSet = false
    ) const;
 
  /*
  Description:
    Changes interval to [-m_t[1],-m_t[0]].
  */
  void Reverse();
 
  /*
  Description:
    Swaps m_t[0] and m_t[1].
  */
  void Swap();
 
  // If the intersection is not empty, then 
  // intersection = [max(this.Min(),arg.Min()), min(this.Max(),arg.Max())]
  // Intersection() returns true if the intersection is not empty.
  // The interval [ON_UNSET_VALUE,ON_UNSET_VALUE] is considered to be
  // the empty set interval.  The result of any intersection involving an
  // empty set interval or disjoint intervals is the empty set interval.
  bool Intersection( // this = this intersect arg
         const ON_Interval&
         );
 
  // If the intersection is not empty, then 
  // intersection = [max(argA.Min(),argB.Min()), min(argA.Max(),argB.Max())]
  // Intersection() returns true if the intersection is not empty.
  // The interval [ON_UNSET_VALUE,ON_UNSET_VALUE] is considered to be
  // the empty set interval.  The result of any intersection involving an
  // empty set interval or disjoint intervals is the empty set interval.
  bool Intersection( // this = intersection of two args
         const ON_Interval&, 
         const ON_Interval&
         );
 
  // The union of an empty set and an increasing interval is the increasing
  // interval.  The union of two empty sets is empty. The union of an empty
  // set an a non-empty interval is the non-empty interval.
  // The union of two non-empty intervals is
  // union = [min(this.Min(),arg.Min()), max(this.Max(),arg.Max()),]
  // Union() returns true if the union is not empty.
  bool Union( // this = this union arg
         const ON_Interval&
         );
 
  // The union of an empty set and an increasing interval is the increasing
  // interval.  The union of two empty sets is empty. The union of an empty
  // set an a non-empty interval is the non-empty interval.
  // The union of two non-empty intervals is
  // union = [min(argA.Min(),argB.Min()), max(argA.Max(),argB.Max()),]
  // Union() returns true if the union is not empty.
  bool Union( // this = union of two args
         const ON_Interval&, 
         const ON_Interval&
         );
};
 
//
//   ON_2dPoint
//
class ON_CLASS ON_2dPoint
{
public:
  double x, y;
 
  static const ON_2dPoint Origin;     // (0.0,0.0)
  static const ON_2dPoint UnsetPoint; // (ON_UNSET_VALUE,ON_UNSET_VALUE)
 
  // use implicit destructor, copy constructor
  ON_2dPoint();                         // x,y not initialized
  ON_2dPoint(double x,double y);
  ON_2dPoint(const ON_3dPoint& );       // from 3d point
  ON_2dPoint(const ON_4dPoint& );       // from 4d point
  ON_2dPoint(const ON_2dVector& );      // from 2d vector
  ON_2dPoint(const ON_3dVector& );      // from 3d vector
  ON_2dPoint(const double*);            // from double[2] array
 
  ON_2dPoint(const class ON_2fPoint&);  // from 2f point
  ON_2dPoint(const class ON_3fPoint&);  // from 3f point
  ON_2dPoint(const class ON_4fPoint&);  // from 4f point
  ON_2dPoint(const class ON_2fVector&); // from 2f point
  ON_2dPoint(const class ON_3fVector&); // from 3f point
  ON_2dPoint(const float*);             // from float[2] array
 
  // (double*) conversion operators
  operator double*();
  operator const double*() const;
 
  // use implicit operator=(const ON_2dPoint&)
  ON_2dPoint& operator=(const ON_3dPoint&);
  ON_2dPoint& operator=(const ON_4dPoint&);
  ON_2dPoint& operator=(const ON_2dVector&);
  ON_2dPoint& operator=(const ON_3dVector&);
  ON_2dPoint& operator=(const double*); // point = double[2] support
 
  ON_2dPoint& operator=(const ON_2fPoint&);
  ON_2dPoint& operator=(const ON_3fPoint&);
  ON_2dPoint& operator=(const ON_4fPoint&);
  ON_2dPoint& operator=(const ON_2fVector&);
  ON_2dPoint& operator=(const ON_3fVector&);
  ON_2dPoint& operator=(const float*);  // point = float[2] support
 
  ON_2dPoint& operator*=(double);
  ON_2dPoint& operator/=(double);
  ON_2dPoint& operator+=(const ON_2dPoint&);  // Adding this was a mistake - cannot remove without breaking SDK
  ON_2dPoint& operator+=(const ON_2dVector&);
  ON_2dPoint& operator+=(const ON_3dVector&); // Adding this was a mistake - cannot remove without breaking SDK
  ON_2dPoint& operator-=(const ON_2dPoint&);  // Adding this was a mistake - cannot remove without breaking SDK
  ON_2dPoint& operator-=(const ON_2dVector&);
  ON_2dPoint& operator-=(const ON_3dVector&); // Adding this was a mistake - cannot remove without breaking SDK
 
  ON_2dPoint  operator*(int) const;
  ON_2dPoint  operator/(int) const;
  ON_2dPoint  operator*(float) const;
  ON_2dPoint  operator/(float) const;
  ON_2dPoint  operator*(double) const;
  ON_2dPoint  operator/(double) const;
 
  ON_2dPoint  operator+(const ON_2dPoint&) const;
  ON_2dPoint  operator+(const ON_2dVector&) const;
  ON_2dVector operator-(const ON_2dPoint&) const;
  ON_2dPoint  operator-(const ON_2dVector&) const;
  ON_3dPoint  operator+(const ON_3dPoint&) const;
  ON_3dPoint  operator+(const ON_3dVector&) const;
  ON_3dVector operator-(const ON_3dPoint&) const;
  ON_3dPoint  operator-(const ON_3dVector&) const;
 
  ON_2dPoint  operator+(const ON_2fPoint&) const;
  ON_2dPoint  operator+(const ON_2fVector&) const;
  ON_2dVector operator-(const ON_2fPoint&) const;
  ON_2dPoint  operator-(const ON_2fVector&) const;
  ON_3dPoint  operator+(const ON_3fPoint&) const;
  ON_3dPoint  operator+(const ON_3fVector&) const;
  ON_3dVector operator-(const ON_3fPoint&) const;
  ON_3dPoint  operator-(const ON_3fVector&) const;
 
  double operator*(const ON_2dPoint&) const; // dot product for points acting as vectors
  double operator*(const ON_2dVector&) const; // dot product for points acting as vectors
  double operator*(const ON_4dPoint&) const;
  ON_2dPoint operator*(const ON_Xform&) const;
 
  bool operator==(const ON_2dPoint&) const;
  bool operator!=(const ON_2dPoint&) const;
 
  // dictionary order comparisons
  bool operator<=(const ON_2dPoint&) const;
  bool operator>=(const ON_2dPoint&) const;
  bool operator<(const ON_2dPoint&) const;
  bool operator>(const ON_2dPoint&) const;
 
  // index operators mimic double[2] behavior
  double& operator[](int);
  double operator[](int) const;
 
  /*
  Returns:
    False if any coordinate is infinte, a nan, or ON_UNSET_VALUE.
  */
  bool IsValid() const;
 
  /*
  Returns:
    True if every coordinate is ON_UNSET_VALUE.
  */
  bool IsUnsetPoint() const;
 
  // set 2d point value
  void Set(double x,double y);
 
  double DistanceTo( const ON_2dPoint& ) const;
 
  int MaximumCoordinateIndex() const;
  double MaximumCoordinate() const; // absolute value of maximum coordinate
 
  int MinimumCoordinateIndex() const;
  double MinimumCoordinate() const; // absolute value of minimum coordinate
 
  void Zero(); // set all coordinates to zero;
 
  // These transform the point in place. The transformation matrix acts on
  // the left of the point; i.e., result = transformation*point
  void Transform( 
        const ON_Xform&
        );
 
  void Rotate( // rotatation in XY plane
        double angle,              // angle in radians
        const ON_2dPoint& center   // center of rotation
        );
 
  void Rotate( // rotatation in XY plane
        double sin_angle,          // sin(angle)
        double cos_angle,          // cos(angle)
        const ON_2dPoint& center   // center of rotation
        );
};
 
ON_DECL
ON_2dPoint operator*(int, const ON_2dPoint&);
 
ON_DECL
ON_2dPoint operator*(float, const ON_2dPoint&);
 
ON_DECL
ON_2dPoint operator*(double, const ON_2dPoint&);
 
//
//   ON_3dPoint
//
class ON_CLASS ON_3dPoint
{
public:
  double x, y, z;
 
  static const ON_3dPoint Origin;     // (0.0,0.0,0.0)
  static const ON_3dPoint UnsetPoint; // (ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE)
 
  // use implicit destructor, copy constructor
  ON_3dPoint();                         // x,y,z not initialized
  ON_3dPoint(double x,double y,double z);
  ON_3dPoint(const ON_2dPoint& );       // from 2d point
  ON_3dPoint(const ON_4dPoint& );       // from 4d point
  ON_3dPoint(const ON_2dVector& );      // from 2d vector
  ON_3dPoint(const ON_3dVector& );      // from 3d vector
  ON_3dPoint(const double*);            // from double[3] array
 
  ON_3dPoint(const class ON_2fPoint&);  // from 2f point
  ON_3dPoint(const class ON_3fPoint&);  // from 3f point
  ON_3dPoint(const class ON_4fPoint&);  // from 4f point
  ON_3dPoint(const class ON_2fVector&); // from 2f point
  ON_3dPoint(const class ON_3fVector&); // from 3f point
  ON_3dPoint(const float*);             // from float[3] array
 
  // (double*) conversion operators
  operator double*();
  operator const double*() const;
 
  // use implicit operator=(const ON_3dPoint&)
  ON_3dPoint& operator=(const ON_2dPoint&);
  ON_3dPoint& operator=(const ON_4dPoint&);
  ON_3dPoint& operator=(const ON_2dVector&);
  ON_3dPoint& operator=(const ON_3dVector&);
  ON_3dPoint& operator=(const double*); // point = double[3] support
 
  ON_3dPoint& operator=(const class ON_2fPoint&);
  ON_3dPoint& operator=(const class ON_3fPoint&);
  ON_3dPoint& operator=(const class ON_4fPoint&);
  ON_3dPoint& operator=(const class ON_2fVector&);
  ON_3dPoint& operator=(const class ON_3fVector&);
  ON_3dPoint& operator=(const float*);  // point = float[3] support
 
  ON_3dPoint& operator*=(double);
  ON_3dPoint& operator/=(double);
  ON_3dPoint& operator+=(const ON_3dPoint&);  // Adding this was a mistake - cannot remove without breaking SDK
  ON_3dPoint& operator+=(const ON_3dVector&);
  ON_3dPoint& operator-=(const ON_3dPoint&);  // Adding this was a mistake - cannot remove without breaking SDK
  ON_3dPoint& operator-=(const ON_3dVector&);
 
  ON_3dPoint  operator*(int) const;
  ON_3dPoint  operator/(int) const;
  ON_3dPoint  operator*(float) const;
  ON_3dPoint  operator/(float) const;
  ON_3dPoint  operator*(double) const;
  ON_3dPoint  operator/(double) const;
 
  ON_3dPoint  operator+(const ON_3dPoint&) const;
  ON_3dPoint  operator+(const ON_3dVector&) const;
  ON_3dVector operator-(const ON_3dPoint&) const;
  ON_3dPoint  operator-(const ON_3dVector&) const;
  ON_3dPoint  operator+(const ON_2dPoint&) const;
  ON_3dPoint  operator+(const ON_2dVector&) const;
  ON_3dVector operator-(const ON_2dPoint&) const;
  ON_3dPoint  operator-(const ON_2dVector&) const;
 
  ON_3dPoint  operator+(const ON_3fPoint&) const;
  ON_3dPoint  operator+(const ON_3fVector&) const;
  ON_3dVector operator-(const ON_3fPoint&) const;
  ON_3dPoint  operator-(const ON_3fVector&) const;
  ON_3dPoint  operator+(const ON_2fPoint&) const;
  ON_3dPoint  operator+(const ON_2fVector&) const;
  ON_3dVector operator-(const ON_2fPoint&) const;
  ON_3dPoint  operator-(const ON_2fVector&) const;
 
  double operator*(const ON_3dPoint&) const; // dot product for points acting as vectors
  double operator*(const ON_3dVector&) const; // dot product for points acting as vectors
  double operator*(const ON_4dPoint&) const;
  ON_3dPoint operator*(const ON_Xform&) const;
 
  bool operator==(const ON_3dPoint&) const;
  bool operator!=(const ON_3dPoint&) const;
 
  // dictionary order comparisons
  bool operator<=(const ON_3dPoint&) const;
  bool operator>=(const ON_3dPoint&) const;
  bool operator<(const ON_3dPoint&) const;
  bool operator>(const ON_3dPoint&) const;
 
  // index operators mimic double[3] behavior
  double& operator[](int);
  double operator[](int) const;
 
  /*
  Returns:
    False if any coordinate is infinte, a nan, or ON_UNSET_VALUE.
  */
  bool IsValid() const;
 
  /*
  Returns:
    True if every coordinate is ON_UNSET_VALUE.
  */
  bool IsUnsetPoint() const;
 
  // set 3d point value
  void Set(double x,double y,double z);
 
  double DistanceTo( const ON_3dPoint& ) const;
 
  int MaximumCoordinateIndex() const;
  double MaximumCoordinate() const; // absolute value of maximum coordinate
  
  int MinimumCoordinateIndex() const;
  double MinimumCoordinate() const; // absolute value of minimum coordinate
 
  double Fuzz( double tolerance = ON_ZERO_TOLERANCE ) const; // tolerance to use when comparing 3d points
 
  void Zero(); // set all coordinates to zero;
 
  // These transform the point in place. The transformation matrix acts on
  // the left of the point; i.e., result = transformation*point
  void Transform( 
        const ON_Xform&
        );
 
  void Rotate( 
        double angle,             // angle in radians
        const ON_3dVector& axis,  // axis of rotation
        const ON_3dPoint& center  // center of rotation
        );
 
  void Rotate( 
        double sin_angle,         // sin(angle)
        double cos_angle,         // cos(angle)
        const ON_3dVector& axis,  // axis of rotation
        const ON_3dPoint& center  // center of rotation
        );
};
 
ON_DECL
ON_3dPoint operator*(int, const ON_3dPoint&);
 
ON_DECL
ON_3dPoint operator*(float, const ON_3dPoint&);
 
ON_DECL
ON_3dPoint operator*(double, const ON_3dPoint&);
 
//
//   ON_4dPoint (homogeneous coordinates)
//
class ON_CLASS ON_4dPoint
{
public:
  double x, y, z, w;
  
  // use implicit destructor, copy constructor
  ON_4dPoint();                       // x,y,z,w not initialized
  ON_4dPoint(double x,double y,double z,double w);
 
  ON_4dPoint(const ON_2dPoint& );     // from 2d point
  ON_4dPoint(const ON_3dPoint& );     // from 3d point
  ON_4dPoint(const ON_2dVector& );    // from 2d vector
  ON_4dPoint(const ON_3dVector& );    // from 3d vector
  ON_4dPoint(const double*);          // from double[4] array
 
  ON_4dPoint(const ON_2fPoint& );     // from 2f point
  ON_4dPoint(const ON_3fPoint& );     // from 3f point
  ON_4dPoint(const ON_4fPoint& );     // from 3f point
  ON_4dPoint(const ON_2fVector& );    // from 2f vector
  ON_4dPoint(const ON_3fVector& );    // from 3f vector
  ON_4dPoint(const float*);           // from float[4] array
 
  // (double*) conversion operators
  operator double*();
  operator const double*() const;
 
  // use implicit operator=(const ON_4dPoint&)
  ON_4dPoint& operator=(const ON_2dPoint&);
  ON_4dPoint& operator=(const ON_3dPoint&);
  ON_4dPoint& operator=(const ON_2dVector&);
  ON_4dPoint& operator=(const ON_3dVector&);
  ON_4dPoint& operator=(const double*); // point = double[4] support
 
  ON_4dPoint& operator=(const class ON_2fPoint&);
  ON_4dPoint& operator=(const class ON_3fPoint&);
  ON_4dPoint& operator=(const class ON_4fPoint&);
  ON_4dPoint& operator=(const class ON_2fVector&);
  ON_4dPoint& operator=(const class ON_3fVector&);
  ON_4dPoint& operator=(const float*);  // point = float[4] support
 
  ON_4dPoint& operator*=(double);
  ON_4dPoint& operator/=(double);
  ON_4dPoint& operator+=(const ON_4dPoint&); // sum w = sqrt(|w1*w2|)
  ON_4dPoint& operator-=(const ON_4dPoint&); // difference w = sqrt(|w1*w2|)
 
  ON_4dPoint  operator*(double) const;
  ON_4dPoint  operator/(double) const;
  ON_4dPoint  operator+(const ON_4dPoint&) const; // sum w = sqrt(|w1*w2|)
  ON_4dPoint  operator-(const ON_4dPoint&) const; // difference w = sqrt(|w1*w2|)
 
  double operator*(const ON_4dPoint&) const;
  ON_4dPoint operator*(const ON_Xform&) const;
 
  // projective comparison 
  // (i.e., [x,y,z,w] == [c*x,c*y,c*z,c*w] is true for nonzero c)
  bool operator==(ON_4dPoint) const;
  bool operator!=(const ON_4dPoint&) const;
 
  // index operators mimic double[4] behavior
  double& operator[](int);
  double operator[](int) const;
 
  /*
  Returns:
    False if any coordinate is infinte, a nan, or ON_UNSET_VALUE.
  */
  bool IsValid() const;
 
  /*
  Returns:
    True if every coordinate is ON_UNSET_VALUE.
  */
  bool IsUnsetPoint() const;
 
  // set 4d point value
  void Set(double x,double y,double z,double w);
 
  int MaximumCoordinateIndex() const;
  double MaximumCoordinate() const; // absolute value of maximum coordinate
 
  int MinimumCoordinateIndex() const;
  double MinimumCoordinate() const; // absolute value of minimum coordinate
 
  void Zero();      // set all 4 coordinates to zero;
  bool Normalize(); // set so x^2 + y^2 + z^2 + w^2 = 1
 
  // These transform the point in place. The transformation matrix acts on
  // the left of the point; i.e., result = transformation*point
  void Transform( 
        const ON_Xform&
        );
};
 
ON_DECL
ON_4dPoint operator*(double, const ON_4dPoint&);
 
//
//   ON_2dVector
//
class ON_CLASS ON_2dVector
{
public:
  double x, y;
 
  static const ON_2dVector ZeroVector;  // (0.0,0.0)
  static const ON_2dVector XAxis;       // (1.0,0.0)
  static const ON_2dVector YAxis;       // (0.0,1.0)
  static const ON_2dVector UnsetVector; // (ON_UNSET_VALUE,ON_UNSET_VALUE)
 
  // Description:
  //   A index driven function to get unit axis vectors.
  // Parameters:
  //   index - [in] 0 returns (1,0), 1 returns (0,1)
  // Returns:
  //   Unit 2d vector with vector[i] = (i==index)?1:0;
  static const ON_2dVector& UnitVector(
    int // index
    );
 
  // use implicit destructor, copy constructor
  ON_2dVector();                     // x,y not initialized
  ON_2dVector(double x,double y);
 
  ON_2dVector(const ON_3dVector& ); // from 3d vector
  ON_2dVector(const ON_2dPoint& );  // from 2d point
  ON_2dVector(const ON_3dPoint& );  // from 3d point
  ON_2dVector(const double*);       // from double[2] array
 
  ON_2dVector(const ON_2fVector& ); // from 2f vector
  ON_2dVector(const ON_3fVector& ); // from 3f vector
  ON_2dVector(const ON_2fPoint& );  // from 2f point
  ON_2dVector(const ON_3fPoint& );  // from 3f point
  ON_2dVector(const float*);        // from double[2] array
 
  // (double*) conversion operators
  operator double*();
  operator const double*() const;
 
  // use implicit operator=(const ON_2dVector&)
  ON_2dVector& operator=(const ON_3dVector&);
  ON_2dVector& operator=(const ON_2dPoint&);
  ON_2dVector& operator=(const ON_3dPoint&);
  ON_2dVector& operator=(const double*); // vector = double[2] support
 
  ON_2dVector& operator=(const ON_2fVector&);
  ON_2dVector& operator=(const ON_3fVector&);
  ON_2dVector& operator=(const ON_2fPoint&);
  ON_2dVector& operator=(const ON_3fPoint&);
  ON_2dVector& operator=(const float*);  // vector = float[2] support
 
  ON_2dVector  operator-() const;
 
  ON_2dVector& operator*=(double);
  ON_2dVector& operator/=(double);
  ON_2dVector& operator+=(const ON_2dVector&);
  ON_2dVector& operator-=(const ON_2dVector&);
  // DO NOT ADD ANY MORE overrides of += or -=
 
  double operator*(const ON_2dVector&) const; // inner (dot) product
  double operator*(const ON_2dPoint&) const; // inner (dot) product (point acting as vector)
  double operator*(const ON_2fVector&) const; // inner (dot) product    
 
  ON_2dVector  operator*(int) const;
  ON_2dVector  operator/(int) const;
  ON_2dVector  operator*(float) const;
  ON_2dVector  operator/(float) const;
  ON_2dVector  operator*(double) const;
  ON_2dVector  operator/(double) const;
 
  ON_2dVector  operator+(const ON_2dVector&) const;
  ON_2dPoint   operator+(const ON_2dPoint&) const;
  ON_2dVector  operator-(const ON_2dVector&) const;
  ON_2dPoint   operator-(const ON_2dPoint&) const;
  ON_3dVector  operator+(const ON_3dVector&) const;
  ON_3dPoint   operator+(const ON_3dPoint&) const;
  ON_3dVector  operator-(const ON_3dVector&) const;
  ON_3dPoint   operator-(const ON_3dPoint&) const;
 
  ON_2dVector  operator+(const ON_2fVector&) const;
  ON_2dPoint   operator+(const ON_2fPoint&) const;
  ON_2dVector  operator-(const ON_2fVector&) const;
  ON_2dPoint   operator-(const ON_2fPoint&) const;
  ON_3dVector  operator+(const ON_3fVector&) const;
  ON_3dPoint   operator+(const ON_3fPoint&) const;
  ON_3dVector  operator-(const ON_3fVector&) const;
  ON_3dPoint   operator-(const ON_3fPoint&) const;
 
  double operator*(const ON_4dPoint&) const;
  ON_2dVector operator*(const ON_Xform&) const;
 
  bool operator==(const ON_2dVector&) const;
  bool operator!=(const ON_2dVector&) const;
 
  // dictionary order comparisons
  bool operator<=(const ON_2dVector&) const;
  bool operator>=(const ON_2dVector&) const;
  bool operator<(const ON_2dVector&) const;
  bool operator>(const ON_2dVector&) const;
 
  // index operators mimic double[2] behavior
  double& operator[](int);
  double operator[](int) const;
 
  /*
  Returns:
    False if any coordinate is infinte, a nan, or ON_UNSET_VALUE.
  */
  bool IsValid() const;
 
  /*
  Returns:
    True if every coordinate is ON_UNSET_VALUE.
  */
  bool IsUnsetVector() const;
 
  // set 2d vector value
  void Set(double x,double y);
 
  int MaximumCoordinateIndex() const;
  double MaximumCoordinate() const; // absolute value of maximum coordinate
 
  int MinimumCoordinateIndex() const;
  double MinimumCoordinate() const; // absolute value of minimum coordinate
 
  double LengthSquared() const;
  double Length() const;
 
        // Signed area of the parallelagram.  The volume element.
        // returns x*B.y - y*B.x
        double WedgeProduct(const ON_2dVector& B) const;
 
  bool Decompose( // Computes a, b such that this vector = a*X + b*Y
         // Returns false if unable to solve for a,b.  This happens
         // when X,Y is not really a basis.
         //
         // If X,Y is known to be an orthonormal frame,
         // then a = V*X, b = V*Y will compute
         // the same result more quickly.
         const ON_2dVector&, // X
         const ON_2dVector&, // Y
         double*, // a
         double*  // b
         ) const;
 
  int IsParallelTo( 
        // returns  1: this and other vectors are parallel
        //         -1: this and other vectors are anti-parallel
        //          0: this and other vectors are not parallel
        //             or at least one of the vectors is zero
        const ON_2dVector& other,                           // other vector     
        double angle_tolerance = ON_DEFAULT_ANGLE_TOLERANCE // optional angle tolerance (radians)
        ) const;
 
  bool IsPerpendicularTo(
        // returns true:  this and other vectors are perpendicular
        //         false: this and other vectors are not perpendicular
        //                or at least one of the vectors is zero
        const ON_2dVector& other,                           // other vector     
        double angle_tolerance = ON_DEFAULT_ANGLE_TOLERANCE // optional angle tolerance (radians)
        ) const;
 
  void Zero(); // set all coordinates to zero;
  void Reverse(); // negate all coordinates
  bool Unitize();  // returns false if vector has zero length
 
  // Description:
  //   Test a vector to see if it is very short
  //
  // Parameters:
  //   tiny_tol - [in] (default = ON_ZERO_TOLERANCE) a nonzero
  //              value used as the coordinate zero tolerance.
  //
  // Returns:
  //   ( fabs(x) <= tiny_tol && fabs(y) <= tiny_tol )
  //
  bool IsTiny(
         double tiny_tol = ON_ZERO_TOLERANCE // tiny_tol
         ) const;
 
  // Returns:
  //   true if vector is the zero vector.
  bool IsZero() const;
 
  // Returns:
  //   true if vector is valid and has length 1.
  bool IsUnitVector() const;
 
  // set this vector to be perpendicular to another vector
  bool PerpendicularTo( // Result is not unitized. 
                        // returns false if input vector is zero
        const ON_2dVector& 
        );
 
  // set this vector to be perpendicular to a line defined by 2 points
  bool PerpendicularTo( 
        const ON_2dPoint&, 
        const ON_2dPoint& 
        );
 
  // These transform the vector in place. The transformation matrix acts on
  // the left of the vector; i.e., result = transformation*vector
  void Transform( 
        const ON_Xform& // can use ON_Xform here
        );
 
  void Rotate( 
        double angle            // angle in radians
        );
 
  void Rotate( 
        double sin_angle,       // sin(angle)
        double cos_angle        // cos(angle)
        );
};
 
ON_DECL
ON_2dVector operator*(int, const ON_2dVector&);
 
ON_DECL
ON_2dVector operator*(float, const ON_2dVector&);
 
ON_DECL
ON_2dVector operator*(double, const ON_2dVector&);
 
//
// ON_2dVector utilities
//
 
ON_DECL
double 
ON_DotProduct( 
    const ON_2dVector&, 
    const ON_2dVector& 
    );
 
ON_DECL
ON_3dVector 
ON_CrossProduct(
    const ON_2dVector&, 
    const ON_2dVector& 
    );
 
ON_DECL
double                   
ON_WedgeProduct(                // signed area of the parallelagram.  Volume element.
    const ON_2dVector& A, // returns A.x * B.y - A.y * B.x 
    const ON_2dVector& B 
    );
 
ON_DECL
bool 
ON_IsOrthogonalFrame( // true if X, Y are nonzero and mutually perpindicular
    const ON_2dVector&, // X
    const ON_2dVector&  // Y
    );
 
ON_DECL
bool 
ON_IsOrthonormalFrame( // true if X, Y are orthogonal and unit length
    const ON_2dVector&, // X
    const ON_2dVector&  // Y
    );
 
ON_DECL
bool 
ON_IsRightHandFrame( // true if X, Y are orthonormal and right handed
    const ON_2dVector&, // X
    const ON_2dVector&  // Y
    );
 
//
//   ON_3dVector
//
class ON_CLASS ON_3dVector
{
public:
  double x, y, z;
 
  static const ON_3dVector ZeroVector;  // (0.0,0.0,0.0)
  static const ON_3dVector XAxis;       // (1.0,0.0,0.0)
  static const ON_3dVector YAxis;       // (0.0,1.0,0.0)
  static const ON_3dVector ZAxis;       // (0.0,0.0,1.0)
  static const ON_3dVector UnsetVector; // (ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE)
 
  // Description:
  //   A index driven function to get unit axis vectors.
  // Parameters:
  //   index - [in] 0 returns (1,0,0), 1 returns (0,1,0), 
  //                2 returns (0,0,1)
  // Returns:
  //   Unit 3d vector with vector[i] = (i==index)?1:0;
  static const ON_3dVector& UnitVector(
    int // index
    );
 
  // use implicit destructor, copy constructor
  ON_3dVector();                     // x,y,z not initialized
  ON_3dVector(double x,double y,double z);
  ON_3dVector(const ON_2dVector& );  // from 2d vector
  ON_3dVector(const ON_2dPoint& );   // from 2d point
  ON_3dVector(const ON_3dPoint& );   // from 3d point
  ON_3dVector(const double*);        // from double[3] array
 
  ON_3dVector(const ON_2fVector& );  // from 2f vector
  ON_3dVector(const ON_3fVector& );  // from 3f vector
  ON_3dVector(const ON_2fPoint& );   // from 2f point
  ON_3dVector(const ON_3fPoint& );   // from 3f point
  ON_3dVector(const float*);         // from float[3] array
 
  // (double*) conversion operators
  operator double*();
  operator const double*() const;
 
  // use implicit operator=(const ON_3dVector&)
  ON_3dVector& operator=(const ON_2dVector&);
  ON_3dVector& operator=(const ON_2dPoint&);
  ON_3dVector& operator=(const ON_3dPoint&);
  ON_3dVector& operator=(const double*); // vector = double[3] support
  
  ON_3dVector& operator=(const ON_2fVector&);
  ON_3dVector& operator=(const ON_3fVector&);
  ON_3dVector& operator=(const ON_2fPoint&);
  ON_3dVector& operator=(const ON_3fPoint&);
  ON_3dVector& operator=(const float*);  // vector = float[3] support
 
  ON_3dVector  operator-() const;
 
  ON_3dVector& operator*=(double);
  ON_3dVector& operator/=(double);
  ON_3dVector& operator+=(const ON_3dVector&);
  ON_3dVector& operator-=(const ON_3dVector&);
  // DO NOT ADD ANY MORE overrides of += or -=
 
  double operator*(const ON_3dVector&) const; // inner (dot) product
  double operator*(const ON_3dPoint&) const; // inner (dot) product
  double operator*(const ON_3fVector&) const; // inner (dot) product
 
  ON_3dVector  operator*(int) const;
  ON_3dVector  operator/(int) const;
  ON_3dVector  operator*(float) const;
  ON_3dVector  operator/(float) const;
  ON_3dVector  operator*(double) const;
  ON_3dVector  operator/(double) const;
 
  ON_3dVector  operator+(const ON_3dVector&) const;
  ON_3dPoint   operator+(const ON_3dPoint&) const;
  ON_3dVector  operator-(const ON_3dVector&) const;
  ON_3dPoint   operator-(const ON_3dPoint&) const;
  ON_3dVector  operator+(const ON_2dVector&) const;
  ON_3dPoint   operator+(const ON_2dPoint&) const;
  ON_3dVector  operator-(const ON_2dVector&) const;
  ON_3dPoint   operator-(const ON_2dPoint&) const;
 
  ON_3dVector  operator+(const ON_3fVector&) const;
  ON_3dPoint   operator+(const ON_3fPoint&) const;
  ON_3dVector  operator-(const ON_3fVector&) const;
  ON_3dPoint   operator-(const ON_3fPoint&) const;
  ON_3dVector  operator+(const ON_2fVector&) const;
  ON_3dPoint   operator+(const ON_2fPoint&) const;
  ON_3dVector  operator-(const ON_2fVector&) const;
  ON_3dPoint   operator-(const ON_2fPoint&) const;
 
  double operator*(const ON_4dPoint&) const;
  ON_3dVector operator*(const ON_Xform&) const;
 
  bool operator==(const ON_3dVector&) const;
  bool operator!=(const ON_3dVector&) const;
 
  // dictionary order comparisons
  bool operator<=(const ON_3dVector&) const;
  bool operator>=(const ON_3dVector&) const;
  bool operator<(const ON_3dVector&) const;
  bool operator>(const ON_3dVector&) const;
 
  // index operators mimic double[3] behavior
  double& operator[](int);
  double operator[](int) const;
 
  /*
  Returns:
    False if any coordinate is infinte, a nan, or ON_UNSET_VALUE.
  */
  bool IsValid() const;
 
  /*
  Returns:
    True if every coordinate is ON_UNSET_VALUE.
  */
  bool IsUnsetVector() const;
 
  // set 3d vector value
  void Set(double x,double y,double z);
 
  int MaximumCoordinateIndex() const;
  double MaximumCoordinate() const; // absolute value of maximum coordinate
 
  int MinimumCoordinateIndex() const;
  double MinimumCoordinate() const; // absolute value of minimum coordinate
 
  double LengthSquared() const;
  double Length() const;
 
  bool Decompose( // Computes a, b, c such that this vector = a*X + b*Y + c*Z
         // Returns false if unable to solve for a,b,c.  This happens
         // when X,Y,Z is not really a basis.
         //
         // If X,Y,Z is known to be an orthonormal frame,
         // then a = V*X, b = V*Y, c = V*Z will compute
         // the same result more quickly.
         const ON_3dVector&, // X
         const ON_3dVector&, // Y
         const ON_3dVector&, // Z
         double*, // a
         double*, // b
         double*  // c
         ) const;
 
  int IsParallelTo( 
        // returns  1: this and other vectors are parallel
        //         -1: this and other vectors are anti-parallel
        //          0: this and other vectors are not parallel
        //             or at least one of the vectors is zero
        const ON_3dVector& other,                           // other vector     
        double angle_tolerance = ON_DEFAULT_ANGLE_TOLERANCE // optional angle tolerance (radians)
        ) const;
 
  bool IsPerpendicularTo(
        // returns true:  this and other vectors are perpendicular
        //         false: this and other vectors are not perpendicular
        //                or at least one of the vectors is zero
        const ON_3dVector& other,                           // other vector     
        double angle_tolerance = ON_DEFAULT_ANGLE_TOLERANCE // optional angle tolerance (radians)
        ) const;
 
  double Fuzz( double tolerance = ON_ZERO_TOLERANCE ) const; // tolerance to use when comparing 3d vectors
 
  void Zero(); // set all coordinates to zero;
  void Reverse(); // negate all coordinates
  bool Unitize();  // returns false if vector has zero length
  double LengthAndUnitize(); // unitizes and returns initial length
 
  // Description:
  //   Test a vector to see if it is very short
  //
  // Parameters:
  //   tiny_tol - [in] (default = ON_ZERO_TOLERANCE) a nonzero
  //              value used as the coordinate zero tolerance.
  //
  // Returns:
  //   ( fabs(x) <= tiny_tol && fabs(y) <= tiny_tol && fabs(z) <= tiny_tol )
  //
  bool IsTiny(
         double tiny_tol = ON_ZERO_TOLERANCE // tiny_tol
         ) const;
 
  // Returns:
  //   true if vector is the zero vector.
  bool IsZero() const;
 
  // Returns:
  //   true if vector is valid and has length 1.
  bool IsUnitVector() const;
 
  // set this vector to be perpendicular to another vector
  bool PerpendicularTo( // Result is not unitized. 
                        // returns false if input vector is zero
        const ON_3dVector& 
        );
 
  // set this vector to be perpendicular to a plane defined by 3 points
  bool PerpendicularTo(
               // about 3 times slower than
               //    ON_3dVector N = ON_CrossProduct(P1-P0,P2-P0); 
               //    N.Unitize();
               // returns false if points are coincident or colinear
         const ON_3dPoint&, const ON_3dPoint&, const ON_3dPoint& 
         );
 
  // These transform the vector in place. The transformation matrix acts on
  // the left of the vector; i.e., result = transformation*vector
  void Transform( 
        const ON_Xform& // can use ON_Xform here
        );
 
  void Rotate( 
        double angle,           // angle in radians
        const ON_3dVector& axis // axis of rotation
        );
 
  void Rotate( 
        double sin_angle,        // sin(angle)
        double cos_angle,        // cos(angle)
        const ON_3dVector& axis  // axis of rotation
        );
};
 
class ON_CLASS ON_3dRay
{
public:
  ON_3dRay();
  ~ON_3dRay();
 
  ON_3dPoint  m_P;
  ON_3dVector m_V;
};
 
/*
Description:
  Typically the vector portion is a unit vector and
  m_d = -(x*P.x + y*P.y + z*P.z) for a point P on the plane.
*/
class ON_CLASS ON_PlaneEquation : public ON_3dVector
{
public:
  // C++ defaults for construction, destruction, copys, and operator=
  // work fine.
 
  bool IsValid() const;
 
  /*
  Description:
    Sets (x,y,z) to a unitized N and then sets
    d = -(x*P.x + y*P.y + z*P.z).
  Parameters:
    P - [in] point on the plane
    N - [in] vector perpindicular to the plane
  Returns:
     true if input is valid.
  */
  bool Create( ON_3dPoint P, ON_3dVector N );
 
  /*
  Description:
    Evaluate the plane at a point.
  Parameters:
    P - [in]
  Returns:
    x*P.x + y*P.y + z*P.z + d;
  */
  double ValueAt(ON_3dPoint P) const;
  double ValueAt(ON_4dPoint P) const;
  double ValueAt(ON_3dVector P) const;
  double ValueAt(double x, double y, double z) const;
 
  /*
  Description:
    Transform the plane equation so that, if e0 is the initial
    equation, e1 is transformed equation and P is a point,
    then e0.ValueAt(P) = e1.ValueAt(xform*P).
  Parameters:
    xform - [in]
      Invertable transformation.
  Returns:
    True if the plane equation was successfully transformed.
    False if xform is not invertable or the equation is not
    valid.
  Remarks:
    This function has to invert xform.  If you have apply the
    same transformation to a bunch of planes, then it will be
    more efficient to calculate xform's inverse transpose
    and apply the resultingt transformation to the equation's
    coefficients as if they were 4d point coordinates.
  */
  bool Transform( const ON_Xform& xform );
 
  /*
  Description:
    Get point on plane that is closest to a given point.
  Parameters:
    point - [in]
  Returns:
    A 3d point on the plane that is closest to the input point.
  */
  ON_3dPoint ClosestPointTo( ON_3dPoint point ) const;
 
  /*
  Description:
    Get the minimum value of the plane equation
    on a bounding box.
  Parameters:
    bbox - [in] 
  Returns:
    Minimum value of the plane equation on the bounding box.
  */
  double MinimumValueAt(const ON_BoundingBox& bbox) const;
 
  /*
  Description:
    Get the maximum value of the plane equation
    on a bounding box.
  Parameters:
    bbox - [in] 
  Returns:
    Maximum value of the plane equation on the bounding box.
  */
  double MaximumValueAt(const ON_BoundingBox& bbox) const;
 
 
  /*
  Description:
    Get the minimum value of the plane equation
    on a bounding box.
  Parameters:
    crvleafbox - [in] 
  Returns:
    Minimum value of the plane equation on the curve leaf box.
  */
  double MinimumValueAt(const class ON_CurveLeafBox& crvleafbox) const;
 
  /*
  Description:
    Get the maximum value of the plane equation
    on a bounding box.
  Parameters:
    crvleafbox - [in] 
  Returns:
    Maximum value of the plane equation on the curve leaf box.
  */
  double MaximumValueAt(const class ON_CurveLeafBox& crvleafbox) const;
 
  /*
  Description:
    Get the minimum value of the plane equation
    on a bounding box.
  Parameters:
    bbox - [in] 
  Returns:
    Minimum value of the plane equation on the bounding box.
  */
  double MinimumValueAt(const class ON_SurfaceLeafBox& srfleafbox) const;
 
  /*
  Description:
    Get the maximum value of the plane equation
    on a bounding box.
  Parameters:
    bbox - [in] 
  Returns:
    Maximum value of the plane equation on the bounding box.
  */
  double MaximumValueAt(const class ON_SurfaceLeafBox& srfleafbox) const;
 
  /*
  Description:
    Get the maximum value of the plane equation on a set of 3d points.
  Parameters:
    bRational - [in]
      False if the points are euclidean (x,y,z)
      True if the points are homogenous rational (x,y,z,w)
      (x/w,y/w,z/w) is used to evaluate the value.
    point_count - [in]
    point_stride - [in]
      i-th point's x coordinate = points[i*point_stride]
    points - [in]
      coordinates of points
    stop_value - [in]
      If stop_value is valid and not ON_UNSET_VALUE, then the 
      evaulation stops if a value > stop_value is found. 
      If stop_value = ON_UNSET_VALUE, then stop_value is ignored.
  Returns:
    Maximum value of the plane equation on the point list.
    If the input is not valid, then ON_UNSET_VALUE is returned.
  */
  double MaximumValueAt(
    bool bRational,
    int point_count,
    int point_stride,
    const double* points,
    double stop_value
    ) const;
 
  /*
  Description:
    Get the minimum value of the plane equation on a set of 3d points.
  Parameters:
    bRational - [in]
      False if the points are euclidean (x,y,z)
      True if the points are homogenous rational (x,y,z,w)
      (x/w,y/w,z/w) is used to evaluate the value.
    point_count - [in]
    point_stride - [in]
      i-th point's x coordinate = points[i*point_stride]
    points - [in]
      coordinates of points
    stop_value - [in]
      If stop_value is valid and not ON_UNSET_VALUE, then the 
      evaulation stops if a value < stop_value is found. 
      If stop_value = ON_UNSET_VALUE, then stop_value is ignored.
  Returns:
    Maximum value of the plane equation on the point list.
    If the input is not valid, then ON_UNSET_VALUE is returned.
  */
  double MinimumValueAt(
    bool bRational,
    int point_count,
    int point_stride,
    const double* points,
    double stop_value
    ) const;
 
  /*
  Description:
    Get the maximum absolute value of the plane equation 
    on a set of 3d points.
  Parameters:
    bRational - [in]
      False if the points are euclidean (x,y,z)
      True if the points are homogenous rational (x,y,z,w)
      (x/w,y/w,z/w) is used to evaluate the value.
    point_count - [in]
    point_stride - [in]
      i-th point's x coordinate = points[i*point_stride]
    points - [in]
      coordinates of points
    stop_value - [in]
      If stop_value >= 0.0, then the evaulation stops if an
      absolute value > stop_value is found. If stop_value < 0.0 
      or stop_value is invalid, then stop_value is ignored.
  Returns:
    Maximum value of the plane equation on the point list.
    If the input is not valid, then ON_UNSET_VALUE is returned.
  */
  double MaximumAbsoluteValueAt(
    bool bRational,
    int point_count,
    int point_stride,
    const double* points,
    double stop_value
    ) const;
 
  /*
  Description:
    Test points on a bezier curve to see if they are near the plane.
  Parameters:
    bezcrv - [in]
    s0 - [in]
    s1 - [in] the interval from s0 to s1 is tested (s0 < s1)
    sample_count - [in] number of interior points to test.  
                Numbers like 1, 3, 7, 15, ... work best.
    endpoint_tolerance - [in] If >= 0, then the end points are 
              tested to see if the distance from the endpoints 
              is <= endpoint_tolerance.
    interior_tolerance - [in] (>=0 and >=endpoint_tolerance) 
              This tolerance is used to test the interior sample points.
    smin - [put]  If not NULL, *smin = bezier parameter of nearest
                  test point.
    smax - [put]  If not NULL, *smax = bezier parameter of farthest
                  test point.  If false is returned, this is the
                  parameter of the test point that failed.
  Returns:
    True if all the tested points passed the tolerance test.
    False if at least one tested point failed the tolerance test.
    (The test terminates when the first failure is encountered.)
  */
  bool IsNearerThan( 
          const class ON_BezierCurve& bezcrv,
          double s0,
          double s1,
          int sample_count,
          double endpoint_tolerance,
          double interior_tolerance,
          double* smin,
          double* smax
          ) const;
 
  double d; // 4th coefficient of the plane equation.
};
 
ON_DECL
ON_3dVector operator*(int, const ON_3dVector&);
 
ON_DECL
ON_3dVector operator*(float, const ON_3dVector&);
 
ON_DECL
ON_3dVector operator*(double, const ON_3dVector&);
 
//
// ON_3dVector utilities
//
 
ON_DECL
double 
ON_DotProduct( 
    const ON_3dVector&, 
    const ON_3dVector& 
    );
 
 
ON_DECL
ON_3dVector 
ON_CrossProduct(
    const ON_3dVector&, 
    const ON_3dVector& 
    );
 
ON_DECL
ON_3dVector 
ON_CrossProduct( // 3d cross product for old fashioned arrays
    const double*, // array of 3d doubles
    const double*  // array of 3d doubles
    );
 
ON_DECL
double 
ON_TripleProduct( 
    const ON_3dVector&,
    const ON_3dVector&,
    const ON_3dVector&
    );
 
ON_DECL
double 
ON_TripleProduct(  // 3d triple product for old fashioned arrays
    const double*, // array of 3d doubles
    const double*, // array of 3d doubles
    const double*  // array of 3d doubles
    );
 
ON_DECL
bool 
ON_IsOrthogonalFrame( // true if X, Y, Z are nonzero and mutually perpindicular
    const ON_3dVector&, // X
    const ON_3dVector&, // Y
    const ON_3dVector&  // Z 
    );
 
ON_DECL
bool 
ON_IsOrthonormalFrame( // true if X, Y, Z are orthogonal and unit length
    const ON_3dVector&, // X
    const ON_3dVector&, // Y
    const ON_3dVector&  // Z 
    );
 
ON_DECL
bool 
ON_IsRightHandFrame( // true if X, Y, Z are orthonormal and right handed
    const ON_3dVector&, // X
    const ON_3dVector&, // Y
    const ON_3dVector&  // Z 
    );
 
//
// common points and vectors
//
// ON_unset_point is obsolete - use ON_3dPoint::UnsetPoint
#define ON_unset_point ON_UNSET_POINT
 
// ON_UNSET_POINT is OBSOLETE - use ON_3dPoint::UnsetPoint
extern ON_EXTERN_DECL const ON_3dPoint  ON_UNSET_POINT; // (ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE)
 
// ON_UNSET_VECTOR is OBSOLETE - use ON_3dPoint::UnsetVector
extern ON_EXTERN_DECL const ON_3dVector ON_UNSET_VECTOR; // (ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE)
 
// ON_origin is OBSOLETE - use ON_3dPoint::Origin
extern ON_EXTERN_DECL const ON_3dPoint  ON_origin; // (0.0, 0.0, 0.0)
 
// ON_xaxis is OBSOLETE - use ON_3dPoint::XAxis
extern ON_EXTERN_DECL const ON_3dVector ON_xaxis; // (1.0, 0.0, 0.0)
 
// ON_yaxis is OBSOLETE - use ON_3dPoint::YAxis
extern ON_EXTERN_DECL const ON_3dVector ON_yaxis; // (0.0, 1.0, 0.0)
 
// ON_zaxis is OBSOLETE - use ON_3dPoint::ZAxis
extern ON_EXTERN_DECL const ON_3dVector ON_zaxis; // (0.0, 0.0, 1.0)
 
#include "opennurbs_fpoint.h"
 
//
//   ON_SurfaceCurvature
//
class ON_CLASS ON_SurfaceCurvature
{
public:
  double k1, k2; // principal curvatures
 
  double GaussianCurvature() const;
  double MeanCurvature() const;
  double MinimumRadius() const;
  double MaximumRadius() const;
};
 
#endif