struct affine3d {

   rotor3 rotor_;
   vector3 trans_;

   //
   // constructors
   //

   affine3d() = default;

   affine3d( const rotor3& rotor, const vector3& trans )
      : rotor_( rotor ), trans_( trans ) {
   }

   affine3d( const rotor3& rotor )
      : rotor_( rotor ), trans_() {
   }


   //
   // TODO figure out how to not do this...
   //
   vector3 map1( const vector3& xx ) const {
      vector3 translated = xx + trans_;
      vector3 rotated = rotor_.rotate( translated );
      return rotated;
   }

   //
   // apply the full affine transform to the given vector
   //
   vector3 map( const vector3& xx ) const {
      vector3 rotated = rotor_.rotate( xx );
      vector3 translated = rotated + trans_;
      return translated;
   }

};

//
// create an affine transformation from ECR coordinates to ENU
// coordinates where the origin of the ENU coordinate system is
// at the given geodetic point
//
static inline affine3d ecr_to_enu( const geodetic_t& lla ) {

   const vector3 center = lla_to_ecr( lla );

   const double lon = M_PI / 2.0 + lla.lon * deg_to_rad;
   const double lat = M_PI / 2.0 - lla.lat * deg_to_rad;

   // build a rotor for the z axis...

   vector3 zz( 0.0, 0.0, 1.0 );
   rotor3 zrot( zz, lon );

   // build a rotor for the x axis...

   vector3 xx( 1.0, 0.0, 0.0 );
   rotor3 xrot( xx, lat );

   // compose the rotors...

   rotor3 total_rot = xrot * zrot;
   // create the transform...

   affine3d affine( total_rot, -center );

   return affine;
}