geometry.cpp

robocup 3d, a 3d base team similar to UvA 2d

    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 )
{
  // determine point on line that lies at fraction dFrac of whole line
  // example: this --- 0.25 ---------  p
  // formula: this + dFrac * ( p - this ) = this - dFrac * this + dFrac * p =
  //          ( 1 - dFrac ) * this + dFrac * p
  return ( ( *this ) * ( 1.0 - dFrac ) + ( p * dFrac ) );
}

/*! This method converts a polar representation of a VecPosition into
    a Cartesian representation.

    \param dMag a double representing the polar r-coordinate, i.e. the
    distance from the point to the origin

    \param theta the angle that the polar vector makes with the xy-plane,
    i.e. the polar theta-coordinate

    \param phi the angle that the polar vector makes with the z-axis,
    i.e. the polar phi-coordinate

    \return the result of converting the given polar representation
    into a Cartesian representation thus yielding a Cartesian
    VecPosition */
VecPosition VecPosition::getVecPositionFromPolar( double dMag, AngDeg theta, AngDeg phi )
{
  double z  = dMag * sinDeg(  phi  );
  double XY = dMag * cosDeg(  phi  );
  double x  = XY   * cosDeg( theta );
  double y  = XY   * sinDeg( theta );
  return ( VecPosition( x, y, z ) );
}

/*! This method normalizes an angle. This means that the resulting
    angle lies between -180 and 180 degrees.

    \param angle the angle which must be normalized

    \return the result of normalizing the given angle */
AngDeg VecPosition::normalizeAngle( AngDeg angle )
{
  while( angle > 180.0  ) angle -= 360.0;
  while( angle < -180.0 ) angle += 360.0;

  return ( angle );
}


/*****************************************************************************/
/********************** CLASS GEOMETRY ***************************************/
/*****************************************************************************/

/*! A geometric series is one in which there is a constant ratio between each
    element and the one preceding it. This method determines the
    length of a geometric series given its first element, the sum of the
    elements in the series and the constant ratio between the elements.
    Normally: s = a + ar + ar^2 + ...  + ar^n
    Now: dSum = dFirst + dFirst*dRatio + dFirst*dRatio^2 + .. + dFist*dRatio^n
    \param dFirst first term of the series
    \param dRatio ratio with which the the first term is multiplied
    \param dSum the total sum of all the serie
    \return the length(n in above example) of the series */
double Geometry::getLengthGeomSeries( double dFirst, double dRatio, double dSum )
{
  if( dRatio < 0 )
    cerr << "(Geometry:getLengthGeomSeries): negative ratio" << endl;

  // s = a + ar + ar^2 + .. + ar^n-1 and thus sr = ar + ar^2 + .. + ar^n
  // subtract: sr - s = - a + ar^n) =>  s(1-r)/a + 1 = r^n = temp
  // log r^n / n = n log r / log r = n = length
  double temp = (dSum * ( dRatio - 1 ) / dFirst) + 1;
  if( temp <= 0 )
    return -1.0;
  return log( temp ) / log( dRatio ) ;
}

/*! A geometric series is one in which there is a constant ratio between each
    element and the one preceding it. This method determines the sum of a
    geometric series given its first element, the ratio and the number of steps
    in the series
    Normally: s = a + ar + ar^2 + ...  + ar^n
    Now: dSum = dFirst + dFirst*dRatio + ... + dFirst*dRatio^dSteps
    \param dFirst first term of the series
    \param dRatio ratio with which the the first term is multiplied
    \param dLength the number of steps to be taken into account
    \return the sum of the series */
double Geometry::getSumGeomSeries( double dFirst, double dRatio, double dLength)
{
  // s = a + ar + ar^2 + .. + ar^n-1 and thus sr = ar + ar^2 + .. + ar^n
  // subtract: s - sr = a - ar^n) =>  s = a(1-r^n)/(1-r)
  return dFirst * ( 1 - pow( dRatio, dLength ) ) / ( 1 - dRatio ) ;
}

/*! A geometric series is one in which there is a constant ratio between each
    element and the one preceding it. This method determines the sum of an
    infinite geometric series given its first element and the constant ratio
    between the elements. Note that such an infinite series will only converge
    when 0<r<1.
    Normally: s = a + ar + ar^2 + ar^3 + ....
    Now: dSum = dFirst + dFirst*dRatio + dFirst*dRatio^2...
    \param dFirst first term of the series
    \param dRatio ratio with which the the first term is multiplied
    \return the sum of the series */
double Geometry::getSumInfGeomSeries( double dFirst, double dRatio )
{
  if( dRatio > 1 )
    cerr << "(Geometry:CalcLengthGeomSeries): series does not converge" <<endl;

  // s = a(1-r^n)/(1-r) with n->inf and 0<r<1 => r^n = 0
  return dFirst / ( 1 - dRatio );
}

/*! A geometric series is one in which there is a constant ratio between each
    element and the one preceding it. This method determines the first element
    of a geometric series given its element, the ratio and the number of steps
    in the series
    Normally: s = a + ar + ar^2 + ...  + ar^n
    Now: dSum = dFirst + dFirst*dRatio + ... + dFirst*dRatio^dSteps
    \param dSum sum of the series
    \param dRatio ratio with which the the first term is multiplied
    \param dLength the number of steps to be taken into account
    \return the first element (a) of a serie */
double Geometry::getFirstGeomSeries( double dSum, double dRatio, double dLength)
{
  // s = a + ar + ar^2 + .. + ar^n-1 and thus sr = ar + ar^2 + .. + ar^n
  // subtract: s - sr = a - ar^n) =>  s = a(1-r^n)/(1-r) => a = s*(1-r)/(1-r^n)
  return dSum *  ( 1 - dRatio )/( 1 - pow( dRatio, dLength ) ) ;
}

/*! A geometric series is one in which there is a constant ratio between each
    element and the one preceding it. This method determines the first element
    of an infinite geometric series given its first element and the constant
    ratio between the elements. Note that such an infinite series will only
    converge when 0<r<1.
    Normally: s = a + ar + ar^2 + ar^3 + ....
    Now: dSum = dFirst + dFirst*dRatio + dFirst*dRatio^2...
    \param dSum sum of the series
    \param dRatio ratio with which the the first term is multiplied
    \return the first term of the series */
double Geometry::getFirstInfGeomSeries( double dSum, double dRatio )
{
  if( dRatio > 1 )
    cerr << "(Geometry:getFirstInfGeomSeries):series does not converge" <<endl;

  // s = a(1-r^n)/(1-r) with r->inf and 0<r<1 => r^n = 0 => a = s ( 1 - r)
  return dSum * ( 1 - dRatio );
}

/*! This method performs the abc formula (Pythagoras' Theorem) on the given
    parameters and puts the result in *s1 en *s2. It returns the number of
    found coordinates.
    \param a a parameter in abc formula
    \param b b parameter in abc formula
    \param c c parameter in abc formula
    \param *s1 first result of abc formula
    \param *s2 second result of abc formula
    \return number of found x-coordinates */
int Geometry::abcFormula(double a, double b, double c, double *s1, double *s2)
{
  double dDiscr = b*b - 4*a*c;       // discriminant is b^2 - 4*a*c
  if (fabs(dDiscr) < EPSILON )       // if discriminant = 0
  {
    *s1 = -b / (2 * a);              //  only one solution
    return 1;
  }
  else if (dDiscr < 0)               // if discriminant < 0
    return 0;                        //  no solutions
  else                               // if discriminant > 0
  {
    dDiscr = sqrt(dDiscr);           //  two solutions
    *s1 = (-b + dDiscr ) / (2 * a);
    *s2 = (-b - dDiscr ) / (2 * a);
    return 2;
  }
}

/*****************************************************************************/
/********************* CLASS CIRCLE ******************************************/
/*****************************************************************************/

/*! This is the constructor of a circle.
    \param pos first point that defines the center of circle
    \param dR the radius of the circle
    \return circle with pos as center and radius as radius*/
Circle::Circle( VecPosition pos, double dR )
{
  setCircle( pos, dR );
}

/*! This is the constructor of a circle which initializes a circle with a
    radius of zero. */
Circle::Circle( )
{
  setCircle( VecPosition(-1000.0,-1000.0, -1000.0), 0);
}

/*! This method prints the circle information to the specified output stream
    in the following format: "c: (c_x,c_y,c_z), r: rad" where (c_x,c_y,z_z) denotes
    the center of the circle and rad the radius.
    \param os output stream to which output is written. */
void Circle::show( ostream& os)
{
  os << "c:" << m_posCenter << ", r:" << m_dRadius;
}

/*! This method sets the values of the circle.
    \param pos new center of the circle
    \param dR new radius of the circle
    ( > 0 )
    \return bool indicating whether radius was set */
bool Circle::setCircle( VecPosition pos, double dR )
{
  setCenter( pos );
  return setRadius( dR  );
}
/*! This method sets the radius of the circle.
    \param dR new radius of the circle ( > 0 )
    \return bool indicating whether radius was set */
bool Circle::setRadius( double dR )
{
  if( dR > 0 )
  {
    m_dRadius = dR;
    return true;
  }
  else
  {
    m_dRadius = 0.0;
    return false;
  }
}

/*! This method returns the radius of the circle.
    \return radius of the circle */
double Circle::getRadius() const
{
  return m_dRadius;
}

/*! This method sets the center of the circle.
    \param pos new center of the circle
    \return bool indicating whether center was set */
bool Circle::setCenter( VecPosition pos )
{
  m_posCenter = pos;
  return true;
}

/*! This method returns the center of the circle.
    \return center of the circle */
VecPosition Circle::getCenter()
{
  return m_posCenter;
}

/*! This method returns the circumference of the circle.
    \return circumference of the circle */
double Circle::getCircumference()
{
  return 2.0*M_PI*getRadius();
}

/*! This method returns the area inside the circle.
    \return area inside the circle */
double Circle::getArea()
{
  return M_PI*getRadius()*getRadius();
}

/*! This method returns the volume of a circle.
    \return volume inside the circle */
double Circle::getVolume() const
{
  return M_PI*4/3*getRadius()*getRadius()*getRadius();
}

/*! This method returns a boolean that indicates whether 'pos' is
    located inside the circle.
 
   \param pos position of which should be checked whether it is
   located in the circle
   \param bCircle denotes wheather the check is made for a 
   circle or a sphere

   \return bool indicating whether pos lies inside the circle */
bool Circle::isInside( VecPosition pos, bool bCircle )
{
  if( bCircle )