#ifndef SpiceRotation_h
#define SpiceRotation_h
/**
 * @file
 * $Revision: 1.20 $
 * $Date: 2010/03/27 07:04:26 $
 *
 *   Unless noted otherwise, the portions of Isis written by the USGS are public
 *   domain. See individual third-party library and package descriptions for
 *   intellectual property information,user agreements, and related information.
 *
 *   Although Isis has been used by the USGS, no warranty, expressed or implied,
 *   is made by the USGS as to the accuracy and functioning of such software
 *   and related material nor shall the fact of distribution constitute any such
 *   warranty, and no responsibility is assumed by the USGS in connection
 *   therewith.
 *
 *   For additional information, launch
 *   $ISISROOT/doc//documents/Disclaimers/Disclaimers.html in a browser or see
 *   the Privacy &amp; Disclaimers page on the Isis website,
 *   http://isis.astrogeology.usgs.gov, and the USGS privacy and disclaimers on
 *   http://www.usgs.gov/privacy.html.
 */

#include <string>
#include <vector>

//#include <SpiceUsr.h>
//#include <SpiceZfc.h>
//#include <SpiceZmc.h>

#include "Angle.h"
#include "Table.h"
#include "PolynomialUnivariate.h"
#include "Quaternion.h"

#define J2000Code    1

namespace Isis {
  /**
   * @brief Obtain SPICE rotation information for a body
   *
   * This class will obtain the rotation from J2000 to a particular reference
   * frame, for example the rotation from J2000 to MOC NA.
   *
   * It is essentially used to convert position vectors from one frame to
   * another, making it is a C++ wrapper to the NAIF routines pxform_c and
   * mxv or mtxv.  Therefore, appropriate NAIF kernels are expected to be
   * loaded prior to using this class.  A position can be returned in either
   * the J2000 frame or the selected reference frame.  See NAIF required
   * reading for more information regarding this subject at
   * ftp://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/spk.html
   * <p>
   * An important functionality of this class is the ability to cache the
   * rotations so they do not have to be constantly read from the NAIF kernels
   * and they can be more conveniently updated.  Once the data is cached, the
   * NAIF kernels can be unloaded.  If the rotation has a fixed part and a time-
   * based part, the rotation is computed and stored in those two parts.
   *
   * @ingroup SpiceInstrumentsAndCameras
   *
   * @author 2005-12-01 Debbie A. Cook
   *
   * @internal
   *   @history 2005-12-01 Debbie A. Cook Original Version modified from
   *                           SpicePosition class by Jeff Anderson
   *   @history 2006-03-23 Jeff Anderson modified SetEphemerisTime to return
   *                           if the time did not change to improve speed.
   *   @history 2006-10-18 Debbie A. Cook Added method, WrapAngle, to wrap
   *                           angles around 2 pi
   *   @history 2007-12-05 Debbie A. Cook added method SetPolynomialDegree to
   *                           allow the degree of the polynomials fit to the
   *                           camera angles to be changed.  Also changed the
   *                           polynomial from a fixed 2nd order polynomial to
   *                           an nth degree polynomial with one independent
   *                           variable.  PartialType was revised and the calls
   *                           to SetReferencePartial (has an added argument,
   *                           coefficient index) and DPolynomial (argument type
   *                           changed to int) were revised. The function was
   *                           changed from Parabola to Polynomial1Variable, now
   *                           called PolynomialUnivariate. New methods
   *                           GetBaseTime and SetOverrideBaseTime were added
   *   @history 2008-02-15 Debbie A. Cook added a new error message to handle
   *                           the case where the Naif reference frame code is
   *                           not recognized.
   *   @history 2008-06-18 Unknown - Fixed documentation, added NaifStatus calls
   *   @history 2008-11-26 Debbie A. Cook Added method to set axes of rotation.
   *                           Default axes are still 3,1,3 so existing software
   *                           will not be affected by the change.  Also added
   *                           timeScale to the the class and made some
   *                           parameters protected instead of private so they
   *                           are available to inheriting classes.
   *   @history 2008-12-12 Debbie A. Cook Added method to return frame code
   *   @history 2009-01-26 Debbie A. Cook Added wrap of 3rd camera angle when
   *                           crossing +-180
   *   @history 2009-04-21 Debbie A. Cook Added methods MinimizeCache and
   *                           LoadTimeCache, variable p_minimizeCache, and
   *                           enum constants DownsizeStatus
   *   @history 2009-06-29 Debbie A. Cook Fixed memory overwrite problem in
   *                           LoadTimeCache when reading a type 3 ck
   *   @history 2009-07-24 Debbie A. Cook Removed downsizing for Nadir
   *                           instrument pointing tables (LoadTimeCache) so
   *                           that radar instruments will work.  Current
   *                           downsizing code requires sclk and radar has no
   *                           sclk.
   *   @history 2009-10-01 Debbie A. Cook Divided the rotation into a constant
   *                           (in time) part and a time-based part and
   *                           added keywords listing the frame chains for both
   *                           the constant part and the time-based part.
   *   @history 2009-10-09 Debbie A. Cook Added angular velocity when it is
   *                           available
   *   @history 2009-10-30 Unknown - Modified J2000Vector and ReferenceVector
   *                           to work on either length 3 vectors (position
   *                           only) or lenght 6 vectors (position and velocity)
   *                           and added private method StateTJ()
   *   @history 2009-12-03 Debbie A. Cook Modified tests in LoadTimeCache to
   *                           allow observation to cross segment boundary for
   *                           LRO
   *   @history 2010-03-19 Debbie A. Cook Revised ReloadCache including removing
   *                           obsolete arguments.  Added initialization of
   *                           members p_fullCacheStartTime, p_fullCacheEndTime,
   *                           and p_fullCacheSize.  Added these same values to
   *                           the table label in method Cache and the reading
   *                           of these values to the method LoadCache(table).
   *                           Improved error message in FrameTrace.  Also
   *                           corrected a comment in StateTJ
   *   @history 2010-09-23 Debbie A. Cook Revised to write out line cache for
   *                           updated pointing when cache size is 1. If the
   *                           original pointing had an angular velocity in
   *                           this case, the original angular velocity is
   *                           written out along with the updated quaternion.
   *                           Also added method Extrapolate, to extrapolate
   *                           pointing assuming a constant angular velocity.
   *                           This method was designed to compute the pointing
   *                           at the start and end of the exposure for framing
   *                           cameras to create a ck that would cover a single
   *                           framing observation.
   *   @history 2010-12-22 Debbie A. Cook  Added new method
   *                           SetFullCacheParameters to upgrade appjit to
   *                           current instrument Rotation group labels.
   *   @history 2011-02-17 Debbie A. Cook  Fixed bug in method LineCache and
   *                           fixed computation of angular velocity in method
   *                           DCJdt (derivative was with respect to scaled et
   *                           instead of et)
   *   @history 2011-02-22 Debbie A. Cook - Corrected Extrapolation method
   *   @history 2011-03-25 Debbie A. Cook - Added method GetCenterAngles()
   *   @history 2011-07-20 Kris J Becker - Modified
   *                           SpiceRotation::LoadCache(Table &table) to be
   *                           reentrant.  This mod was necessitated by the Dawn
   *                           VIR instrument.
   *   @history 2012-05-28 Debbie A. Cook - Programmer notes - A new
   *                           interpolation algorithm, PolyFunctionOverSpice,
   *                           was added and new supporting methods:
   *                           SetEphemerisTimePolyOverSpice,  SetEphemerisTimeSpice,
   *                           SetEphemerisTimeNadir, SetEphemerisTimeMemcache,
   *                           and SetEphemerisTimePolyFunction.
   *                           PolyFunctionOverSpice is never output, but is
   *                           converted to a line cache and reduced.  Methods
   *                           LineCache and ReloadCache were modified to do the
   *                           reduction and a copy constructor was added to
   *                           support the reduction.  Also an argument was
   *                           added to SetPolynomial methods for function type,
   *                           since PolyFunction is no longer the only function
   *                           supported.  These changes help the BundleAdjust
   *                           applications to better fit line scan images where
   *                           the pointing was not modeled well with a regular
   *                           polynomial.
   *   @history 2012-10-25 Jeannie Backer - Brought class closer to Isis3
   *                           standards: Ordered includes in cpp file, replaced
   *                           quotation marks with angle braces in 3rd party
   *                           includes, fixed history indentation and line
   *                           length. References #1181.
   *   @history 2013-03-27 Jeannie Backer - Added methods for MsiCamera. Brought
   *                           class closer to Isis3 standards: moved method
   *                           implementation to cpp file, fixed documentation.
   *                           References #1248.
   *   @history 2013-11-12 Ken Edmundson Programmers notes - Commented out cout
   *                           debug statements on lines 637 and 642 that appeared
   *                           onscreen during jigsaw runs when images are updated.
   *                           References #1521.
   *   @history 2014-03-11 Tracie Sucharski - In the LoadTimeCache method, do not throw error if
   *                           if first segment in kernel is not type 3 or 5.  As long as the
   *                           segment needed is type 3 or 5, we're ok.  This was changed for
   *                           New Horizons which had ck's with both type 2 and type 3 segments.
   *   @history 2014-03-11 Stuart Sides - Programmers notes - Fixed a bug in the copy constructor
   *                           that was going out of array bounds.
   *   @history 2015-02-20 Jeannie Backer - Improved error messages.
   *   @history 2015-07-21 Kristin Berry - Added additional NaifStatus::CheckErrors() calls to see if
   *                           any NAIF errors were signaled. References #2248.
   *   @history 2015-08-05 Debbie A. Cook - Programmer notes - Modified LoadCache, 
   *                           and ComputeAv.
   *                           Added new methods 
   *                           loadPCFromSpice, loadPCFromTable, toJ2000Partial, poleRaCoefs,
   *                           poleDecCoefs, pmCoefs, poleRaNutPrecCoefs, poleDecNutPrecCoefs, 
   *                           pmNutPrecCoefs, sysNutPrecConstants, sysNutPrecCoefs,
   *                           usePckPolynomial, setPckPolynomial(raCoef, decCoef, pmCoef),
   *                           getPckPolynomial, setEphemerisTimePckPolyFunction, getFrameType
   *                           and members m_frameType, m_tOrientationAvailable, 
   *                           m_raPole, m_decPole, m_pm, m_raNutPrec, m_decNutPrec, m_pmNutPrec,
   *                           m_sysNutPrec0, m_sysNutPrec1, m_dscale, m_Tscale to support request for 
   *                           solving for target body parameters.
   *                           Also added a new enumerated value for Source, PckPolyFunction, 
   *                           and PartialType, WRT_RotationRate.
   *   @history 2016-02-15 Debbie A. Cook - Programmer notes - Added private method
   *                           setFrameType to set the frame type.  It also loads the planetary 
   *                           constants for a PCK type. 
   *   @history 2016-06-28 Ian Humphrey - Updated documentation and coding standards. Added new
   *                           tests to unit test. Fixes #3972.
   *   @history 2017-12-13 Ken Edmundson - Added "case DYN:" to methods ToReferencePartial and toJ2000Partial. Fixes #5251.
   *                           This problem was found when trying to bundle M3 images that had been spiceinited with nadir
   *                           pointing. The nadir frame is defined as a Dynamic Frame by Naif.
   *
   *  @todo Downsize using Hermite cubic spline and allow Nadir tables to be downsized again.
   *  @todo Consider making this a base class with child classes based on frame type or 
   *              storage type (polynomial, polynomial over cache, cache, etc.)
   */
  class SpiceRotation {
    public:
      // Constructors
      SpiceRotation(int frameCode);
      /*      SpiceRotation( int NaifCode );
      We would like to call refchg instead to avoid the strings.  Currently Naif does
      not have refchg_c, but only the f2c'd refchg.c.*/
      SpiceRotation(int frameCode, int targetCode);
      SpiceRotation(const SpiceRotation &rotToCopy);

      // Destructor
      virtual ~SpiceRotation();

      // Change the frame (has no effect if cached)
      void SetFrame(int frameCode);
      int Frame();

      void SetTimeBias(double timeBias);

      /**
       * The rotation can come from one of 3 places for an Isis cube.  The class
       * expects function to be after Memcache.
       *       Spice - the rotation is calculated by Naif Spice routines with data 
       *                  read directly from Naif kernels.
       *       Nadir - the rotation is calculated using the Naif routine twovec with 
       *                  the position and velocity vectors of the spacecraft.
       *       Memcache - the rotation is linearly interpolated from time-based 
       *                  values in a table.
       *       PolyFunction - the rotation is calculated from an nth degree 
       *                  polynomial in one variable (time in scaled seconds)
       *       PolyFunctionOverSpice - the rotation is calculated from an nth
       *                  degree polynomial fit over the Naif Spice results.
       *       PckPolyFunction - The rotation is calculated using the IAU fit 
       *                  polynomials in one variable (time in Julian centuries and days).
       */
      enum Source {            
        Spice,                   //!< Directly from the kernels 
        Nadir,                   //!< Nadir pointing
        Memcache,                //!< From cached table
        PolyFunction,            //!< From nth degree polynomial
        PolyFunctionOverSpice ,  //!< Kernels plus nth degree polynomial 
        PckPolyFunction          //!< Quadratic polynomial function with linear trignometric terms
      };            

      /** 
       * This enumeration indicates whether the partial derivative is taken with 
       * respect to Right Ascension, Declination, or Twist (or Rotation). 
       */ 
      enum PartialType { 
        WRT_RightAscension, //!< With respect to Right Ascension
        WRT_Declination,    //!< With respect to Declination
        WRT_Twist           //!< With respect to Twist or Prime Meridian Rotation
      };

      /** 
       * Status of downsizing the cache
       */ 
      enum DownsizeStatus { 
        Yes,  //!< Downsize the cache 
        Done, //!< Cache is downsized
        No    //!< Do not downsize the cache 
      };

      /** 
       * Enumeration for the frame type of the rotation  
       */ 
      enum FrameType {
        UNKNOWN = 0,      //!< Isis specific code for unknown frame type
        INERTL = 1,       //!< See Naif Frames.req document for 
        PCK  = 2,         //!< definitions
        CK = 3,           //!< 
        TK = 4,           //!< 
        DYN = 5,          //!<
        BPC = 6,          //!< Isis specific code for binary pck
        NOTJ2000PCK = 7   //!< PCK frame not referenced to J2000
      };                                   

      void SetEphemerisTime(double et);
      double EphemerisTime() const;

      std::vector<double> GetCenterAngles();
      
      std::vector<double> Matrix();
      std::vector<double> AngularVelocity();

      // TC
      std::vector<double> ConstantRotation();
      std::vector<double> &ConstantMatrix();
      void SetConstantMatrix(std::vector<double> constantMatrix);

      // CJ
      std::vector<double> TimeBasedRotation();
      std::vector<double> &TimeBasedMatrix();
      void SetTimeBasedMatrix(std::vector<double> timeBasedMatrix);

      std::vector<double> J2000Vector(const std::vector<double> &rVec);

      std::vector<Angle> poleRaCoefs();

      std::vector<Angle> poleDecCoefs();

      std::vector<Angle> pmCoefs();

      std::vector<double> poleRaNutPrecCoefs();

      std::vector<double> poleDecNutPrecCoefs();

      std::vector<double> pmNutPrecCoefs();

      std::vector<Angle> sysNutPrecConstants();

      std::vector<Angle> sysNutPrecCoefs();

      std::vector<double> ReferenceVector(const std::vector<double> &jVec);

      std::vector<double> EvaluatePolyFunction();

      void loadPCFromSpice(int CenterBodyCode);
      void loadPCFromTable(const PvlObject &Label);

      void MinimizeCache(DownsizeStatus status);

      void LoadCache(double startTime, double endTime, int size);

      void LoadCache(double time);

      void LoadCache(Table &table);

      Table LineCache(const QString &tableName);

      void ReloadCache();

      Table Cache(const QString &tableName);
      void CacheLabel(Table &table);

      void LoadTimeCache();

      std::vector<double> Angles(int axis3, int axis2, int axis1);
      void SetAngles(std::vector<double> angles, int axis3, int axis2, int axis1);

      bool IsCached() const;

      void SetPolynomial(const Source type=PolyFunction);

      void SetPolynomial(const std::vector<double> &abcAng1,
                         const std::vector<double> &abcAng2,
                         const std::vector<double> &abcAng3,
                         const Source type = PolyFunction);

      void usePckPolynomial();
      void setPckPolynomial(const std::vector<Angle> &raCoeff,
                            const std::vector<Angle> &decCoeff,
                            const std::vector<Angle> &pmCoeff);

      void GetPolynomial(std::vector<double> &abcAng1,
                         std::vector<double> &abcAng2,
                         std::vector<double> &abcAng3);

      void getPckPolynomial(std::vector<Angle> &raCoeff,
                            std::vector<Angle> &decCoeff,
                            std::vector<Angle> &pmCoeff);

      // Set the polynomial degree
      void SetPolynomialDegree(int degree);
      Source GetSource();
      void SetSource(Source source);
      void ComputeBaseTime();
      FrameType getFrameType();
      double GetBaseTime();
      double GetTimeScale();

      void SetOverrideBaseTime(double baseTime, double timeScale);

      // Derivative methods
      double DPolynomial(const int coeffIndex);
      double DPckPolynomial(PartialType partialVar, const int coeffIndex);

      std::vector<double> toJ2000Partial(const std::vector<double> &lookT,
                                         PartialType partialVar, int coeffIndex);
      std::vector<double> ToReferencePartial(std::vector<double> &lookJ,
                                             PartialType partialVar, int coeffIndex);
      void DCJdt(std::vector<double> &dRJ);

      double WrapAngle(double compareAngle, double angle);
      void SetAxes(int axis1, int axis2, int axis3);
      std::vector<double> GetFullCacheTime();
      void FrameTrace(double et);

      // Return the frame chain for the constant part of the rotation (ends in target)
      std::vector<int>  ConstantFrameChain();
      std::vector<int>  TimeFrameChain();
      void InitConstantRotation(double et);
      bool HasAngularVelocity();

      void ComputeAv();
      std::vector<double> Extrapolate(double timeEt);

      void checkForBinaryPck();

    protected:
      void SetFullCacheParameters(double startTime, double endTime, int cacheSize);
      void setEphemerisTimeMemcache();
      void setEphemerisTimeNadir();
      void setEphemerisTimeSpice();
      void setEphemerisTimePolyFunction();
      void setEphemerisTimePolyFunctionOverSpice();
      void setEphemerisTimePckPolyFunction();
      std::vector<double> p_cacheTime;  //!< iTime for corresponding rotation
      std::vector<std::vector<double> > p_cache; /**< Cached rotations, stored as 
                                                      rotation matrix from J2000 
                                                      to 1st constant frame (CJ) or 
                                                      coefficients of polynomial
                                                      fit to rotation angles.*/
      int p_degree;                     //!< Degree of fit polynomial for angles
      int p_axis1;                      //!< Axis of rotation for angle 1 of rotation
      int p_axis2;                      //!< Axis of rotation for angle 2 of rotation
      int p_axis3;                      //!< Axis of rotation for angle 3 of rotation

    private:
      // method
      void setFrameType();
      std::vector<int> p_constantFrames;  /**< Chain of Naif frame codes in constant 
                                               rotation TC. The first entry will always 
                                               be the target frame code*/
      std::vector<int> p_timeFrames;      /**< Chain of Naif frame codes in time-based 
                                               rotation CJ. The last entry will always 
                                               be 1 (J2000 code)*/
      double p_timeBias;                  //!< iTime bias when reading kernels

      double p_et;                           //!< Current ephemeris time
      Quaternion p_quaternion;            /**< Quaternion for J2000 to reference
                                                                  rotation at et*/

      bool p_matrixSet;                    //!< Flag indicating p_TJ has been set
      bool m_tOrientationAvailable;  //!< Target orientation constants are available
 

      FrameType m_frameType;  //!< The type of rotation frame
      Source p_source;                    //!< The source of the rotation data
      int p_axisP;                        /**< The axis defined by the spacecraft
                                               vector for defining a nadir rotation*/
      int p_axisV;                        /**< The axis defined by the velocity
                                               vector for defining a nadir rotation*/
      int p_targetCode;                   //!< For computing Nadir rotation only

      double p_baseTime;                  //!< Base time used in fit equations
      double p_timeScale;                 //!< Time scale used in fit equations
      bool p_degreeApplied;               /**< Flag indicating whether or not a polynomial
                                               of degree p_degree has been created and
                                               used to fill the cache*/
      std::vector<double> p_coefficients[3];  /**< Coefficients defining functions fit 
                                                   to 3 pointing angles*/
      bool p_noOverride;                  //!< Flag to compute base time;
      double p_overrideBaseTime;          //!< Value set by caller to override computed base time
      double p_overrideTimeScale;         //!< Value set by caller to override computed time scale
      DownsizeStatus p_minimizeCache;     //!< Status of downsizing the cache (set to No to ignore)
      double p_fullCacheStartTime;        //!< Initial requested starting time of cache
      double p_fullCacheEndTime;          //!< Initial requested ending time of cache
      int p_fullCacheSize;                //!< Initial requested cache size
      std::vector<double> p_TC;           /**< Rotation matrix from first constant rotation 
                                          (after all time-based rotations in frame chain from
                                           J2000 to target) to the target frame*/
      std::vector<double> p_CJ;           /**< Rotation matrix from J2000 to first constant 
                                               rotation*/
      std::vector<std::vector<double> > p_cacheAv;
      //!< Cached angular velocities for corresponding rotactions in p_cache
      std::vector<double> p_av;           //!< Angular velocity for rotation at time p_et
      bool p_hasAngularVelocity;          /**< Flag indicating whether the rotation 
                                               includes angular velocity*/
      std::vector<double> StateTJ();      /**< State matrix (6x6) for rotating state 
                                               vectors from J2000 to target frame*/
      // The remaining items are only used for PCK frame types.  In this case the  
      // rotation is  stored as a cache, but the coefficients are available for display
      // or comparison, and the first three coefficient sets can be solved for and 
      // updated in jigsaw.   The initial coefficient values are read from a Naif PCK.
      //
      // The general equation for the right ascension of the pole is
      //
      // raPole  =  raPole[0] + raPole[1]*Time  + raPole[2]*Time**2 + raNutPrec,
      //    where 
      //    raNutPrec  =  raNutPrec1[0]*sin(sysNutPrec[0][0] + sysNutPrec[0][1]*Time) + 
      //                  raNutPrec1[1]*sin(sysNutPrec[1][0] + sysNutPrec[1][1]*Time) + ...
      //                  raNutPrec1[N-1]*sin(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time) +
      // (optional for multiples of nutation precession angles)
      //                  raNutPrec2[0]*sin(2*(sysNutPrec[0][0] + sysNutPrec[0][1]*Time)) +
      //                  raNutPrec2[1]*sin(2*(sysNutPrec[1][0] + sysNutPrec[1][1]*Time)) + ...
      //                  raNutPrec2[N-1]*sin(2*(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time)) + 
      //                  raNutPrecM[0]*sin(M*(sysNutPrec[0][0] + sysNutPrec[0][1]*Time)) +
      //                  raNutPrecM[1]*sin(M*(sysNutPrec[1][0] + sysNutPrec[1][1]*Time)) + ...
      //                  raNutPrecM[N-1]*sin(M*(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time)) +
      //
      // The general equation for the declination of the pole is
      //
      // decPole  =  p_decPole[0] + p_decPole[1]*Time  + p_decPole[2]*Time**2 + decNutPrec,
      //    where 
      //    decNutPrec  =  decNutPrec1[0]*cos(sysNutPrec[0][0] + sysNutPrec[0][1]*Time) + 
      //                   decNutPrec1[1]*cos(sysNutPrec[1][0] + sysNutPrec[1][1]*Time) + ...
      //                   decNutPrec1[N-1]*cos(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time) +
      //                   decNutPrec2[0]*cos(2*(sysNutPrec[0][0] + sysNutPrec[0][1]*Time)) +
      //                   decNutPrec2[1]*cos(2*(sysNutPrec[1][0] + sysNutPrec[1][1]*Time)) + ...
      //                   decNutPrec2[N-1]*cos(2*(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time)) +
      // (optional for multiples of nutation precession angles)
      //                   decNutPrecM[0]*sin(M*(sysNutPrec[0][0] + sysNutPrec[0][1]*Time)) +
      //                   decNutPrecM[1]*sin(M*(sysNutPrec[1][0] + sysNutPrec[1][1]*Time)) + ...
      //                   decNutPrecM[N-1]*sin(M*(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time)) 
      //
      //     and Time is julian centuries since J2000.
      //
      // The general equation for the prime meridian rotation is
      //
      // pm  =  p_pm[0] + p_pm[1]*Dtime  + p_pm[2]*Dtime**2 + pmNutPrec,
      //    where 
      //    pmNutPrec  =  pmNutPrec1[0]*sin(sysNutPrec[0][0] + sysNutPrec[0][1]*Time) + 
      //                  pmNutPrec1[1]*sin(sysNutPrec[1][0] + sysNutPrec[1][1]*Time) + ...
      //                  pmNutPrec1[N-1]*sin(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time) +
      // (optional for multiples of nutation precession angles)
      //                  pmNutPrec2[0]*sin(2*(sysNutPrec[0][0] + sysNutPrec[0][1]*Time)) +
      //                  pmNutPrec2[1]*sin(2*(sysNutPrec[1][0] + sysNutPrec[1][1]*Time)) + ...
      //                  pmNutPrec2[N-1]*sin(2*(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time)) +
      //                  pmNutPrecM[0]*sin(M*(sysNutPrec[0][0] + sysNutPrec[0][1]*Time)) +
      //                  pmNutPrecM[1]*sin(M*(sysNutPrec[1][0] + sysNutPrec[1][1]*Time)) + ...
      //                  pmNutPrecM[N-1]*sin(M*(sysNutPrec[N-1][0] + sysNutPrec[N-1][1]*Time)) 
      //
      //     Time is interval in Julian centuries since the standard epoch, 
      //     dTime is interval in days from the standard epoch (J2000),
      //
      //     N is the number of nutation/precession terms for the planetary system of the target 
      //     body,  (possibly including multiple angles as unique terms, 
      //             ie. 2*sysNutPrec[0][0] + sysNutPrec[][1]*Time).
      //
      //     Many of the constants in this equation are 0. for a given body.
      //
      //     M is included as an option for future improvements.  M = highest multiple (period) 
      //     of any of the nutation/precession angles included in the equations.
      //
      //     ***NOTE*** Currently Naif stores multiples (amplitudes) as if they were additional 
      //                nutation/precession terms (periods) in the equation.  This method works as 
      //                long as jigsaw does not solve for those values.  In order to solve for 
      //                those values, the multiples will need to be known so that the partial 
      //                derivatives can be correctly calculated.  Some possible ways of doing this
      //                are 1) Convince Naif to change their data format indicating the relation
      //                      2) Make an Isis version of the PCK data and have Isis software to
      //                          calculate the rotation and partials.
      //                      3) Have an Isis addendum file that identifies the repeated periods
      //                          and software to apply them when calculating the rotation and partials.
      //
      //                For now this software will handle any terms with the same period and different
      //                amplitudes as unique terms in the equation (raNutPrec, decNutPrec, 
      //                and pmNutPrec).
      //
      // The next three vectors will have length 3 (for a quadratic polynomial) if used.
      std::vector<Angle>m_raPole;       //!< Coefficients of a quadratic polynomial fitting pole ra.
      std::vector<Angle>m_decPole;      //!< Coefficients of a quadratic polynomial fitting pole dec.
      std::vector<Angle>m_pm ;          //!< Coefficients of a quadratic polynomial fitting pole pm.
      //
      // Currently multiples (terms with periods matching other terms but varying amplitudes) 
      // are handled as additional terms added to the end of the vector as Naif does (see 
      // comments in any of the standard Naif PCK. 
      std::vector<double>m_raNutPrec;    //!< Coefficients of pole right ascension nut/prec terms.  
      std::vector<double>m_decNutPrec;  //!< Coefficients of pole decliniation nut/prec terms. 
      std::vector<double>m_pmNutPrec;   //!< Coefficients of prime meridian nut/prec terms.  

      // The periods of bodies in the same system are modeled with a linear equation
      std::vector<Angle>m_sysNutPrec0; //!< Constants of planetary system nut/prec periods
      std::vector<Angle>m_sysNutPrec1; //!< Linear terms of planetary system nut/prec periods

      // The following scalars are used in the IAU equations to convert p_et to the appropriate time
      // units for calculating target body ra, dec, and w.  These need to be initialized in every 
      // constructor.
      //! Seconds per Julian century for scaling time in seconds
      static const double m_centScale;
      //! Seconds per day for scaling time in seconds to get target body w
      static const double m_dayScale;
  };
};

#endif

