Added alpha-beta projection to cubed sphere.

src/atlas/CMakeLists.txt

@@ -721,6 +721,7 @@ util/Rotation.h
 util/Registry.h
 util/SphericalPolygon.cc
 util/SphericalPolygon.h
+util/SquareMatrix.h
 util/UnitSphere.h
 util/vector.h
 util/VectorOfAbstract.h

src/atlas/grid/CubedSphereGrid.h

@@ -295,9 +295,19 @@ class CubedSphereGrid : public Grid {
     // Return the size of the cubed sphere grid, where N is the number of grid boxes along the edge of a tile
     inline int N() const { return grid_->N(); }
 
-    // Return the number of tiles
+    /// @brief return tiles object.
     inline atlas::grid::CubedSphereTiles tiles() const { return grid_->tiles(); }
 
+    /// @brief return cubed sphere projection object.
+    inline const projection::detail::CubedSphereProjectionBase& cubedSphereProjection() const {
+
+        const auto projPtr =
+            dynamic_cast<const projection::detail::CubedSphereProjectionBase*>
+            (projection().get());
+
+        return *projPtr;
+    };
+
     temporary::IterateTIJ tij() const { return temporary::IterateTIJ(*grid_); }
 
     const std::string& stagger() const { return grid_->stagger(); }

src/atlas/grid/Tiles.cc

@@ -72,5 +72,13 @@ std::ostream& operator<<(std::ostream& os, const CubedSphereTiles& t) {
     return os;
 }
 
+const PointXY& CubedSphereTiles::tileCentre(size_t t) const {
+    return get()->tileCentre(t);
+}
+
+const JacobianXY& CubedSphereTiles::tileJacobian(size_t t) const {
+    return get()->tileJacobian(t);
+}
+
 }  // namespace grid
 }  // namespace atlas

src/atlas/grid/Tiles.h

@@ -28,6 +28,7 @@ class Hash;
 //---------------------------------------------------------------------------------------------------------------------
 
 namespace atlas {
+class JacobianXY;
 class PointXY;
 class PointLonLat;
 
@@ -85,6 +86,13 @@ class CubedSphereTiles : DOXYGEN_HIDE(public util::ObjectHandle<atlas::grid::det
     // a "diagonal" extension over corners of the cube.
     atlas::PointXY tileCubePeriodicity(const atlas::PointXY& xyExtended, const atlas::idx_t tile) const;
 
+    /// @brief Return the position of the tile centre in xy space.
+    const PointXY& tileCentre(size_t t) const;
+
+    /// @brief Return the Jacobian of xy with respect to the curvilinear
+    ///        coordinates of the tile.
+    const JacobianXY& tileJacobian(size_t t) const;
+
 private:
     /// Output to stream
     void print(std::ostream&) const;

src/atlas/grid/detail/tiles/FV3Tiles.cc

@@ -453,6 +453,15 @@ void FV3CubedSphereTiles::print(std::ostream& os) const {
 }
 
 
+const PointXY& FV3CubedSphereTiles::tileCentre(size_t t) const {
+    throw_NotImplemented("tileCentre not implemented for FV3Tiles", Here());
+}
+
+const JacobianXY& FV3CubedSphereTiles::tileJacobian(size_t t) const {
+    throw_NotImplemented("tileJacobian not implemented for FV3Tiles", Here());;
+}
+
+
 namespace {
 static CubedSphereTilesBuilder<FV3CubedSphereTiles> register_builder(FV3CubedSphereTiles::static_type());
 }

src/atlas/grid/detail/tiles/FV3Tiles.h

@@ -46,6 +46,11 @@ class FV3CubedSphereTiles : public CubedSphereTiles {
 
     virtual void print(std::ostream&) const override;
 
+    virtual const PointXY& tileCentre(size_t t) const override;
+
+    virtual const JacobianXY& tileJacobian(size_t t) const override;
+
+
 private:
 };