Added Mollweide Projection. Fixes #4262

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/**

 * @file

 * $Revision: 1.4 $

 * $Date: 2008/05/09 18:49:25 $

 *

 *   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 & 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 "Mollweide.h"

#include <cfloat>

#include <cmath>

#include <iomanip>

#include "Constants.h"

#include "IException.h"

#include "TProjection.h"

#include "Pvl.h"

#include "PvlGroup.h"

#include "PvlKeyword.h"

using namespace std;

namespace Isis {

  /**

   * @brief Constructs a Mollweide object.

   *

   * @param label This argument must be a Label containing the proper mapping

   *              information as indicated in the Projection class. Additionally,

   *              the Mollweide projection requires the center longitude and the

   *              equatorial radius to be defined in the keyword CenterLongitude

   *              and EquatorialRadius.

   *

   * @param allowDefaults If set to false the constructor expects that a keyword

   *                      of CenterLongitude will be in the label. Otherwise it

   *                      will attempt to compute the center longitude using the

   *                      middle of the longitude range specified in the labels.

   *                      Defaults to false

   *

   * @throws IException

   */  

  Mollweide::Mollweide(Pvl &label, bool allowDefaults) :

      TProjection::TProjection(label) {

    try {

      // Try to read the mapping group

      PvlGroup &mapGroup = label.findGroup("Mapping", Pvl::Traverse);

      // Compute and write the default center longitude if allowed and

      // necessary

      if ((allowDefaults) && (!mapGroup.hasKeyword("CenterLongitude"))) {

        double lon = (m_minimumLongitude + m_maximumLongitude) / 2.0;

        mapGroup += PvlKeyword("CenterLongitude", toString(lon));

      }

      // Get the center longitude

      m_centerLongitude = mapGroup["CenterLongitude"];

      // convert to radians, adjust for longitude direction

      m_centerLongitude *= PI / 180.0;

      if (m_longitudeDirection == PositiveWest) m_centerLongitude *= -1.0;

    }

    catch(IException &e) {

      QString message = "Invalid label group [Mapping]";

      throw IException(e, IException::Io, message, _FILEINFO_);

    }

  }

  //! Destroys the Mollweide object

  Mollweide::~Mollweide() {

  }

  /**

   * @brief Compares two Projection objects to see if they are equal

   *

   * @param proj Projection object to do comparison on

   *

   * @return bool Returns true if the Projection objects are equal, and false if

   *              they are not

   */

  bool Mollweide::operator== (const Projection &proj) {

    if (!TProjection::operator==(proj)) return false;

    // dont do the below it is a recursive plunge

    //  if (TProjection::operator!=(proj)) return false;

    Mollweide *moll = (Mollweide *) &proj;

    if (moll->m_centerLongitude != m_centerLongitude) return false;

    return true;

  }

  /**

   * @brief Returns the name of the map projection, "Mollweide"

   *

   * @return QString Name of projection, "Mollweide"

   */

  QString Mollweide::Name() const {

    return "Mollweide";

  }

  /**

   * @brief Returns the version of the map projection

   * @return QString Version number

   */

  QString Mollweide::Version() const {

    return "1.0";

  }

  /**

   * @brief The Newton-Rapheson method is used to find an iterative solution for:

   *

   *       @f[ 2\theta+\sin(2\theta) = \pi \sin(\phi) @f]

   *

   * Where:

   *

   * @f{eqnarray*}

   * &\theta = \text{ The\;\;auxiliary\;\;variable\;\;being\;\;solved\;\;for.}\\

   * &\phi = \text{ The\;\;latitude\;\;(in radians).}\\

   * @f]

   *

   * This method achieves rapid convergence for small latitudes, and slower convergence near

   * the poles.

   *

   * @param phi The latitude value.

   * @param result  The final theta value.

   * @return @b bool Returns true if the method converges, and false if it does not.

   */

  bool Mollweide::newton_rapheson(double phi, double &result) {

    double dtheta = 1.0;

    int niter = 0;

    double theta[2];

    theta[0] = asin(2*phi/PI);

    theta[1]=0.0;

    //If this condition is too strict, a larger epsilon value than DBL_EPSILON

    //can be used to decrease the number of iterations.

    while (dtheta > DBL_EPSILON) {

      theta[1] = theta[0] - (2*theta[0]+sin(2*theta[0]) -(Isis::PI)*sin(phi))/(2+2*cos(theta[0]));

      dtheta = fabs(theta[1]-theta[0]);

      theta[0] = theta[1];

      niter++;

      if (niter > 15000000) {

        //cout << setprecision(10) << phi*(180/PI) << "," << niter << endl;

        return false;

      }

    }

    result = theta[1];

    //cout << setprecision(10) << phi*(180/PI) << "," << niter << endl;

    return true;

  }

  /**

   * @description This method is used to set the latitude/longitude (assumed to be of the

   * correct LatitudeType, LongitudeDirection, and LongitudeDomain. The Set

   * forces an attempted calculation of the projection X/Y values. This may or

   * may not be successful and a status is returned as such.

   *

   * @param lat Latitude value to project

   *

   * @param lon Longitude value to project

   *

   * @return @b bool Returns true if successful, false otherwise.

   */

  bool Mollweide::SetGround(const double lat, const double lon) {

    // Convert to radians   

    m_latitude = lat;

    m_longitude = lon;

    double theta;

    double latRadians = lat * PI / 180.0;

    double lonRadians = lon * PI / 180.0;

    if (m_longitudeDirection == PositiveWest) lonRadians *= -1.0;

    // Compute the coordinate

    double deltaLon = lonRadians - m_centerLongitude;

    if (newton_rapheson(latRadians,theta) ) {

      double x = (2*sqrt(2)/PI )*m_equatorialRadius*(deltaLon)*cos(theta);   

      double y = sqrt(2)*m_equatorialRadius*sin(theta);

      SetComputedXY(x, y);

      m_good = true;

      return m_good;

    }

    else {

      m_good = false;

      return m_good;

    }

  }

  /**

   * @brief This method is used to set the projection x/y. The Set forces an attempted

   * calculation of the corresponding latitude/longitude position. This may or

   * may not be successful and a status is returned as such.

   *

   * @param x X coordinate of the projection in units that are the same as the

   *          radii in the label

   *

   * @param y Y coordinate of the projection in units that are the same as the

   *          radii in the label

   *

   * @return @b bool Returns true if successful, false otherwise.

   */

  bool Mollweide::SetCoordinate(const double x, const double y) {

    // Save the coordinate

    SetXY(x, y);

    double theta = asin(y/(m_equatorialRadius*sqrt(2)));

    // Compute latitude and make sure it is not above 90

    m_latitude = asin((2*theta+sin(2*theta))/(Isis::PI));

    if (fabs(m_latitude) > HALFPI) {

      if (fabs(HALFPI - fabs(m_latitude)) > DBL_EPSILON) {

        m_good = false;

        return m_good;

      }

      else if (m_latitude < 0.0) {

        m_latitude = -HALFPI;

      }

      else {

        m_latitude = HALFPI;

      }

    }

    // Compute longitude

    double cosLat = cos(m_latitude);

    if (cosLat <= DBL_EPSILON) {

      m_longitude = m_centerLongitude;

    }

    else {

    m_longitude = m_centerLongitude+(Isis::PI)*GetX()/(2*m_equatorialRadius*sqrt(2)*cos(theta));

    }

    // Convert to degrees

    m_latitude *= 180.0 / PI;

    m_longitude *= 180.0 / PI;

    // Cleanup the longitude

    if (m_longitudeDirection == PositiveWest) m_longitude *= -1.0;

    // Our double precision is not good once we pass a certain magnitude of

    //   longitude. Prevent failures down the road by failing now.

    m_good = (fabs(m_longitude) < 1E10);

    return m_good;

  }

  /**

   * @description This method is used to determine the x/y range which completely covers the

   * area of interest specified by the lat/lon range. The latitude/longitude

   * range may be obtained from the labels. The purpose of this method is to

   * return the x/y range so it can be used to compute how large a map may need

   * to be. For example, how big a piece of paper is needed or how large of an

   * image needs to be created. The method may fail as indicated by its return

   * value.

   *

   * @param minX Minimum x projection coordinate which covers the latitude

   *             longitude range specified in the labels.

   *

   * @param maxX Maximum x projection coordinate which covers the latitude

   *             longitude range specified in the labels.

   *

   * @param minY Minimum y projection coordinate which covers the latitude

   *             longitude range specified in the labels.

   *

   * @param maxY Maximum y projection coordinate which covers the latitude

   *             longitude range specified in the labels.

   *

   * @return @b bool Returns true if successful, false otherwise.

   */

  bool Mollweide::XYRange(double &minX, double &maxX,

                           double &minY, double &maxY) {

    // Check the corners of the lat/lon range

    XYRangeCheck(m_minimumLatitude, m_minimumLongitude);

    XYRangeCheck(m_maximumLatitude, m_minimumLongitude);

    XYRangeCheck(m_minimumLatitude, m_maximumLongitude);

    XYRangeCheck(m_maximumLatitude, m_maximumLongitude);

    // If the latitude crosses the equator check there

    if ((m_minimumLatitude < 0.0) && (m_maximumLatitude > 0.0)) {

      XYRangeCheck(0.0, m_minimumLongitude);

      XYRangeCheck(0.0, m_maximumLongitude);

    }

    // Make sure everything is ordered

    if (m_minimumX >= m_maximumX) return false;

    if (m_minimumY >= m_maximumY) return false;

    // Return X/Y min/maxs

    minX = m_minimumX;

    maxX = m_maximumX;

    minY = m_minimumY;

    maxY = m_maximumY;

    return true;

  }

  /**

   * This function returns the keywords that this projection uses.

   *

   * @return @b PvlGroup The keywords that this projection uses.

   */

  PvlGroup Mollweide::Mapping()  {

    PvlGroup mapping = TProjection::Mapping();

    mapping += m_mappingGrp["CenterLongitude"];

    return mapping;

  }

  /**

   * This function returns the latitude keywords that this projection uses.

   *

   * @return @b PvlGroup The latitude keywords that this projection uses.

   */

  PvlGroup Mollweide::MappingLatitudes() {

    PvlGroup mapping = TProjection::MappingLatitudes();

    return mapping;

  }

  /**

   * This function returns the longitude keywords that this projection uses.

   *

   * @return @b PvlGroup The longitude keywords that this projection uses

   */

  PvlGroup Mollweide::MappingLongitudes() {

    PvlGroup mapping = TProjection::MappingLongitudes();

    mapping += m_mappingGrp["CenterLongitude"];

    return mapping;

  }

} // end namespace isis

/** 

 * This is the function that is called in order to instantiate a 

 * Mollweide object.

 *  

 * @param lab Cube labels with appropriate Mapping information.

 *  

 * @param allowDefaults Indicates whether CenterLongitude are allowed to 

 *                      be computed using the middle of the longitude

 *                      range specified in the labels.

 * 

 * @return @b Isis::Projection* Pointer to a Mollweide projection object.

 */

extern "C" Isis::TProjection *MollweidePlugin(Isis::Pvl &lab,

    bool allowDefaults) {

  return new Isis::Mollweide(lab, allowDefaults);

}

#ifndef Mollweide_h

#define Mollweide_h

/**

 * @file

 * $Revision: 1.3 $

 * $Date: 2008/05/09 18:49:25 $

 *

 *   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 & 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 "TProjection.h"

namespace Isis {

  class Pvl;

  class PvlGroup;

  /**

   * @description Mollweide Map Projection

   *

   * This class provides methods for the forward and inverse equations of a

   * Mollweide Equal-Area map projection (for a sphere).

   *  

   *  

   * The Mollweide projection is an equal-area, pseudo-cylindrical projection

   * presented by Carl B. Mollweide (1774-1825) of Halle, Germany in 1805.

   * The sphere is projected as an ellipse where it's Equator (the major axis)

   * is twice as long as as the prime meridian (the minor axis).  All other

   * meridians are elliptical arcs.   Combined with their opposite members, they form 

   * ellipses where they meet at the two poles.  The meridians 90 degrees to the east

   * and west of the prime meridian form a perfect circle.  

   *

   * The lines of latitude are straight lines, but they are not qquidistant from

   * each other.  The regions along the Equator are stretched 23 percent in

   * a north-south direction relative to the east-west directions.

   *

   * The only two points of the projection free of distortion are where the 

   * prime meridian crosses the latitudinal lines at 44 degrees, 44 minutes to the N and S.  

   * North and south of these latitudes, the stretching turns into compression near the poles.

   *

   * The Mollweide projection is usually applied at a small scale.

   *

   *  

   * Please see the Projection class for a full accounting of all the methods 

   * available. 

   *

   * @ingroup MapProjection

   *

   * @author 2016-08-24 Tyler Wilson

   *

   * @internal

   *

   */

  class Mollweide : public TProjection {

    public:

      Mollweide(Pvl &label, bool allowDefaults = false);

      ~Mollweide();

      bool operator== (const Projection &proj);

      QString Name() const;

      QString Version() const;

      bool newton_rapheson(double gamma, double &result);

      bool SetGround(const double lat, const double lon);

      bool SetCoordinate(const double x, const double y);     

      bool XYRange(double &minX, double &maxX, double &minY, double &maxY);

      PvlGroup Mapping();

      PvlGroup MappingLatitudes();

      PvlGroup MappingLongitudes();

    private:

      double m_centerLongitude; //!< The center longitude for the map projection

  };

};

#endif

Unit Test For the Mollweide Projection

Test missing center longitude keyword ...

**I/O ERROR** Invalid label group [Mapping].

**ERROR** PVL Keyword [CenterLongitude] does not exist in [Group = Mapping].

Test SetGround method ... 

Longitude = 90, while latitude is in the range [0:90]:

Latitude:	90.000000	XCoord:		0.000000	YCoord:		1.000000

Latitude:	85.000000	XCoord:		0.206844	YCoord:		0.978374

Latitude:	80.000000	XCoord:		0.325934	YCoord:		0.945393

Latitude:	75.000000	XCoord:		0.423159	YCoord:		0.906055

Latitude:	70.000000	XCoord:		0.507061	YCoord:		0.861910

Latitude:	65.000000	XCoord:		0.581112	YCoord:		0.813824

Latitude:	60.000000	XCoord:		0.647122	YCoord:		0.762386

Latitude:	55.000000	XCoord:		0.706170	YCoord:		0.708043

Latitude:	50.000000	XCoord:		0.758943	YCoord:		0.651158

Latitude:	45.000000	XCoord:		0.805907	YCoord:		0.592042

Latitude:	40.000000	XCoord:		0.847389	YCoord:		0.530973

Latitude:	35.000000	XCoord:		0.883620	YCoord:		0.468204

Latitude:	30.000000	XCoord:		0.914771	YCoord:		0.403973

Latitude:	25.000000	XCoord:		0.940965	YCoord:		0.338504

Latitude:	20.000000	XCoord:		0.962293	YCoord:		0.272015

Latitude:	15.000000	XCoord:		0.978822	YCoord:		0.204715

Latitude:	10.000000	XCoord:		0.990597	YCoord:		0.136811

Latitude:	5.000000	XCoord:		0.997651	YCoord:		0.068506

Latitude:	0.000000	XCoord:		1.000000	YCoord:		0.000000

Test SetCoordinate method ... 

Setting coordinate to (0.0,1.0)

Latitude:               90.000000

Longitude:              0.000000

Setting coordinate to (1.0,0.0)

Latitude:               0.000000

Longitude:              90.000000

Setting coordinate to (0.8059072939585296690978566,0.5920417498322624316742235)

Latitude:               45.000000

Longitude:              90.000000

Test XYRange method ... 

Minimum X:  -2.000000

Maximum X:  2.000000

Minimum Y:  -1.000000

Maximum Y:  1.000000

Test Name and comparision method ... 

Name:       Mollweide

operator==  1

Test default computation ... 

Group = Mapping

  EquatorialRadius   = 0.70710678118655

  PolarRadius        = 0.70710678118655

  LatitudeType       = Planetocentric

  LongitudeDirection = PositiveEast

  LongitudeDomain    = 180

  MinimumLatitude    = -90.0

  MaximumLatitude    = 90.0

  MinimumLongitude   = -180.0

  MaximumLongitude   = 180.0

  ProjectionName     = Mollweide

  CenterLongitude    = 0.0

End_Group

End

Testing Mapping() methods ... 

Mapping() = 

Group = Mapping

  ProjectionName     = Mollweide

  EquatorialRadius   = 0.70710678118655

  PolarRadius        = 0.70710678118655

  LatitudeType       = Planetocentric

  LongitudeDirection = PositiveEast

  LongitudeDomain    = 180

  MinimumLatitude    = -90.0

  MaximumLatitude    = 90.0

  MinimumLongitude   = -180.0

  MaximumLongitude   = 180.0

  CenterLongitude    = 0.0

End_Group

End

MappingLatitudes() = 

Group = Mapping

  MinimumLatitude = -90.0

  MaximumLatitude = 90.0

End_Group

End

MappingLongitudes() = 

Group = Mapping

  MinimumLongitude = -180.0

  MaximumLongitude = 180.0

  CenterLongitude  = 0.0

End_Group

End

Unit test was obtained from:

  Map Projections - A Working Manual

  USGS Professional Paper 1395 by John P. Snyder

  Pages 249-252

Group = Mollweide

  Library = Mollweide

  Routine = MollweidePlugin

  Keyword = CenterLongitude

EndGroup