srs.h

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#ifndef SQL_GIS_SRS_SRS_H_INCLUDED
#define SQL_GIS_SRS_SRS_H_INCLUDED
 
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//
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#include <assert.h>
#include <cmath>
#include <cstdint>
#include <sstream>
#include <string>
 
#include "sql/gis/srid.h"
 
namespace gis {
namespace srs {
 
/// Spatial reference system type.
enum class Srs_type : std::uint8_t { UNKNOWN = 0, PROJECTED, GEOGRAPHIC };
 
/// Projection method. Values are EPSG codes.
enum class Projection_type : std::uint32_t {
  UNKNOWN = 0,
  POPULAR_VISUALISATION_PSEUDO_MERCATOR = 1024,
  LAMBERT_AZIMUTHAL_EQUAL_AREA_SPHERICAL = 1027,
  EQUIDISTANT_CYLINDRICAL = 1028,
  EQUIDISTANT_CYLINDRICAL_SPHERICAL = 1029,
  KROVAK_NORTH_ORIENTATED = 1041,
  KROVAK_MODIFIED = 1042,
  KROVAK_MODIFIED_NORTH_ORIENTATED = 1043,
  LAMBERT_CONIC_CONFORMAL_2SP_MICHIGAN = 1051,
  COLOMBIA_URBAN = 1052,
  LAMBERT_CONIC_CONFORMAL_1SP = 9801,
  LAMBERT_CONIC_CONFORMAL_2SP = 9802,
  LAMBERT_CONIC_CONFORMAL_2SP_BELGIUM = 9803,
  MERCATOR_VARIANT_A = 9804,
  MERCATOR_VARIANT_B = 9805,
  CASSINI_SOLDNER = 9806,
  TRANSVERSE_MERCATOR = 9807,
  TRANSVERSE_MERCATOR_SOUTH_ORIENTATED = 9808,
  OBLIQUE_STEREOGRAPHIC = 9809,
  POLAR_STEREOGRAPHIC_VARIANT_A = 9810,
  NEW_ZEALAND_MAP_GRID = 9811,
  HOTINE_OBLIQUE_MERCATOR_VARIANT_A = 9812,
  LABORDE_OBLIQUE_MERCATOR = 9813,
  HOTINE_OBLIQUE_MERCATOR_VARIANT_B = 9815,
  TUNISIA_MINING_GRID = 9816,
  LAMBERT_CONIC_NEAR_CONFORMAL = 9817,
  AMERICAN_POLYCONIC = 9818,
  KROVAK = 9819,
  LAMBERT_AZIMUTHAL_EQUAL_AREA = 9820,
  ALBERS_EQUAL_AREA = 9822,
  TRANSVERSE_MERCATOR_ZONED_GRID_SYSTEM = 9824,
  LAMBERT_CONIC_CONFORMAL_WEST_ORIENTATED = 9826,
  BONNE_SOUTH_ORIENTATED = 9828,
  POLAR_STEREOGRAPHIC_VARIANT_B = 9829,
  POLAR_STEREOGRAPHIC_VARIANT_C = 9830,
  GUAM_PROJECTION = 9831,
  MODIFIED_AZIMUTHAL_EQUIDISTANT = 9832,
  HYPERBOLIC_CASSINI_SOLDNER = 9833,
  LAMBERT_CYLINDRICAL_EQUAL_AREA_SPHERICAL = 9834,
  LAMBERT_CYLINDRICAL_EQUAL_AREA = 9835
};
 
/// Coordinate axis direction.
enum class Axis_direction : std::uint8_t {
  UNSPECIFIED = 0,
  NORTH,
  SOUTH,
  EAST,
  WEST,
  OTHER
};
 
/// Superclass for all spatial reference systems.
class Spatial_reference_system {
 public:
  Spatial_reference_system() = default;
  Spatial_reference_system(const Spatial_reference_system &) = default;
  Spatial_reference_system(Spatial_reference_system &&) = default;
 
  virtual ~Spatial_reference_system() = default;
 
  /**
    Get the type of spatial reference system: projected, geometric,
    etc.
 
    @return SRS type
  */
  virtual Srs_type srs_type() const = 0;
 
  /**
    Clone the object.
 
    @return A new Spatial_reference_system object
  */
  virtual Spatial_reference_system *clone() = 0;
 
  /**
    Retrieve the axis direction of the spatial
    reference system.
 
    @param axis axis number, zero indexed
    @return Axis direction
  */
  virtual Axis_direction axis_direction(const int axis) const = 0;
 
  /**
    Retrieve the angular unit relative to radians.
 
    @return Conversion factor.
   */
  virtual double angular_unit() const = 0;
 
  /**
   * Retrieve how long the unit of the spatial reference system is in meters.
   *
   * @return Conversion factor
   */
  virtual double linear_unit() const = 0;
  /**
    Retrieve the prime meridian relative to Greenwich.
 
    The prime meridian is returned in the angular unit of the
    SRS. Positive numbers are East of Greenwich.
 
    @see angular_unit
 
    @return Prime meridian.
   */
  virtual double prime_meridian() const = 0;
 
  /// Checks if this SRS can be changed to another SRS without causing
  /// computational incompatibilities.
  ///
  /// This means checking that all values in the two SRSs that affect
  /// computations are the same. The syntax of the SRS definitions may still
  /// vary, e.g., by using different names or by having different authority
  /// codes.
  ///
  /// In some cases, e.g., unknown projection methods, we don't know how to
  /// compare the two SRSs. In that case, we fail by saying that the SRSs are
  /// not the same.
  ///
  /// The operation is not commutative. The SRS parameter is allowed to have a
  /// TOWGS84 specification even though this object doesn't. The opposite is not
  /// necessarily true. If this object lacks TOWGS84 information, transformation
  /// operations are forbidden on this SRS. Adding that possibility changes what
  /// computations are available, but it doesn't change the result of any
  /// computation that can currently be done.
  ///
  /// An SRS that is currently identified as WGS 84 may both add and remove
  /// TOWGS84 information as long as the parameters are all 0. Adding a
  /// non-all-zero TOWGS84 clause to a WGS 84 SRS is not allowed.
  ///
  /// @param srs The SRS to compare with.
  ///
  /// @retval true The two SRSs are semantically the same.
  /// @retval false The two SRSs are semantically different, or we don't know
  /// how to compare them.
  virtual bool can_be_modified_to(
      const Spatial_reference_system &srs) const = 0;
 
  /// Retrieve the proj4 parameter string.
  ///
  /// If the SRS can't be represented as a proj4 parameter string, an empty
  /// string is returned.
  ///
  /// @return Proj4 parameter string or empty string.
  virtual std::string proj4_parameters() const { return std::string(); }
 
  /// Checks if this SRS has valid Bursa Wolf parameters.
  ///
  /// @retval true Transformation parameters are specified.
  /// @retval false Transformation parameters are not specified.
  virtual bool has_towgs84() const = 0;
 
  /// Checks if this SRS is WGS 84 or a projection based on WGS 84.
  ///
  /// @retval true This SRS is WGS 84 or a projection of WGS 84.
  /// @retval false This SRS is neither WGS 84 or a projection of WGS 84.
  virtual bool is_wgs84_based() const = 0;
};
 
namespace wkt_parser {
struct Geographic_cs;
}  // namespace wkt_parser
 
/// A geographic (longitude-latitude) spatial reference system.
class Geographic_srs : public Spatial_reference_system {
 private:
  /// Semi-major axis of ellipsoid
  double m_semi_major_axis;
  /// Inverse flattening of ellipsoid
  double m_inverse_flattening;
  /// Bursa Wolf transformation parameters used to transform to WGS84.
  double m_towgs84[7];
  /// Longitude of the prime meridian relative to the Greenwich
  /// Meridian (measured in m_angular_unit). Positive values are East
  /// of Greenwich.
  double m_prime_meridian;
  /// Conversion factor for the angular unit relative to radians.
  double m_angular_unit;
  /// Direction of x and y axis, respectively.
  Axis_direction m_axes[2];
  /// Whether this SRS is WGS 84.
  bool m_is_wgs84;
 
 public:
  Geographic_srs()
      : m_semi_major_axis(NAN),
        m_inverse_flattening(NAN),
        m_prime_meridian(NAN),
        m_angular_unit(NAN),
        m_is_wgs84(false) {
    for (double &d : m_towgs84) d = NAN;
    for (Axis_direction &d : m_axes) d = Axis_direction::UNSPECIFIED;
  }
 
  Srs_type srs_type() const override { return Srs_type::GEOGRAPHIC; }
 
  Spatial_reference_system *clone() override {
    return new Geographic_srs(*this);
  }
 
  /**
    Initialize from parse tree.
 
    @param[in] srid Spatial reference system ID to use when reporting errors
    @param[in] g Parser output
 
    @retval true An error has occurred. The error has been flagged.
    @retval false Success
  */
  virtual bool init(srid_t srid, wkt_parser::Geographic_cs *g);
 
  bool has_towgs84() const override {
    // Either none or all parameters are specified.
    return !std::isnan(m_towgs84[0]);
  }
 
  bool is_wgs84_based() const override { return m_is_wgs84; }
 
  Axis_direction axis_direction(const int axis) const override {
    assert(axis >= 0 && axis <= 1);
    return m_axes[axis];
  }
 
  std::string partial_proj4_parameters() const;
 
  double semi_major_axis() const { return m_semi_major_axis; }
 
  double inverse_flattening() const { return m_inverse_flattening; }
 
  double linear_unit() const override { return 1.0; }
  double angular_unit() const override { return m_angular_unit; }
 
  double prime_meridian() const override { return m_prime_meridian; }
 
  bool can_be_modified_to(const Spatial_reference_system &srs) const override;
 
  std::string proj4_parameters() const override;
};
 
namespace wkt_parser {
struct Projected_cs;
}  // namespace wkt_parser
 
/// A projected spatial reference system.
class Projected_srs : public Spatial_reference_system {
 private:
  /// The geographic SRS this SRS is projected from.
  Geographic_srs m_geographic_srs;
  /// Converson factor for the linar unit relative to meters.
  double m_linear_unit;
  /// Direction of x and y axis, respectively.
  Axis_direction m_axes[2];
 
 protected:
  /// Checks if the parameters that are common to all projections can safely be
  /// modified to another SRS without causing computational differences.
  ///
  /// This function is called by can_be_modified_to() in subclasses to check if
  /// the common parameters match. Projected_srs::can_be_modified_to is abstract
  /// to avoid that subclasses forget to implement can_be_modified_to().
  ///
  /// @see Spatial_reference_system::can_be_modified_to
  ///
  /// @param srs The SRS to compare with.
  ///
  /// @retval true The common projection parameters are the same in both SRSs.
  /// @retval false The two SRSs differ in the common projection parameters.
  bool common_proj_parameters_can_be_modified_to(
      const Spatial_reference_system &srs) const;
 
 public:
  Projected_srs() : m_linear_unit(NAN) {
    for (Axis_direction &d : m_axes) d = Axis_direction::UNSPECIFIED;
  }
 
  Srs_type srs_type() const override { return Srs_type::PROJECTED; }
 
  /**
    Initialize from parse tree.
 
    @param[in] srid Spatial reference system ID to use when reporting errors
    @param[in] p Parser output
 
    @retval true An error has occurred. The error has been flagged.
    @retval false Success
  */
  virtual bool init(srid_t srid, wkt_parser::Projected_cs *p);
 
  /**
    Get the map projection method.
 
    @return Projection type
  */
  virtual Projection_type projection_type() const = 0;
 
  Axis_direction axis_direction(const int axis) const override {
    assert(axis >= 0 && axis <= 1);
    return m_axes[axis];
  }
 
  double linear_unit() const override { return m_linear_unit; }
  double angular_unit() const override {
    return m_geographic_srs.angular_unit();
  }
 
  double prime_meridian() const override {
    return m_geographic_srs.prime_meridian();
  }
 
  bool has_towgs84() const override { return m_geographic_srs.has_towgs84(); }
 
  bool is_wgs84_based() const override {
    return m_geographic_srs.is_wgs84_based();
  }
 
  std::string partial_proj4_parameters() const {
    // return the result in the units of the srs
    return m_geographic_srs.partial_proj4_parameters() +
           " +to_meter=" + std::to_string(linear_unit());
  }
};
 
/// A projected SRS of an unknown projection type.
///
/// This SRS can be used as any other projected SRS, but since the
/// projection type is unknown, geometries in this SRS can't be
/// transformed to other SRSs.
class Unknown_projected_srs : public Projected_srs {
 public:
  Spatial_reference_system *clone() override {
    return new Unknown_projected_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::UNKNOWN;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override {
    // We don't know how to compare this SRS with other SRSs.
    return false;
  }
};
 
/// A Popular Visualisation Pseudo Mercator projection (EPSG 1024).
class Popular_visualisation_pseudo_mercator_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Popular_visualisation_pseudo_mercator_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Popular_visualisation_pseudo_mercator_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::POPULAR_VISUALISATION_PSEUDO_MERCATOR;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Azimuthal Equal Area (Spherical) projection (EPSG 1027).
class Lambert_azimuthal_equal_area_spherical_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Lambert_azimuthal_equal_area_spherical_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_azimuthal_equal_area_spherical_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_AZIMUTHAL_EQUAL_AREA_SPHERICAL;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// An Equidistant Cylindrical projection (EPSG 1028).
class Equidistant_cylindrical_srs : public Projected_srs {
 private:
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Equidistant_cylindrical_srs()
      : m_standard_parallel_1(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Equidistant_cylindrical_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::EQUIDISTANT_CYLINDRICAL;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// An Equidistant Cylindrical (Spherical) projection (EPSG 1029).
class Equidistant_cylindrical_spherical_srs : public Projected_srs {
 private:
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Equidistant_cylindrical_spherical_srs()
      : m_standard_parallel_1(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Equidistant_cylindrical_spherical_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::EQUIDISTANT_CYLINDRICAL_SPHERICAL;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Krovak (North Orientated) projection (EPSG 1041).
class Krovak_north_orientated_srs : public Projected_srs {
 private:
  /// Latitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8811).
  double m_latitude_of_center;
  /// The meridian along which the northing axis increments and also
  /// across which parallels of latitude increment towards the north
  /// pole (EPSG 8833).
  double m_longitude_of_center;
  /// The rotation applied to spherical coordinates, measured on the
  /// conformal sphere in the plane of the meridian of origin (EPSG
  /// 1036).
  double m_azimuth;
  /// Latitude of the parallel on which the projection is based. This
  /// latitude is not geographic, but is defined on the conformal
  /// sphere AFTER its rotation to obtain the oblique aspect of the
  /// projection (EPSG 8818).
  double m_pseudo_standard_parallel_1;
  /// The factor by which the map grid is reduced or enlarged at the
  /// pseudo-standard parallel (EPSG 8819).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Krovak_north_orientated_srs()
      : m_latitude_of_center(NAN),
        m_longitude_of_center(NAN),
        m_azimuth(NAN),
        m_pseudo_standard_parallel_1(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Krovak_north_orientated_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::KROVAK_NORTH_ORIENTATED;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Krovak Modified projection (EPSG 1042).
class Krovak_modified_srs : public Projected_srs {
 private:
  /// Latitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8811).
  double m_latitude_of_center;
  /// The meridian along which the northing axis increments and also
  /// across which parallels of latitude increment towards the north
  /// pole (EPSG 8833).
  double m_longitude_of_center;
  /// The rotation applied to spherical coordinates, measured on the
  /// conformal sphere in the plane of the meridian of origin (EPSG
  /// 1036).
  double m_azimuth;
  /// Latitude of the parallel on which the projection is based. This
  /// latitude is not geographic, but is defined on the conformal
  /// sphere AFTER its rotation to obtain the oblique aspect of the
  /// projection (EPSG 8818).
  double m_pseudo_standard_parallel_1;
  /// The factor by which the map grid is reduced or enlarged at the
  /// pseudo-standard parallel (EPSG 8819).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
  /// The first ordinate of the evaluation point (EPSG 8617).
  double m_evaluation_point_ordinate_1;
  /// The second ordinate of the evaluation point(EPSG 8618).
  double m_evaluation_point_ordinate_2;
  /// Coefficient C1 used in polynomial transformation (EPSG 1026).
  double m_c1;
  /// Coefficient C2 used in polynomial transformation (EPSG 1027).
  double m_c2;
  /// Coefficient C3 used in polynomial transformation (EPSG 1028).
  double m_c3;
  /// Coefficient C4 used in polynomial transformation (EPSG 1029).
  double m_c4;
  /// Coefficient C5 used in polynomial transformation (EPSG 1030).
  double m_c5;
  /// Coefficient C6 used in polynomial transformation (EPSG 1031).
  double m_c6;
  /// Coefficient C7 used in polynomial transformation (EPSG 1032).
  double m_c7;
  /// Coefficient C8 used in polynomial transformation (EPSG 1033).
  double m_c8;
  /// Coefficient C9 used in polynomial transformation (EPSG 1034).
  double m_c9;
  /// Coefficient C10 used in polynomial transformation (EPSG 1035).
  double m_c10;
 
 public:
  Krovak_modified_srs()
      : m_latitude_of_center(NAN),
        m_longitude_of_center(NAN),
        m_azimuth(NAN),
        m_pseudo_standard_parallel_1(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN),
        m_evaluation_point_ordinate_1(NAN),
        m_evaluation_point_ordinate_2(NAN),
        m_c1(NAN),
        m_c2(NAN),
        m_c3(NAN),
        m_c4(NAN),
        m_c5(NAN),
        m_c6(NAN),
        m_c7(NAN),
        m_c8(NAN),
        m_c9(NAN),
        m_c10(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Krovak_modified_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::KROVAK_MODIFIED;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
};
 
/// A Krovak Modified (North Orientated) projection (EPSG 1043).
class Krovak_modified_north_orientated_srs : public Projected_srs {
 private:
  /// Latitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8811).
  double m_latitude_of_center;
  /// The meridian along which the northing axis increments and also
  /// across which parallels of latitude increment towards the north
  /// pole (EPSG 8833).
  double m_longitude_of_center;
  /// The rotation applied to spherical coordinates, measured on the
  /// conformal sphere in the plane of the meridian of origin (EPSG
  /// 1036).
  double m_azimuth;
  /// Latitude of the parallel on which the projection is based. This
  /// latitude is not geographic, but is defined on the conformal
  /// sphere AFTER its rotation to obtain the oblique aspect of the
  /// projection (EPSG 8818).
  double m_pseudo_standard_parallel_1;
  /// The factor by which the map grid is reduced or enlarged at the
  /// pseudo-standard parallel (EPSG 8819).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
  /// The first ordinate of the evaluation point (EPSG 8617).
  double m_evaluation_point_ordinate_1;
  /// The second ordinate of the evaluation point(EPSG 8618).
  double m_evaluation_point_ordinate_2;
  /// Coefficient C1 used in polynomial transformation (EPSG 1026).
  double m_c1;
  /// Coefficient C2 used in polynomial transformation (EPSG 1027).
  double m_c2;
  /// Coefficient C3 used in polynomial transformation (EPSG 1028).
  double m_c3;
  /// Coefficient C4 used in polynomial transformation (EPSG 1029).
  double m_c4;
  /// Coefficient C5 used in polynomial transformation (EPSG 1030).
  double m_c5;
  /// Coefficient C6 used in polynomial transformation (EPSG 1031).
  double m_c6;
  /// Coefficient C7 used in polynomial transformation (EPSG 1032).
  double m_c7;
  /// Coefficient C8 used in polynomial transformation (EPSG 1033).
  double m_c8;
  /// Coefficient C9 used in polynomial transformation (EPSG 1034).
  double m_c9;
  /// Coefficient C10 used in polynomial transformation (EPSG 1035).
  double m_c10;
 
 public:
  Krovak_modified_north_orientated_srs()
      : m_latitude_of_center(NAN),
        m_longitude_of_center(NAN),
        m_azimuth(NAN),
        m_pseudo_standard_parallel_1(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN),
        m_evaluation_point_ordinate_1(NAN),
        m_evaluation_point_ordinate_2(NAN),
        m_c1(NAN),
        m_c2(NAN),
        m_c3(NAN),
        m_c4(NAN),
        m_c5(NAN),
        m_c6(NAN),
        m_c7(NAN),
        m_c8(NAN),
        m_c9(NAN),
        m_c10(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Krovak_modified_north_orientated_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::KROVAK_MODIFIED_NORTH_ORIENTATED;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
};
 
/// A Lambert Conic Conformal (2SP Michigan) projection (EPSG 1051).
class Lambert_conic_conformal_2sp_michigan_srs : public Projected_srs {
 private:
  /// Latitude of the false origin, at which the false easting and
  /// northing is defined (EPSG 8821).
  double m_latitude_of_origin;
  /// Longitude (central meridian) of the false origin, at which the
  /// false easting and northing is defined (EPSG 8822).
  double m_longitude_of_origin;
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Latitude of the second parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8824).
  double m_standard_parallel_2;
  /// Easting value assigned to the false origin (EPSG 8826).
  double m_false_easting;
  /// Northing value assigned to the false origin (EPSG 8827).
  double m_false_northing;
  /// Ellipsoid scaling factor (EPSG 1038).
  double m_ellipsoid_scale_factor;
 
 public:
  Lambert_conic_conformal_2sp_michigan_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_standard_parallel_1(NAN),
        m_standard_parallel_2(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN),
        m_ellipsoid_scale_factor(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_conic_conformal_2sp_michigan_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CONIC_CONFORMAL_2SP_MICHIGAN;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Colombia Urban projection(EPSG 1052).
class Colombia_urban_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
  /// The height of the projection plane at its origin (EPSG 1039).
  double m_projection_plane_height_at_origin;
 
 public:
  Colombia_urban_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN),
        m_projection_plane_height_at_origin(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Colombia_urban_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::COLOMBIA_URBAN;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Conic Conformal (1SP) projection, alias Lambert Conic
/// Conformal or LCC (EPSG 9801).
class Lambert_conic_conformal_1sp_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Lambert_conic_conformal_1sp_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_conic_conformal_1sp_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CONIC_CONFORMAL_1SP;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Conic Conformal (2SP) projection, alias Lambert Conic
/// Conformal or LCC (EPSG 9802).
class Lambert_conic_conformal_2sp_srs : public Projected_srs {
 private:
  /// Latitude of the false origin, at which the false easting and
  /// northing is defined (EPSG 8821).
  double m_latitude_of_origin;
  /// Longitude (central meridian) of the false origin, at which the
  /// false easting and northing is defined (EPSG 8822).
  double m_longitude_of_origin;
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Latitude of the second parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8824).
  double m_standard_parallel_2;
  /// Easting value assigned to the false origin (EPSG 8826).
  double m_false_easting;
  /// Northing value assigned to the false origin (EPSG 8827).
  double m_false_northing;
 
 public:
  Lambert_conic_conformal_2sp_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_standard_parallel_1(NAN),
        m_standard_parallel_2(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_conic_conformal_2sp_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CONIC_CONFORMAL_2SP;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Conic Conformal (2SP Belgium) projection (EPSG 9803).
class Lambert_conic_conformal_2sp_belgium_srs : public Projected_srs {
 private:
  /// Latitude of the false origin, at which the false easting and
  /// northing is defined (EPSG 8821).
  double m_latitude_of_origin;
  /// Longitude (central meridian) of the false origin, at which the
  /// false easting and northing is defined (EPSG 8822).
  double m_longitude_of_origin;
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Latitude of the second parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8824).
  double m_standard_parallel_2;
  /// Easting value assigned to the false origin (EPSG 8826).
  double m_false_easting;
  /// Northing value assigned to the false origin (EPSG 8827).
  double m_false_northing;
 
 public:
  Lambert_conic_conformal_2sp_belgium_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_standard_parallel_1(NAN),
        m_standard_parallel_2(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_conic_conformal_2sp_belgium_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CONIC_CONFORMAL_2SP_BELGIUM;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Mercator (variant A) projection, alias Mercator (EPSG 9804).
class Mercator_variant_a_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Mercator_variant_a_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Mercator_variant_a_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::MERCATOR_VARIANT_A;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Mercator (variant B) projection, alias Mercator (EPSG 9805).
class Mercator_variant_b_srs : public Projected_srs {
 private:
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Mercator_variant_b_srs()
      : m_standard_parallel_1(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Mercator_variant_b_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::MERCATOR_VARIANT_B;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Cassini-Soldner projection, alias Cassini (EPSG 9806).
class Cassini_soldner_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Cassini_soldner_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Cassini_soldner_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::CASSINI_SOLDNER;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Transverse Mercator projection, alias Gauss-Boaga, Gauss-Krüger
/// or TM (EPSG 9807).
class Transverse_mercator_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Transverse_mercator_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Transverse_mercator_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::TRANSVERSE_MERCATOR;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Transverse Mercator (South Orientated) projection, alias
/// Gauss-Conform (EPSG 9808).
class Transverse_mercator_south_orientated_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Transverse_mercator_south_orientated_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Transverse_mercator_south_orientated_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::TRANSVERSE_MERCATOR_SOUTH_ORIENTATED;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// An Oblique stereographic projection, alias Double stereographic
/// (EPSG 9809).
class Oblique_stereographic_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Oblique_stereographic_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Oblique_stereographic_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::OBLIQUE_STEREOGRAPHIC;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Polar Stereographic (variant A) projection (EPSG 9810).
class Polar_stereographic_variant_a_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Polar_stereographic_variant_a_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Polar_stereographic_variant_a_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::POLAR_STEREOGRAPHIC_VARIANT_A;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A New Zealand Map Grid projection (EPSG 9811).
class New_zealand_map_grid_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  New_zealand_map_grid_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new New_zealand_map_grid_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::NEW_ZEALAND_MAP_GRID;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Hotine Oblique Mercator (variant A) projection, alias Rectified
/// skew orthomorphic (EPSG 9812).
class Hotine_oblique_mercator_variant_a_srs : public Projected_srs {
 private:
  /// Latitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8811).
  double m_latitude_of_center;
  /// Longitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8812).
  double m_longitude_of_center;
  /// Direction east of north of the great circle which is the central
  /// line (EPSG 8813).
  double m_azimuth;
  /// Angle at the natural origin through which the natural SRS is
  /// rotated to make the projection north axis parallel with true
  /// north (EPSG 8814).
  double m_rectified_grid_angle;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8815).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Hotine_oblique_mercator_variant_a_srs()
      : m_latitude_of_center(NAN),
        m_longitude_of_center(NAN),
        m_azimuth(NAN),
        m_rectified_grid_angle(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Hotine_oblique_mercator_variant_a_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::HOTINE_OBLIQUE_MERCATOR_VARIANT_A;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Laborde Oblique Mercator projection (EPSG 9813).
class Laborde_oblique_mercator_srs : public Projected_srs {
 private:
  /// Latitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8811).
  double m_latitude_of_center;
  /// Longitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8812).
  double m_longitude_of_center;
  /// Direction east of north of the great circle which is the central
  /// line (EPSG 8813).
  double m_azimuth;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8815).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Laborde_oblique_mercator_srs()
      : m_latitude_of_center(NAN),
        m_longitude_of_center(NAN),
        m_azimuth(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Laborde_oblique_mercator_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LABORDE_OBLIQUE_MERCATOR;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Hotine Oblique Mercator (variant B) projection, alias Rectified
/// skew orthomorphic (EPSG 9815).
class Hotine_oblique_mercator_variant_b_srs : public Projected_srs {
 private:
  /// Latitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8811).
  double m_latitude_of_center;
  /// Longitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8812).
  double m_longitude_of_center;
  /// Direction east of north of the great circle which is the central
  /// line (EPSG 8813).
  double m_azimuth;
  /// Angle at the natural origin through which the natural SRS is
  /// rotated to make the projection north axis parallel with true
  /// north (EPSG 8814).
  double m_rectified_grid_angle;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8815).
  double m_scale_factor;
  /// Easting value assigned to the projection center (EPSG 8816).
  double m_false_easting;
  /// Northing value assigned to the projection center (EPSG 8817).
  double m_false_northing;
 
 public:
  Hotine_oblique_mercator_variant_b_srs()
      : m_latitude_of_center(NAN),
        m_longitude_of_center(NAN),
        m_azimuth(NAN),
        m_rectified_grid_angle(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Hotine_oblique_mercator_variant_b_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::HOTINE_OBLIQUE_MERCATOR_VARIANT_B;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Tunisia Mining Grid projection (EPSG 9816).
class Tunisia_mining_grid_srs : public Projected_srs {
 private:
  /// Latitude of the false origin, at which the false easting and
  /// northing is defined (EPSG 8821).
  double m_latitude_of_origin;
  /// Longitude (central meridian) of the false origin, at which the
  /// false easting and northing is defined (EPSG 8822).
  double m_longitude_of_origin;
  /// Easting value assigned to the false origin (EPSG 8826).
  double m_false_easting;
  /// Northing value assigned to the false origin (EPSG 8827).
  double m_false_northing;
 
 public:
  Tunisia_mining_grid_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Tunisia_mining_grid_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::TUNISIA_MINING_GRID;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
};
 
/// A Lambert Conic Near-Conformal projection (EPSG 9817).
class Lambert_conic_near_conformal_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Lambert_conic_near_conformal_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_conic_near_conformal_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CONIC_NEAR_CONFORMAL;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// An American Polyconic projection, alias Polyconic (EPSG 9818).
class American_polyconic_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  American_polyconic_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new American_polyconic_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::AMERICAN_POLYCONIC;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Krovak projection (EPSG 9819).
class Krovak_srs : public Projected_srs {
 private:
  /// Latitude of the point at which the azimuth of the central line
  /// is defined (EPSG 8811).
  double m_latitude_of_center;
  /// The meridian along which the northing axis increments and also
  /// across which parallels of latitude increment towards the north
  /// pole (EPSG 8833).
  double m_longitude_of_center;
  /// The rotation applied to spherical coordinates, measured on the
  /// conformal sphere in the plane of the meridian of origin (EPSG
  /// 1036).
  double m_azimuth;
  /// Latitude of the parallel on which the projection is based. This
  /// latitude is not geographic, but is defined on the conformal
  /// sphere AFTER its rotation to obtain the oblique aspect of the
  /// projection (EPSG 8818).
  double m_pseudo_standard_parallel_1;
  /// The factor by which the map grid is reduced or enlarged at the
  /// pseudo-standard parallel (EPSG 8819).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Krovak_srs()
      : m_latitude_of_center(NAN),
        m_longitude_of_center(NAN),
        m_azimuth(NAN),
        m_pseudo_standard_parallel_1(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override { return new Krovak_srs(*this); }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::KROVAK;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Azimuthal Equal Area projection, alias Lambert Equal
/// Area or LAEA (EPSG 9820).
class Lambert_azimuthal_equal_area_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Lambert_azimuthal_equal_area_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_azimuthal_equal_area_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_AZIMUTHAL_EQUAL_AREA;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// An Albers Equal Area projection, alias Albers (EPSG 9822).
class Albers_equal_area_srs : public Projected_srs {
 private:
  /// Latitude of the false origin, at which the false easting and
  /// northing is defined (EPSG 8821).
  double m_latitude_of_origin;
  /// Longitude (central meridian) of the false origin, at which the
  /// false easting and northing is defined (EPSG 8822).
  double m_longitude_of_origin;
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Latitude of the second parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8824).
  double m_standard_parallel_2;
  /// Easting value assigned to the false origin (EPSG 8826).
  double m_false_easting;
  /// Northing value assigned to the false origin (EPSG 8827).
  double m_false_northing;
 
 public:
  Albers_equal_area_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_standard_parallel_1(NAN),
        m_standard_parallel_2(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Albers_equal_area_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::ALBERS_EQUAL_AREA;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Transverse Mercator Zoned Grid System projection (EPSG 9824).
class Transverse_mercator_zoned_grid_system_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// The longitude of the western limit of the first zone (EPSG
  /// 8830).
  double m_initial_longitude;
  /// The longitude width of a zone (EPSG 8831).
  double m_zone_width;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Transverse_mercator_zoned_grid_system_srs()
      : m_latitude_of_origin(NAN),
        m_initial_longitude(NAN),
        m_zone_width(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Transverse_mercator_zoned_grid_system_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::TRANSVERSE_MERCATOR_ZONED_GRID_SYSTEM;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Conic Conformal (West Orientated) projection (EPSG 9826).
class Lambert_conic_conformal_west_orientated_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Multiplier for reducing a distance obtained from a map to the
  /// actual distance on the datum of the map (EPSG 8805).
  double m_scale_factor;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Lambert_conic_conformal_west_orientated_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_scale_factor(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_conic_conformal_west_orientated_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CONIC_CONFORMAL_WEST_ORIENTATED;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
};
 
/// A Bonne (South Orientated) projection (EPSG 9828).
class Bonne_south_orientated_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Bonne_south_orientated_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Bonne_south_orientated_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::BONNE_SOUTH_ORIENTATED;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Polar Stereographic (variant B) projection (EPSG 9829).
class Polar_stereographic_variant_b_srs : public Projected_srs {
 private:
  /// The parallel on which the scale factor is defined to be unity
  /// (EPSG 8832).
  double m_standard_parallel;
  /// The meridian along which the northing axis increments and also
  /// across which parallels of latitude increment towards the north
  /// pole (EPSG 8833).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Polar_stereographic_variant_b_srs()
      : m_standard_parallel(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Polar_stereographic_variant_b_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::POLAR_STEREOGRAPHIC_VARIANT_B;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Polar Stereographic (variant C) projection (EPSG 9830).
class Polar_stereographic_variant_c_srs : public Projected_srs {
 private:
  /// The parallel on which the scale factor is defined to be unity
  /// (EPSG 8832).
  double m_standard_parallel;
  /// The meridian along which the northing axis increments and also
  /// across which parallels of latitude increment towards the north
  /// pole (EPSG 8833).
  double m_longitude_of_origin;
  /// Easting value assigned to the false origin (EPSG 8826).
  double m_false_easting;
  /// Northing value assigned to the false origin (EPSG 8827).
  double m_false_northing;
 
 public:
  Polar_stereographic_variant_c_srs()
      : m_standard_parallel(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Polar_stereographic_variant_c_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::POLAR_STEREOGRAPHIC_VARIANT_C;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Guam Projection projection (EPSG 9831).
class Guam_projection_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Guam_projection_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Guam_projection_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::GUAM_PROJECTION;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Modified Azimuthal Equidistant projection (EPSG 9832).
class Modified_azimuthal_equidistant_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Modified_azimuthal_equidistant_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Modified_azimuthal_equidistant_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::MODIFIED_AZIMUTHAL_EQUIDISTANT;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Hyperbolic Cassini-Soldner projection (EPSG 9833).
class Hyperbolic_cassini_soldner_srs : public Projected_srs {
 private:
  /// Latitude chosen as origin of y-coordinates (EPSG 8801).
  double m_latitude_of_origin;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Hyperbolic_cassini_soldner_srs()
      : m_latitude_of_origin(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Hyperbolic_cassini_soldner_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::HYPERBOLIC_CASSINI_SOLDNER;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Cylindrical Equal Area (Spherical) projection (EPSG
/// 9834).
class Lambert_cylindrical_equal_area_spherical_srs : public Projected_srs {
 private:
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Lambert_cylindrical_equal_area_spherical_srs()
      : m_standard_parallel_1(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_cylindrical_equal_area_spherical_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CYLINDRICAL_EQUAL_AREA_SPHERICAL;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/// A Lambert Cylindrical Equal Area projection (EPSG 9835).
class Lambert_cylindrical_equal_area_srs : public Projected_srs {
 private:
  /// Latitude of the first parallel of intersection between the cone
  /// and the ellipsoid (EPSG 8823).
  double m_standard_parallel_1;
  /// Longitude chosen as origin of x-coordinates (central meridian)
  /// (EPSG 8802).
  double m_longitude_of_origin;
  /// Value added to x-coordinates (EPSG 8806).
  double m_false_easting;
  /// Value added to y-coordinates (EPSG 8807).
  double m_false_northing;
 
 public:
  Lambert_cylindrical_equal_area_srs()
      : m_standard_parallel_1(NAN),
        m_longitude_of_origin(NAN),
        m_false_easting(NAN),
        m_false_northing(NAN) {}
 
  Spatial_reference_system *clone() override {
    return new Lambert_cylindrical_equal_area_srs(*this);
  }
 
  bool init(srid_t srid, wkt_parser::Projected_cs *p) override;
 
  Projection_type projection_type() const override {
    return Projection_type::LAMBERT_CYLINDRICAL_EQUAL_AREA;
  }
 
  bool can_be_modified_to(const Spatial_reference_system &) const override;
 
  std::string proj4_parameters() const override;
};
 
/**
  Parse an SRS definition WKT string.
 
  The parser understands WKT as defined by the <horz cs>
  specification in OGC 01-009.
 
  If the string is successfully parsed, a new SRS object will be
  allocated on the heap. The caller is responsible for deleting it.
 
  If an error occurs, no object is allocated.
 
  @param[in] srid Spatial reference system ID to use when reporting errors
  @param[in] begin Start of WKT string in UTF-8
  @param[in] end End of WKT string (one past the last byte)
  @param[out] result Spatial reference system
 
  @retval true An error has occurred
  @retval false Success
*/
bool parse_wkt(srid_t srid, const char *begin, const char *end,
               Spatial_reference_system **result);
 
}  // namespace srs
}  // namespace gis
 
#endif  // SQL_GIS_SRS_SRS_H_INCLUDED