geometry.cpp

This is an usefull library for Geometry in Mathmatics

/*! This method determines whether the current VecPosition is behind a
    given VecPosition, i.e. whether the x-coordinate of the current
    VecPosition is smaller than the x-coordinate of the given
    VecPosition.

    \param p a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is behind the given
    VecPosition; false otherwise */
bool VecPosition::isBehindOf( const VecPosition &p )
{
  return ( ( m_x < p.getX( ) ) ? true : false );
}

/*! This method determines whether the x-coordinate of the current
    VecPosition is behind (i.e. smaller than) a given double value.

    \param d a double value to which the current x-coordinate must be
    compared

    \return true when the current x-coordinate is behind the given
    value; false otherwise */
bool VecPosition::isBehindOf( const double &d )
{
  return ( ( m_x < d ) ? true : false );
}

/*! This method determines whether the current VecPosition is to the
    left of a given VecPosition, i.e. whether the y-coordinate of the
    current VecPosition is smaller than the y-coordinate of the given
    VecPosition.

    \param p a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is to the left of the
    given VecPosition; false otherwise */
bool VecPosition::isLeftOf( const VecPosition &p )
{
  return ( ( m_y < p.getY( ) ) ? true : false );
}

/*! This method determines whether the y-coordinate of the current
    VecPosition is to the left of (i.e. smaller than) a given double
    value.

    \param d a double value to which the current y-coordinate must be
    compared

    \return true when the current y-coordinate is to the left of the
    given value; false otherwise */
bool VecPosition::isLeftOf( const double &d )
{
  return ( ( m_y < d ) ? true : false );
}

/*! This method determines whether the current VecPosition is to the
    right of a given VecPosition, i.e. whether the y-coordinate of the
    current VecPosition is larger than the y-coordinate of the given
    VecPosition.

    \param p a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is to the right of the
    given VecPosition; false otherwise */
bool VecPosition::isRightOf( const VecPosition &p )
{
  return ( ( m_y > p.getY( ) ) ? true : false );
}

/*! This method determines whether the y-coordinate of the current
    VecPosition is to the right of (i.e. larger than) a given double
    value.

    \param d a double value to which the current y-coordinate must be
    compared

    \return true when the current y-coordinate is to the right of the
    given value; false otherwise */
bool VecPosition::isRightOf( const double &d )
{
  return ( ( m_y > d ) ? true : false );
}

/*! This method determines whether the current VecPosition is to the
    up of a given VecPosition, i.e. whether the z-coordinate of the
    current VecPosition is larger than the z-coordinate of the given
    VecPosition.

    \param p a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is to the up of the
    given VecPosition; false otherwise */
bool VecPosition::isUpOf( const VecPosition &p )
{
  return ( ( m_z > p.getZ( ) ) ? true : false );
}

/*! This method determines whether the z-coordinate of the current
    VecPosition is to the up of (i.e. larger than) a given double
    value.

    \param d a double value to which the current z-coordinate must be
    compared

    \return true when the current z-coordinate is to the right of the
    given value; false otherwise */
bool VecPosition::isUpOf( const double &d )
{
  return ( ( m_z > d ) ? true : false );
}

/*! This method determines whether the current VecPosition is to the
    down of a given VecPosition, i.e. whether the z-coordinate of the
    current VecPosition is less than the z-coordinate of the given
    VecPosition.

    \param p a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is to the down of the
    given VecPosition; false otherwise */
bool VecPosition::isDownOf( const VecPosition &p )
{
  return ( ( m_z < p.getZ( ) ) ? true : false );
}

/*! This method determines whether the z-coordinate of the current
    VecPosition is to the down of (i.e. less than) a given double
    value.

    \param d a double value to which the current z-coordinate must be
    compared

    \return true when the current z-coordinate is to the right of the
    given value; false otherwise */
bool VecPosition::isDownOf( const double &d )
{
  return ( ( m_z < d ) ? true : false );
}

/*! This method determines whether the current VecPosition is in
    between two given VecPositions when looking in the x-direction,
    i.e. whether the current VecPosition is in front of the first
    argument and behind the second.

    \param p1 a VecPosition to which the current VecPosition must be
    compared

    \param p2 a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is in between the two
    given VecPositions when looking in the x-direction; false
    otherwise */
bool VecPosition::isBetweenX( const VecPosition &p1, const VecPosition &p2 )
{
  return ( ( isInFrontOf( p1 ) && isBehindOf( p2 ) ) ? true : false );
}

/*! This method determines whether the x-coordinate of the current
    VecPosition is in between two given double values, i.e. whether
    the x-coordinate of the current VecPosition is in front of the
    first argument and behind the second.

    \param d1 a double value to which the current x-coordinate must be
    compared

    \param d2 a double value to which the current x-coordinate must be
    compared

    \return true when the current x-coordinate is in between the two
    given values; false otherwise */
bool VecPosition::isBetweenX( const double &d1, const double &d2 )
{
  return ( ( isInFrontOf( d1 ) && isBehindOf( d2 ) ) ? true : false );
}

/*! This method determines whether the current VecPosition is in
    between two given VecPositions when looking in the y-direction,
    i.e. whether the current VecPosition is to the right of the first
    argument and to the left of the second.

    \param p1 a VecPosition to which the current VecPosition must be
    compared

    \param p2 a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is in between the two
    given VecPositions when looking in the y-direction; false
    otherwise */
bool VecPosition::isBetweenY( const VecPosition &p1, const VecPosition &p2 )
{
  return ( ( isRightOf( p1 ) && isLeftOf( p2 ) ) ? true : false );
}

/*! This method determines whether the y-coordinate of the current
    VecPosition is in between two given double values, i.e. whether
    the y-coordinate of the current VecPosition is to the right of the
    first argument and to the left of the second.

    \param d1 a double value to which the current y-coordinate must be
    compared

    \param d2 a double value to which the current y-coordinate must be
    compared

    \return true when the current y-coordinate is in between the two
    given values; false otherwise */
bool VecPosition::isBetweenY( const double &d1, const double &d2 )
{
  return ( ( isRightOf( d1 ) && isLeftOf( d2 ) ) ? true : false );
}

/*! This method determines whether the current VecPosition is in
    between two given VecPositions when looking in the z-direction,
    i.e. whether the current VecPosition is in up of the first
    argument and down the second.

    \param p1 a VecPosition to which the current VecPosition must be
    compared

    \param p2 a VecPosition to which the current VecPosition must be
    compared

    \return true when the current VecPosition is in between the two
    given VecPositions when looking in the z-direction; false
    otherwise */
bool VecPosition::isBetweenZ( const VecPosition &p1, const VecPosition &p2 )
{
  return ( ( isUpOf( p1 ) && isDownOf( p2 ) ) ? true : false );
}

/*! This method determines whether the z-coordinate of the current
    VecPosition is in between two given double values, i.e. whether
    the z-coordinate of the current VecPosition is upper than the
    first argument and down the second.

    \param d1 a double value to which the current z-coordinate must be
    compared

    \param d2 a double value to which the current z-coordinate must be
    compared

    \return true when the current z-coordinate is in between the two
    given values; false otherwise */
bool VecPosition::isBetweenZ( const double &d1, const double &d2 )
{
  return ( ( isUpOf( d1 ) && isDownOf( d2 ) ) ? true : false );
}

/*! This method normalizes a VecPosition by setting the magnitude of
    the corresponding vector to 1. This thus changes the VecPosition
    itself.

    \return the result of normalizing the current VecPosition thus
    yielding a different VecPosition */
VecPosition VecPosition::normalize( )
{
  return ( setMagnitude( 1.0 ) );
}

/*! This method rotates the vector corresponding to the current
    VecPosition over a given angle thereby changing the current
    VecPosition itself. This is done by calculating the polar
    coordinates of the current VecPosition and adding the given angle
    to the phi-coordinate in the polar representation. The polar
    coordinates are then converted back to Cartesian coordinates to
    obtain the desired result.

    \param angle an angle in degrees over which the vector
    corresponding to the current VecPosition must be rotated

    \return the result of rotating the vector corresponding to the
    current VecPosition over the given angle thus yielding a different
    VecPosition */
VecPosition VecPosition::rotate( AngDeg angle )
{
  // determine the polar representation of the current VecPosition
  double dMag    = this->getMagnitude( );
  double dNewDir = this->getDirection( ) + angle;  // add rotation angle to theta
  setVecPosition( dMag, dNewDir, this->getPhi( ), POLAR );          // convert back to Cartesian
  return ( *this );
}

/*! This method converts the coordinates of the current VecPosition
    (which are represented in an global coordinate system with the
    origin at (0,0,0)) into relative coordinates in a different
    coordinate system (e.g. relative to a player). The new coordinate
    system is defined by the arguments to the method. The relative
    coordinates are now obtained by aligning the relative coordinate
    system with the global coordinate system using a translation to
    make both origins coincide followed by a rotation to align the
    axes.

    \param origin the origin of the relative coordinate frame

    \param ang the angle between the world frame and the relative
    frame (reasoning from the world frame)

    \return the result of converting the current global VecPosition
    into a relative VecPosition */
VecPosition VecPosition::globalToRelative( VecPosition origin, AngDeg ang )
{
  // convert global coordinates into relative coordinates by aligning
  // relative frame and world frame. First perform translation to make
  // origins of both frames coincide. Then perform rotation to make
  // axes of both frames coincide (use negative angle since you rotate
  // relative frame to world frame).
  *this -= origin;
  return ( rotate( -ang ) );
}

/*! This method converts the coordinates of the current VecPosition
    (which are represented in a relative coordinate system) into
    global coordinates in the world frame (with origin at (0,0,0)). The
    relative coordinate system is defined by the arguments to the
    method. The global coordinates are now obtained by aligning the
    world frame with the relative frame using a rotation to align the
    axes followed by a translation to make both origins coincide.

    \param origin the origin of the relative coordinate frame

    \param ang the angle between the world frame and the relative
    frame (reasoning from the world frame)

    \return the result of converting the current relative VecPosition
    into an global VecPosition */
VecPosition VecPosition::relativeToGlobal( VecPosition origin, AngDeg ang )
{
  // convert relative coordinates into global coordinates by aligning
  // world frame and relative frame. First perform rotation to make
  // axes of both frames coincide (use positive angle since you rotate
  // world frame to relative frame). Then perform translation to make
  // origins of both frames coincide.
  rotate( ang );
  *this += origin;
  return ( *this );
}

/*! This method returns a VecPosition that lies somewhere on the
    vector between the current VecPosition and a given
    VecPosition. The desired position is specified by a given fraction
    of this vector (e.g. 0.5 means exactly in the middle of the
    vector). The current VecPosition itself is left unchanged.

    \param p a VecPosition which defines the vector to the current
    VecPosition

    \param dFrac double representing the fraction of the connecting
    vector at which the desired VecPosition lies.

    \return the VecPosition which lies at fraction dFrac on the vector
    connecting p and the current VecPosition */
VecPosition VecPosition::getVecPositionOnLineFraction( VecPosition &p,
                                                       double      dFrac )