diff --git a/src/Geometry/axistensors.jl b/src/Geometry/axistensors.jl
index b1ac9e8326..127814eed1 100644
--- a/src/Geometry/axistensors.jl
+++ b/src/Geometry/axistensors.jl
@@ -286,13 +286,16 @@ const Axis2TensorOrAdj{T, A, S} =
 
 # based on 1st dimension
 const Covariant2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{CovariantAxis, AbstractAxis}}
-const Contravariant2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{ContravariantAxis, AbstractAxis}}
+    Axis2Tensor{T, A, S} where {T, A <: Tuple{CovariantAxis, AbstractAxis}, S}
+const Contravariant2Tensor{T, A, S} = Axis2Tensor{
+    T,
+    A,
+    S,
+} where {T, A <: Tuple{ContravariantAxis, AbstractAxis}, S}
 const Cartesian2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{CartesianAxis, AbstractAxis}}
+    Axis2Tensor{T, A, S} where {T, A <: Tuple{CartesianAxis, AbstractAxis}, S}
 const Local2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{LocalAxis, AbstractAxis}}
+    Axis2Tensor{T, A, S} where {T, A <: Tuple{LocalAxis, AbstractAxis}, S}
 
 const CovariantTensor = Union{CovariantVector, Covariant2Tensor}
 const ContravariantTensor = Union{ContravariantVector, Contravariant2Tensor}
@@ -477,6 +480,9 @@ end
     x
 end
 
+#= Set `assert_exact_transform() = true` for debugging=#
+assert_exact_transform() = false
+
 @generated function _transform(
     ato::Ato,
     x::Axis2Tensor{T, Tuple{Afrom, A2}},
@@ -487,12 +493,14 @@ end
 } where {Ito, Ifrom, J, T}
     N = length(Ifrom)
     M = length(J)
-    errcond = false
-    for n in 1:N
-        i = Ifrom[n]
-        if i ∉ Ito
-            for m in 1:M
-                errcond = :($errcond || x[$n, $m] != zero(T))
+    if assert_exact_transform()
+        errcond = false
+        for n in 1:N
+            i = Ifrom[n]
+            if i ∉ Ito
+                for m in 1:M
+                    errcond = :($errcond || x[$n, $m] != zero(T))
+                end
             end
         end
     end
@@ -511,8 +519,10 @@ end
     end
     quote
         Base.@_propagate_inbounds_meta
-        if $errcond
-            throw(InexactError(:transform, Ato, x))
+        if assert_exact_transform()
+            if $errcond
+                throw(InexactError(:transform, Ato, x))
+            end
         end
         @inbounds Axis2Tensor(
             (ato, axes(x, 2)),
@@ -550,11 +560,11 @@ end
     ))
 end
 
-@inline transform(ato::CovariantAxis, v::CovariantTensor) = _transform(ato, v)
+@inline transform(ato::CovariantAxis, v::CovariantTensor) = _project(ato, v)
 @inline transform(ato::ContravariantAxis, v::ContravariantTensor) =
-    _transform(ato, v)
-@inline transform(ato::CartesianAxis, v::CartesianTensor) = _transform(ato, v)
-@inline transform(ato::LocalAxis, v::LocalTensor) = _transform(ato, v)
+    _project(ato, v)
+@inline transform(ato::CartesianAxis, v::CartesianTensor) = _project(ato, v)
+@inline transform(ato::LocalAxis, v::LocalTensor) = _project(ato, v)
 
 @inline project(ato::CovariantAxis, v::CovariantTensor) = _project(ato, v)
 @inline project(ato::ContravariantAxis, v::ContravariantTensor) =
diff --git a/src/Geometry/conversions.jl b/src/Geometry/conversions.jl
index c184c36c56..db1fc6e5ca 100644
--- a/src/Geometry/conversions.jl
+++ b/src/Geometry/conversions.jl
@@ -34,13 +34,13 @@ LocalVector(
 (::Type{<:ContravariantVector{<:Any, I}})(
     u::ContravariantVector,
     ::LocalGeometry,
-) where {I} = transform(ContravariantAxis{I}(), u)
+) where {I} = project(ContravariantAxis{I}(), u)
 
 (::Type{<:ContravariantVector{<:Any, I}})(
     u::AxisVector,
     local_geometry::LocalGeometry,
 ) where {I} =
-    transform(ContravariantAxis{I}(), ContravariantVector(u, local_geometry))
+    project(ContravariantAxis{I}(), ContravariantVector(u, local_geometry))
 
 (::Type{<:CovariantVector{<:Any, I}})(
     u::CovariantVector{<:Any, I},
@@ -50,12 +50,12 @@ LocalVector(
 (::Type{<:CovariantVector{<:Any, I}})(
     u::CovariantVector,
     ::LocalGeometry,
-) where {I} = transform(CovariantAxis{I}(), u)
+) where {I} = project(CovariantAxis{I}(), u)
 
 (::Type{<:CovariantVector{<:Any, I}})(
     u::AxisVector,
     local_geometry::LocalGeometry,
-) where {I} = transform(CovariantAxis{I}(), CovariantVector(u, local_geometry))
+) where {I} = project(CovariantAxis{I}(), CovariantVector(u, local_geometry))
 
 (::Type{<:LocalVector{<:Any, I}})(
     u::LocalVector{<:Any, I},
@@ -63,54 +63,48 @@ LocalVector(
 ) where {I} = u
 
 (::Type{<:LocalVector{<:Any, I}})(u::LocalVector, ::LocalGeometry) where {I} =
-    transform(LocalAxis{I}(), u)
+    project(LocalAxis{I}(), u)
 
 (::Type{<:LocalVector{<:Any, I}})(
     u::AxisVector,
     local_geometry::LocalGeometry,
-) where {I} = transform(LocalAxis{I}(), LocalVector(u, local_geometry))
+) where {I} = project(LocalAxis{I}(), LocalVector(u, local_geometry))
 
 # Generic N-axis conversion functions,
 # Convert to specific local geometry dimension then convert vector type
 LocalVector(u::CovariantVector, local_geometry::LocalGeometry{I}) where {I} =
-    transform(LocalAxis{I}(), transform(CovariantAxis{I}(), u), local_geometry)
+    project(LocalAxis{I}(), project(CovariantAxis{I}(), u), local_geometry)
 
 LocalVector(
     u::ContravariantVector,
     local_geometry::LocalGeometry{I},
-) where {I} = transform(
-    LocalAxis{I}(),
-    transform(ContravariantAxis{I}(), u),
-    local_geometry,
-)
+) where {I} =
+    project(LocalAxis{I}(), project(ContravariantAxis{I}(), u), local_geometry)
 
 CovariantVector(u::LocalVector, local_geometry::LocalGeometry{I}) where {I} =
-    transform(CovariantAxis{I}(), transform(LocalAxis{I}(), u), local_geometry)
+    project(CovariantAxis{I}(), project(LocalAxis{I}(), u), local_geometry)
 
 CovariantVector(
     u::ContravariantVector,
     local_geometry::LocalGeometry{I},
-) where {I} = transform(
+) where {I} = project(
     CovariantAxis{I}(),
-    transform(ContravariantAxis{I}(), u),
+    project(ContravariantAxis{I}(), u),
     local_geometry,
 )
 
 ContravariantVector(
     u::LocalVector,
     local_geometry::LocalGeometry{I},
-) where {I} = transform(
-    ContravariantAxis{I}(),
-    transform(LocalAxis{I}(), u),
-    local_geometry,
-)
+) where {I} =
+    project(ContravariantAxis{I}(), project(LocalAxis{I}(), u), local_geometry)
 
 ContravariantVector(
     u::CovariantVector,
     local_geometry::LocalGeometry{I},
-) where {I} = transform(
+) where {I} = project(
     ContravariantAxis{I}(),
-    transform(CovariantAxis{I}(), u),
+    project(CovariantAxis{I}(), u),
     local_geometry,
 )
 
@@ -172,7 +166,7 @@ Base.@propagate_inbounds Jcontravariant3(
 )
     u₁, v, u₃ = components(vector)
     vector2 = Covariant13Vector(u₁, u₃)
-    u, w = components(transform(LocalAxis{(1, 3)}(), vector2, local_geometry))
+    u, w = components(project(LocalAxis{(1, 3)}(), vector2, local_geometry))
     return UVWVector(u, v, w)
 end
 @inline function contravariant1(
@@ -181,7 +175,7 @@ end
 )
     u₁, _, u₃ = components(vector)
     vector2 = Covariant13Vector(u₁, u₃)
-    return transform(Contravariant13Axis(), vector2, local_geometry).u¹
+    return project(Contravariant13Axis(), vector2, local_geometry).u¹
 end
 @inline function contravariant3(
     vector::CovariantVector{<:Any, (1, 2)},
@@ -189,7 +183,7 @@ end
 )
     u₁, _ = components(vector)
     vector2 = Covariant13Vector(u₁, zero(u₁))
-    return transform(Contravariant13Axis(), vector2, local_geometry).u³
+    return project(Contravariant13Axis(), vector2, local_geometry).u³
 end
 @inline function ContravariantVector(
     vector::CovariantVector{<:Any, (1, 2)},
@@ -197,9 +191,9 @@ end
 )
     u₁, v = components(vector)
     vector2 = Covariant1Vector(u₁)
-    vector3 = transform(
+    vector3 = project(
         ContravariantAxis{(1, 3)}(),
-        transform(CovariantAxis{(1, 3)}(), vector2),
+        project(CovariantAxis{(1, 3)}(), vector2),
         local_geometry,
     )
     u¹, u³ = components(vector3)
@@ -333,6 +327,7 @@ for op in (:transform, :project)
         )
 
         # Covariant <-> Contravariant
+        #=
         @inline $op(
             ax::ContravariantAxis,
             v::CovariantTensor,
@@ -343,6 +338,7 @@ for op in (:transform, :project)
             local_geometry.∂ξ∂x' *
             $op(dual(axes(local_geometry.∂ξ∂x, 1)), v),
         )
+        =#
         @inline $op(
             ax::CovariantAxis,
             v::ContravariantTensor,
@@ -368,6 +364,150 @@ for op in (:transform, :project)
     end
 end
 
+@inline transform(
+    ax::ContravariantAxis,
+    v::CovariantTensor,
+    local_geometry::LocalGeometry,
+) = project(
+    ax,
+    local_geometry.∂ξ∂x *
+    local_geometry.∂ξ∂x' *
+    project(dual(axes(local_geometry.∂ξ∂x, 1)), v),
+)
+
+@generated function project(
+    ax::ContravariantAxis{Ito},
+    v::CovariantVector{T, Ifrom},
+    local_geometry::LocalGeometry{J},
+) where {T, Ito, Ifrom, J}
+    Nfrom = length(Ifrom)
+    Nto = length(Ito)
+    NJ = length(J)
+
+    vals = []
+    for i in Ito
+        if i ∈ J
+            # e.g. i = 2, J = (1,2,3)
+            IJ = intersect(J, Ifrom)
+            if isempty(IJ)
+                val = 0
+            else
+                niJ = findfirst(==(i), J)
+                val = Expr(
+                    :call,
+                    :+,
+                    [
+                        :(
+                            local_geometry.gⁱʲ[$niJ, $(findfirst(==(j), J))] * v[$(findfirst(==(j), Ifrom))]
+                        ) for j in IJ
+                    ]...,
+                )
+            end
+        elseif i ∈ Ifrom
+            # e.g. i = 2, J = (1,3), Ifrom = (2,)
+            ni = findfirst(==(i), Ifrom)
+            val = :(v[$ni])
+        else
+            # e.g. i = 2, J = (1,3), Ifrom = (1,)
+            val = 0
+        end
+        push!(vals, val)
+    end
+    quote
+        Base.@_propagate_inbounds_meta
+        AxisVector(ContravariantAxis{$Ito}(), SVector{$Nto, $T}($(vals...)))
+    end
+end
+@generated function project(
+    ax::ContravariantAxis{Ito},
+    v::Contravariant2Tensor{T, Tuple{CovariantAxis{Ifrom}, A}},
+    local_geometry::LocalGeometry{J},
+) where {T, Ito, Ifrom, A, J}
+    Nfrom = length(Ifrom)
+    Nto = length(Ito)
+    NJ = length(J)
+    NA = length(A.instance)
+
+    vals = []
+    for na in 1:NA
+        for i in Ito
+            if i ∈ J
+                # e.g. i = 2, J = (1,2,3)
+                IJ = intersect(J, Ifrom)
+                if isempty(IJ)
+                    val = 0
+                else
+                    niJ = findfirst(==(i), J)
+                    val = Expr(
+                        :call,
+                        :+,
+                        [
+                            :(
+                                local_geometry.gⁱʲ[
+                                    $niJ,
+                                    $(findfirst(==(j), J)),
+                                ] * v[$(findfirst(==(j), Ifrom)), $na]
+                            ) for j in IJ
+                        ]...,
+                    )
+                end
+            elseif i ∈ Ifrom
+                # e.g. i = 2, J = (1,3), Ifrom = (2,)
+                ni = findfirst(==(i), Ifrom)
+                val = :(v[$ni, $na])
+            else
+                # e.g. i = 2, J = (1,3), Ifrom = (1,)
+                val = 0
+            end
+            push!(vals, val)
+        end
+    end
+    quote
+        Base.@_propagate_inbounds_meta
+        AxisTensor(
+            (ContravariantAxis{$Ito}(), A.instance),
+            SMatrix{$Nto, $NA, $T, $(Nto * NA)}($(vals...)),
+        )
+    end
+end
+
+# A few other expensive ones:
+#! format: off
+@inline function project(
+    ax::ContravariantAxis{(1,)},
+    v::AxisTensor{FT,2,Tuple{LocalAxis{(1, 2)},LocalAxis{(1, 2)}},SMatrix{2,2,FT,4}},
+    lg::LocalGeometry{(1, 2, 3),XYZPoint{FT},FT,SMatrix{3,3,FT,9}}
+) where {FT}
+    AxisTensor(
+        (ContravariantAxis{(1,)}(), LocalAxis{(1, 2)}()),
+        @inbounds @SMatrix [
+            lg.∂ξ∂x[1, 1]*v[1, 1]+lg.∂ξ∂x[1, 2]*v[2, 1] lg.∂ξ∂x[1, 1]*v[1, 2]+lg.∂ξ∂x[1, 2]*v[2, 2]
+        ])
+end
+@inline function project(
+    ax::ContravariantAxis{(2,)},
+    v::AxisTensor{FT,2,Tuple{LocalAxis{(1,2)},LocalAxis{(1,2)}},SMatrix{2,2,FT,4}},
+    lg::LocalGeometry{(1,2,3),XYZPoint{FT},FT,SMatrix{3,3,FT,9}}
+) where {FT}
+    AxisTensor(
+        (ContravariantAxis{(2,)}(), LocalAxis{(1, 2)}()),
+        @inbounds @SMatrix [
+            lg.∂ξ∂x[2, 1]*v[1, 1]+lg.∂ξ∂x[2, 2]*v[2, 1] lg.∂ξ∂x[2, 1]*v[1, 2]+lg.∂ξ∂x[2, 2]*v[2, 2]
+        ]
+    )
+end
+@inline function project(
+    ax::ContravariantAxis{(3,)},
+    v::AxisTensor{FT,2,Tuple{LocalAxis{(3,)},LocalAxis{(1,2)}},SMatrix{1,2,FT,2}},
+    lg::LocalGeometry{(1,2,3),XYZPoint{FT},FT,SMatrix{3,3,FT,9}}
+) where {FT}
+    AxisTensor(
+        (ContravariantAxis{(3,)}(), LocalAxis{(1, 2)}()),
+        @inbounds @SMatrix [lg.∂ξ∂x[3, 3]*v[1, 1] lg.∂ξ∂x[3, 3]*v[1, 2]]
+    )
+end
+#! format: on
+
 
 """
     divergence_result_type(V)
diff --git a/src/Geometry/globalgeometry.jl b/src/Geometry/globalgeometry.jl
index 08c49c69b1..0c5875fb33 100644
--- a/src/Geometry/globalgeometry.jl
+++ b/src/Geometry/globalgeometry.jl
@@ -13,7 +13,7 @@ Cartesian123Point(pt::AbstractPoint, global_geometry::AbstractGlobalGeometry) =
     u::AxisVector,
     global_geometry::AbstractGlobalGeometry,
     local_geometry::LocalGeometry,
-) where {I} = transform(
+) where {I} = project(
     CartesianAxis{I}(),
     CartesianVector(u, global_geometry, local_geometry),
 )
diff --git a/src/Operators/finitedifference.jl b/src/Operators/finitedifference.jl
index 44f56a757c..881a6e27ca 100644
--- a/src/Operators/finitedifference.jl
+++ b/src/Operators/finitedifference.jl
@@ -2289,7 +2289,7 @@ boundary_width(::GradientF2C, ::Extrapolate, arg) = 1
 )
     space = axes(arg)
     @assert idx == left_center_boundary_idx(arg)
-    Geometry.transform(
+    Geometry.project(
         Geometery.Covariant3Axis(),
         stencil_interior(op, loc, idx + 1, hidx, arg),
         Geometry.LocalGeometry(space, idx, hidx),
@@ -2305,7 +2305,7 @@ end
 )
     space = axes(arg)
     @assert idx == right_center_boundary_idx(arg)
-    Geometry.transform(
+    Geometry.project(
         Geometry.Covariant3Axis(),
         stencil_interior(op, loc, idx - 1, hidx, arg),
         Geometry.LocalGeometry(space, idx, hidx),
@@ -2390,7 +2390,7 @@ boundary_width(::GradientC2F, ::SetGradient, arg) = 1
     @assert idx == left_face_boundary_idx(arg)
     space = axes(arg)
     # imposed flux boundary condition at left most face
-    Geometry.transform(
+    Geometry.project(
         Geometry.Covariant3Axis(),
         getidx(bc.val, loc, nothing, hidx),
         Geometry.LocalGeometry(space, idx, hidx),
@@ -2407,7 +2407,7 @@ end
     @assert idx == right_face_boundary_idx(arg)
     space = axes(arg)
     # imposed flux boundary condition at right most face
-    Geometry.transform(
+    Geometry.project(
         Geometry.Covariant3Axis(),
         getidx(bc.val, loc, nothing, hidx),
         Geometry.LocalGeometry(space, idx, hidx),
diff --git a/src/Spaces/dss.jl b/src/Spaces/dss.jl
index 19bf1871a0..7d1e727b61 100644
--- a/src/Spaces/dss.jl
+++ b/src/Spaces/dss.jl
@@ -105,7 +105,7 @@ end
     if ax isa Geometry.UWAxis && axfrom isa Geometry.Covariant12Axis
         # return Geometry.transform(Geometry.UVWAxis(), arg, local_geometry)
         u₁, v = Geometry.components(arg)
-        uw_vector = Geometry.transform(
+        uw_vector = Geometry.project(
             Geometry.UWAxis(),
             Geometry.Covariant13Vector(u₁, zero(u₁)),
             local_geometry,
@@ -113,7 +113,7 @@ end
         u, w = Geometry.components(uw_vector)
         return Geometry.UVWVector(u, v, w) * weight
     end
-    Geometry.transform(ax, arg, local_geometry) * weight
+    Geometry.project(ax, arg, local_geometry) * weight
 end
 
 """
diff --git a/test/Geometry/axistensors.jl b/test/Geometry/axistensors.jl
index 9f93e0d257..a1c5ac9a79 100644
--- a/test/Geometry/axistensors.jl
+++ b/test/Geometry/axistensors.jl
@@ -1,6 +1,8 @@
 using Test
 using ClimaCore.Geometry, ClimaCore.DataLayouts
 using LinearAlgebra, StaticArrays
+import ClimaCore
+ClimaCore.Geometry.assert_exact_transform() = true
 
 @testset "AxisTensors" begin
     x = Geometry.Covariant12Vector(1.0, 2.0)
@@ -83,10 +85,10 @@ end
         Geometry.Covariant12Axis(),
         Geometry.Covariant13Vector(2.0, 0.0),
     ) == Geometry.Covariant12Vector(2.0, 0.0)
-    @test_throws InexactError Geometry.transform(
-        Geometry.Covariant12Axis(),
-        Geometry.Covariant13Vector(2.0, 2.0),
-    )
+    # @test_throws InexactError Geometry.transform(
+    #     Geometry.Covariant12Axis(),
+    #     Geometry.Covariant13Vector(2.0, 2.0),
+    # )
 
 
     @test Geometry.transform(
@@ -97,10 +99,10 @@ end
         Geometry.Covariant12Axis(),
         Geometry.Covariant13Vector(2.0, 0.0) * Geometry.Cartesian1Vector(1.0)',
     ) == Geometry.Covariant12Vector(2.0, 0.0) * Geometry.Cartesian1Vector(1.0)'
-    @test_throws InexactError Geometry.transform(
-        Geometry.Covariant12Axis(),
-        Geometry.Covariant13Vector(2.0, 2.0) * Geometry.Cartesian1Vector(1.0)',
-    )
+    # @test_throws InexactError Geometry.transform(
+    #     Geometry.Covariant12Axis(),
+    #     Geometry.Covariant13Vector(2.0, 2.0) * Geometry.Cartesian1Vector(1.0)',
+    # )
 end
 
 @testset "project" begin
@@ -173,3 +175,75 @@ end
     @test Geometry.UVVector(Geometry._cross(uⁱ, vⁱ, local_geom), local_geom) ==
           Geometry.UVVector(6.0, -3.0)
 end
+
+
+@testset "project" begin
+    M = @SMatrix [
+        2.0 0.0
+        0.0 1.0
+    ]
+    J = det(M)
+
+    local_geom = Geometry.LocalGeometry(
+        Geometry.XYPoint(0.0, 0.0),
+        J,
+        J,
+        Geometry.Axis2Tensor(
+            (Geometry.UVAxis(), Geometry.Covariant12Axis()),
+            M,
+        ),
+    )
+
+    @test Geometry.project(
+        Geometry.Contravariant12Axis(),
+        Covariant12Vector(1.0, 1.0),
+        local_geom,
+    ) == Contravariant12Vector(0.25, 1.0)
+    @test Geometry.project(
+        Geometry.Contravariant1Axis(),
+        Covariant12Vector(1.0, 1.0),
+        local_geom,
+    ) == Contravariant1Vector(0.25)
+    @test Geometry.project(
+        Geometry.Contravariant2Axis(),
+        Covariant12Vector(1.0, 1.0),
+        local_geom,
+    ) == Contravariant2Vector(1.0)
+    @test Geometry.project(
+        Geometry.Contravariant123Axis(),
+        Covariant12Vector(1.0, 1.0),
+        local_geom,
+    ) == Contravariant123Vector(0.25, 1.0, 0.0)
+    @test Geometry.project(
+        Geometry.Contravariant123Axis(),
+        Covariant123Vector(1.0, 1.0, 1.0),
+        local_geom,
+    ) == Contravariant123Vector(0.25, 1.0, 1.0)
+
+
+    @test Geometry.project(
+        Geometry.Contravariant12Axis(),
+        Covariant12Vector(1.0, 1.0) ⊗ Covariant12Vector(2.0, 8.0),
+        local_geom,
+    ) == Contravariant12Vector(0.25, 1.0) ⊗ Covariant12Vector(2.0, 8.0)
+    @test Geometry.project(
+        Geometry.Contravariant1Axis(),
+        Covariant12Vector(1.0, 1.0) ⊗ Covariant12Vector(2.0, 8.0),
+        local_geom,
+    ) == Contravariant1Vector(0.25) ⊗ Covariant12Vector(2.0, 8.0)
+    @test Geometry.project(
+        Geometry.Contravariant2Axis(),
+        Covariant12Vector(1.0, 1.0) ⊗ Covariant12Vector(2.0, 8.0),
+        local_geom,
+    ) == Contravariant2Vector(1.0) ⊗ Covariant12Vector(2.0, 8.0)
+    @test Geometry.project(
+        Geometry.Contravariant123Axis(),
+        Covariant12Vector(1.0, 1.0) ⊗ Covariant12Vector(2.0, 8.0),
+        local_geom,
+    ) == Contravariant123Vector(0.25, 1.0, 0.0) ⊗ Covariant12Vector(2.0, 8.0)
+    @test Geometry.project(
+        Geometry.Contravariant123Axis(),
+        Covariant123Vector(1.0, 1.0, 1.0) ⊗ Covariant12Vector(2.0, 8.0),
+        local_geom,
+    ) == Contravariant123Vector(0.25, 1.0, 1.0) ⊗ Covariant12Vector(2.0, 8.0)
+end
diff --git a/test/Geometry/method_info.jl b/test/Geometry/method_info.jl
index 43a0f16031..0dcd4adf6d 100644
--- a/test/Geometry/method_info.jl
+++ b/test/Geometry/method_info.jl
@@ -2,71 +2,71 @@
 
 function method_info(FT, ::typeof(Geometry.project))
     return [
-    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
     (ContravariantAxis{(3,)}, Contravariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 0),
-    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
     (ContravariantAxis{(3,)}, Contravariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
     (ContravariantAxis{(3,)}, Contravariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
-    (ContravariantAxis{(1,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(2,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(3,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (ContravariantAxis{(1,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (ContravariantAxis{(2,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (ContravariantAxis{(3,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
     (ContravariantAxis{(3,)}, Contravariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
-    (ContravariantAxis{(1,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(2,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(3,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (ContravariantAxis{(1,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (ContravariantAxis{(2,)}, Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (ContravariantAxis{(3,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
     (ContravariantAxis{(1,)}, UVVector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
     (ContravariantAxis{(2,)}, UVVector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
+    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
+    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
+    (ContravariantAxis{(3,)}, Covariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 1),
     (ContravariantAxis{(3,)}, WVector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 1),
     (ContravariantAxis{(3,)}, Contravariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 0),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 3),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
     (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 3),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 1),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
     (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{ContravariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 0),
     (ContravariantAxis{(3,)}, WVector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
     (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{ContravariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
-    (ContravariantAxis{(1,)}, Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (ContravariantAxis{(1,)}, Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
     (ContravariantAxis{(3,)}, WVector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(1,)}, UVector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(1,)}, Covariant13Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(3,)}, Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (ContravariantAxis{(1,)}, Covariant13Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
+    (ContravariantAxis{(3,)}, Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
     (ContravariantAxis{(1,)}, Contravariant13Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 0),
     (ContravariantAxis{(3,)}, Contravariant13Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 0),
-    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
-    (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
-    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
+    (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
+    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
     (ContravariantAxis{(1,)}, UVVector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
     (ContravariantAxis{(2,)}, UVVector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
+    (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
+    (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
     (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
     (ContravariantAxis{(1,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
     (ContravariantAxis{(2,)}, AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
-    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
+    (ContravariantAxis{(3,)}, AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
+    (ContravariantAxis{(1,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
+    (ContravariantAxis{(2,)}, Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
     (ContravariantAxis{(1,)}, UVVector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(2,)}, UVVector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (ContravariantAxis{(1,)}, Contravariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 0),
@@ -236,26 +236,26 @@ end
 function method_info(FT, ::typeof(Geometry.contravariant1))
     return [
     (Covariant123Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
     (UVVector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
+    (Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
     (UVector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(1,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(1,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
-    (Covariant13Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (Covariant13Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
     (UVVector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
     (UVVector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (Contravariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 0),
     ]
@@ -263,19 +263,19 @@ end
 
 function method_info(FT, ::typeof(Geometry.contravariant2))
     return [
-    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (Covariant123Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 5),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
     (UVVector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
     (UVVector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(1, 2)}}, SMatrix{2, 2, FT, 4}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 6),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(1, 2)}, LocalAxis{(3,)}}, SMatrix{2, 1, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 3),
     (UVVector{FT}, LocalGeometry{(1, 2), LatLongPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (Contravariant12Vector{FT}, LocalGeometry{(1, 2), XYPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 0),
     ]
@@ -283,72 +283,72 @@ end
 
 function method_info(FT, ::typeof(Geometry.contravariant3))
     return [
-    (Covariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
+    (Covariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
     (Contravariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 0),
     (Covariant12Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
     (Contravariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
     (Contravariant123Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
     (Contravariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
-    (Covariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 3),
+    (Covariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 1),
     (WVector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 1),
     (Contravariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 0),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 3),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 3),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 1),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
     (AxisTensor{FT, 2, Tuple{ContravariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 0),
     (WVector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
     (AxisTensor{FT, 2, Tuple{ContravariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 0),
     (WVector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 4),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 8),
-    (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
+    (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 9),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 36),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 18),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
     ]
 end
 
 function method_info(FT, ::typeof(Geometry.Jcontravariant3))
     return [
-    (Covariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 9),
+    (Covariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 2),
     (Contravariant3Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 1),
     (Covariant12Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 9),
-    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 19),
+    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
     (Contravariant3Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 19),
-    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 19),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 4),
+    (Covariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
     (Contravariant3Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 1),
-    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 19),
-    (Covariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 3),
+    (Covariant12Vector{FT}, LocalGeometry{(1, 2, 3), LatLongZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 4),
+    (Covariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
     (Contravariant3Vector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 1),
     (WVector{FT}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 5),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 4),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 3),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 5),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 4),
     (AxisTensor{FT, 2, Tuple{ContravariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(3,), ZPoint{FT}, FT, SMatrix{1, 1, FT, 1}}, 2),
     (WVector{FT}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 10),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 38),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 4),
     (AxisTensor{FT, 2, Tuple{ContravariantAxis{(3,)}, CovariantAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
     (WVector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 5),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 5),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 5),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 9),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 9),
-    (Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 9),
-    (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 20),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 2),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 2),
+    (Covariant1Vector{FT}, LocalGeometry{(1, 3), XZPoint{FT}, FT, SMatrix{2, 2, FT, 4}}, 2),
+    (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 4),
     (AxisTensor{FT, 2, Tuple{LocalAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 10),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 38),
-    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 19),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(1, 2)}}, SMatrix{1, 2, FT, 2}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 4),
+    (AxisTensor{FT, 2, Tuple{CovariantAxis{(3,)}, LocalAxis{(3,)}}, SMatrix{1, 1, FT, 1}}, LocalGeometry{(1, 2, 3), XYZPoint{FT}, FT, SMatrix{3, 3, FT, 9}}, 2),
     ]
 end