diff --git a/Manifest.toml b/Manifest.toml
index 4375000..f30a246 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -1,39 +1,42 @@
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.10.0"
+julia_version = "1.11.1"
 manifest_format = "2.0"
-project_hash = "7d1ba2483e6ee20f9bd06aae356903d7e540f599"
+project_hash = "12bacc9f7a3024e6d7a84766247f5ca88c289b1c"
 
 [[deps.ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
-version = "1.1.1"
+version = "1.1.2"
 
 [[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+version = "1.11.0"
 
 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+version = "1.11.0"
 
 [[deps.CodecZlib]]
 deps = ["TranscodingStreams", "Zlib_jll"]
-git-tree-sha1 = "59939d8a997469ee05c4b4944560a820f9ba0d73"
+git-tree-sha1 = "bce6804e5e6044c6daab27bb533d1295e4a2e759"
 uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
-version = "0.7.4"
+version = "0.7.6"
 
 [[deps.CommonSubexpressions]]
-deps = ["MacroTools", "Test"]
-git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
+deps = ["MacroTools"]
+git-tree-sha1 = "cda2cfaebb4be89c9084adaca7dd7333369715c5"
 uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
-version = "0.3.0"
+version = "0.3.1"
 
 [[deps.CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
-version = "1.0.5+1"
+version = "1.1.1+0"
 
 [[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+version = "1.11.0"
 
 [[deps.DiffResults]]
 deps = ["StaticArraysCore"]
@@ -49,9 +52,9 @@ version = "1.15.1"
 
 [[deps.Distances]]
 deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
-git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0"
+git-tree-sha1 = "c7e3a542b999843086e2f29dac96a618c105be1d"
 uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
-version = "0.10.11"
+version = "0.10.12"
 
     [deps.Distances.extensions]
     DistancesChainRulesCoreExt = "ChainRulesCore"
@@ -95,12 +98,13 @@ version = "1.0.0"
 
 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
+version = "1.11.0"
 
 [[deps.FillArrays]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "bfe82a708416cf00b73a3198db0859c82f741558"
+git-tree-sha1 = "6a70198746448456524cb442b8af316927ff3e1a"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
-version = "1.10.0"
+version = "1.13.0"
 
     [deps.FillArrays.extensions]
     FillArraysPDMatsExt = "PDMats"
@@ -114,18 +118,14 @@ version = "1.10.0"
 
 [[deps.ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"]
-git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad"
+git-tree-sha1 = "a2df1b776752e3f344e5116c06d75a10436ab853"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.36"
+version = "0.10.38"
 weakdeps = ["StaticArrays"]
 
     [deps.ForwardDiff.extensions]
     ForwardDiffStaticArraysExt = "StaticArrays"
 
-[[deps.InteractiveUtils]]
-deps = ["Markdown"]
-uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
-
 [[deps.IrrationalConstants]]
 git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
@@ -133,9 +133,9 @@ version = "0.2.2"
 
 [[deps.JLLWrappers]]
 deps = ["Artifacts", "Preferences"]
-git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
+git-tree-sha1 = "be3dc50a92e5a386872a493a10050136d4703f9b"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
-version = "1.5.0"
+version = "1.6.1"
 
 [[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
@@ -145,16 +145,17 @@ version = "0.6.4"
 [[deps.LibCURL_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
 uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
-version = "8.4.0+0"
+version = "8.6.0+0"
 
 [[deps.LibGit2]]
 deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
+version = "1.11.0"
 
 [[deps.LibGit2_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
 uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
-version = "1.6.4+0"
+version = "1.7.2+0"
 
 [[deps.LibSSH2_jll]]
 deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
@@ -163,12 +164,13 @@ version = "1.11.0+1"
 
 [[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
+version = "1.11.0"
 
 [[deps.Libiconv_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175"
+git-tree-sha1 = "61dfdba58e585066d8bce214c5a51eaa0539f269"
 uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
-version = "1.17.0+0"
+version = "1.17.0+1"
 
 [[deps.LightXML]]
 deps = ["Libdl", "XML2_jll"]
@@ -179,12 +181,13 @@ version = "0.9.1"
 [[deps.LinearAlgebra]]
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+version = "1.11.0"
 
 [[deps.LogExpFunctions]]
 deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "18144f3e9cbe9b15b070288eef858f71b291ce37"
+git-tree-sha1 = "13ca9e2586b89836fd20cccf56e57e2b9ae7f38f"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.27"
+version = "0.3.29"
 
     [deps.LogExpFunctions.extensions]
     LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
@@ -198,6 +201,7 @@ version = "0.3.27"
 
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
+version = "1.11.0"
 
 [[deps.MacroTools]]
 deps = ["Markdown", "Random"]
@@ -208,15 +212,16 @@ version = "0.5.13"
 [[deps.Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
+version = "1.11.0"
 
 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
-version = "2.28.2+1"
+version = "2.28.6+0"
 
 [[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
-version = "2023.1.10"
+version = "2023.12.12"
 
 [[deps.NaNMath]]
 deps = ["OpenLibm_jll"]
@@ -226,9 +231,9 @@ version = "1.0.2"
 
 [[deps.NearestNeighbors]]
 deps = ["Distances", "StaticArrays"]
-git-tree-sha1 = "ded64ff6d4fdd1cb68dfcbb818c69e144a5b2e4c"
+git-tree-sha1 = "8a3271d8309285f4db73b4f662b1b290c715e85e"
 uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
-version = "0.4.16"
+version = "0.4.21"
 
 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
@@ -237,7 +242,7 @@ version = "1.2.0"
 [[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
-version = "0.3.23+2"
+version = "0.3.27+1"
 
 [[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -256,9 +261,15 @@ uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.6.3"
 
 [[deps.Pkg]]
-deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
+deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
-version = "1.10.0"
+version = "1.11.0"
+
+    [deps.Pkg.extensions]
+    REPLExt = "REPL"
+
+    [deps.Pkg.weakdeps]
+    REPL = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 
 [[deps.PrecompileTools]]
 deps = ["Preferences"]
@@ -275,14 +286,12 @@ version = "1.4.3"
 [[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
-
-[[deps.REPL]]
-deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
-uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
+version = "1.11.0"
 
 [[deps.Random]]
 deps = ["SHA"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+version = "1.11.0"
 
 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
@@ -295,26 +304,24 @@ version = "0.7.0"
 
 [[deps.SIMD]]
 deps = ["PrecompileTools"]
-git-tree-sha1 = "d8911cc125da009051fb35322415641d02d9e37f"
+git-tree-sha1 = "52af86e35dd1b177d051b12681e1c581f53c281b"
 uuid = "fdea26ae-647d-5447-a871-4b548cad5224"
-version = "3.4.6"
+version = "3.7.0"
 
 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
-
-[[deps.Sockets]]
-uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
+version = "1.11.0"
 
 [[deps.SparseArrays]]
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
-version = "1.10.0"
+version = "1.11.0"
 
 [[deps.SpecialFunctions]]
 deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
-git-tree-sha1 = "e2cfc4012a19088254b3950b85c3c1d8882d864d"
+git-tree-sha1 = "64cca0c26b4f31ba18f13f6c12af7c85f478cfde"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "2.3.1"
+version = "2.5.0"
 
     [deps.SpecialFunctions.extensions]
     SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"
@@ -324,9 +331,9 @@ version = "2.3.1"
 
 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
-git-tree-sha1 = "bf074c045d3d5ffd956fa0a461da38a44685d6b2"
+git-tree-sha1 = "777657803913ffc7e8cc20f0fd04b634f871af8f"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.9.3"
+version = "1.9.8"
 
     [deps.StaticArrays.extensions]
     StaticArraysChainRulesCoreExt = "ChainRulesCore"
@@ -337,14 +344,19 @@ version = "1.9.3"
     Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[deps.StaticArraysCore]]
-git-tree-sha1 = "36b3d696ce6366023a0ea192b4cd442268995a0d"
+git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682"
 uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
-version = "1.4.2"
+version = "1.4.3"
 
 [[deps.Statistics]]
-deps = ["LinearAlgebra", "SparseArrays"]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
-version = "1.10.0"
+version = "1.11.1"
+weakdeps = ["SparseArrays"]
+
+    [deps.Statistics.extensions]
+    SparseArraysExt = ["SparseArrays"]
 
 [[deps.StatsAPI]]
 deps = ["LinearAlgebra"]
@@ -355,7 +367,7 @@ version = "1.7.0"
 [[deps.SuiteSparse_jll]]
 deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
 uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
-version = "7.2.1+1"
+version = "7.7.0+0"
 
 [[deps.TOML]]
 deps = ["Dates"]
@@ -373,25 +385,19 @@ git-tree-sha1 = "957f256fb380cad64cae4da39e562ecfb5c3fec9"
 uuid = "48a634ad-e948-5137-8d70-aa71f2a747f4"
 version = "1.16.1"
 
-[[deps.Test]]
-deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
-uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
 [[deps.TranscodingStreams]]
-git-tree-sha1 = "71509f04d045ec714c4748c785a59045c3736349"
+git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
-version = "0.10.7"
-weakdeps = ["Random", "Test"]
-
-    [deps.TranscodingStreams.extensions]
-    TestExt = ["Test", "Random"]
+version = "0.11.3"
 
 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
+version = "1.11.0"
 
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+version = "1.11.0"
 
 [[deps.VTKBase]]
 git-tree-sha1 = "c2d0db3ef09f1942d08ea455a9e252594be5f3b6"
@@ -400,15 +406,15 @@ version = "1.0.1"
 
 [[deps.WriteVTK]]
 deps = ["Base64", "CodecZlib", "FillArrays", "LightXML", "TranscodingStreams", "VTKBase"]
-git-tree-sha1 = "48b9e8e9c83865e99e57f027d4edfa94e0acddae"
+git-tree-sha1 = "1d8042d58334ab7947ce505709df7009da6f3375"
 uuid = "64499a7a-5c06-52f2-abe2-ccb03c286192"
-version = "1.19.1"
+version = "1.21.1"
 
 [[deps.XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
-git-tree-sha1 = "532e22cf7be8462035d092ff21fada7527e2c488"
+git-tree-sha1 = "a2fccc6559132927d4c5dc183e3e01048c6dcbd6"
 uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
-version = "2.12.6+0"
+version = "2.13.5+0"
 
 [[deps.Zlib_jll]]
 deps = ["Libdl"]
@@ -418,12 +424,12 @@ version = "1.2.13+1"
 [[deps.libblastrampoline_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
-version = "5.8.0+1"
+version = "5.11.0+0"
 
 [[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
-version = "1.52.0+1"
+version = "1.59.0+0"
 
 [[deps.p7zip_jll]]
 deps = ["Artifacts", "Libdl"]
diff --git a/Project.toml b/Project.toml
index 6e1eacc..2dd2c3c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,10 +6,12 @@ version = "1.0.0"
 [deps]
 Ferrite = "c061ca5d-56c9-439f-9c0e-210fe06d3992"
 OrderedCollections = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [compat]
 Ferrite = "1.0"
 OrderedCollections = "1"
+StaticArraysCore = "1.4.3"
 julia = "1.10"
 
 [extras]
diff --git a/docs/src/reference/cellvalues.md b/docs/src/reference/cellvalues.md
index 5f62539..7464bd8 100644
--- a/docs/src/reference/cellvalues.md
+++ b/docs/src/reference/cellvalues.md
@@ -14,6 +14,7 @@ function_value_average
 function_gradient_average
 function_value_jump
 function_gradient_jump
+midplane_rotation
 getdetJdV_average
 get_side_and_baseindex
 ```
\ No newline at end of file
diff --git a/src/FerriteInterfaceElements.jl b/src/FerriteInterfaceElements.jl
index db4e242..a315887 100644
--- a/src/FerriteInterfaceElements.jl
+++ b/src/FerriteInterfaceElements.jl
@@ -1,11 +1,10 @@
 module FerriteInterfaceElements
 
-import Ferrite
-import Ferrite: AbstractCell, AbstractRefShape, AbstractCellValues,
+import Ferrite: Ferrite, AbstractCell, AbstractRefShape, AbstractCellValues,
     RefLine, RefQuadrilateral, RefTriangle, RefPrism, RefHexahedron,
     Line, QuadraticLine, Triangle, QuadraticTriangle, Quadrilateral, QuadraticQuadrilateral, Tetrahedron, Hexahedron,
     ScalarInterpolation, VectorizedInterpolation, Lagrange,
-    CellValues, QuadratureRule, CellCache, Grid, ExclusiveTopology, FacetIndex, Vec,
+    CellValues, QuadratureRule, CellCache, Grid, ExclusiveTopology, FacetIndex, Vec, Tensor,
     getnbasefunctions, getngeobasefunctions, getorder, n_components, getrefshape,
     vertexdof_indices, edgedof_interior_indices, facedof_interior_indices, volumedof_interior_indices,
     vertices, facets, edges,
@@ -13,28 +12,28 @@ import Ferrite: AbstractCell, AbstractRefShape, AbstractCellValues,
     checkbounds, checkquadpoint, function_value_init, function_gradient_init,
     shape_value_type, shape_gradient_type,
     reinit!, getnquadpoints, getdetJdV, shape_value, shape_gradient, function_value, function_gradient,
-    getcellset, getcells, getneighborhood
+    getcellset, getcells, getneighborhood,
+    ×, norm
 import OrderedCollections: OrderedSet
+import StaticArraysCore: SMatrix, SVector
 
 include("cells.jl")
+export InterfaceCell
+
 include("interpolations.jl")
-include("cellvalues.jl")
-include("grid.jl")
+export InterfaceCellInterpolation
 
-export
-    InterfaceCell,
-    InterfaceCellInterpolation,
-    InterfaceCellValues,
+include("cellvalues.jl")
+export InterfaceCellValues,
     get_side_and_baseindex,
-    shape_value_average,
-    shape_gradient_average,
-    shape_value_jump,
-    shape_gradient_jump,
-    function_value_average,
-    function_gradient_average,
-    function_value_jump,
-    function_gradient_jump,
-    getdetJdV_average,
-    insert_interfaces
+    shape_value_average, shape_gradient_average,
+    shape_value_jump, shape_gradient_jump,
+    function_value_average, function_gradient_average,
+    function_value_jump, function_gradient_jump,
+    midplane_rotation,
+    getdetJdV_average
+
+include("grid.jl")
+export insert_interfaces
 
 end
diff --git a/src/cellvalues.jl b/src/cellvalues.jl
index 532051b..d1b1cee 100644
--- a/src/cellvalues.jl
+++ b/src/cellvalues.jl
@@ -4,6 +4,8 @@
 An `InterfaceCellValues` is based on two `CellValues`: one for each facet of an `InterfaceCell`.
 Since one can use the same `CellValues` for both sides, be default the same object is used for better performance.
 The keyword argument `use_same_cv` can be set to `false` to disable this behavior, if needed.
+Furthermore, the rotation matrix of the midplane in the quadrature points can be computed.
+To do so, set `include_R=true`.
 
 # Fields
 - `ip::InterfaceCellInterpolation`: interpolation on the interface
@@ -12,30 +14,47 @@ The keyword argument `use_same_cv` can be set to `false` to disable this behavio
 - `base_indices_here::Vector{Int}`: base function indices on facet "here"
 - `base_indices_there::Vector{Int}`: base function indices on facet "there"
 - `sides_and_baseindices::Tuple`: side and base function for the base `CellValues` for each base function of the `InterfaceCellValues`
+- `R::Union{AbstractVector,Nothing}`: rotation matrix of the midplane in the quadrature points
 """
-struct InterfaceCellValues{CV} <: AbstractCellValues
+struct InterfaceCellValues{CV,TR} <: AbstractCellValues
     here::CV
     there::CV
     base_indices_here::Vector{Int}
     base_indices_there::Vector{Int}
     sides_and_baseindices::Tuple
+    R::TR # Union{AbstractVector,Nothing} Rotation matrix in quadrature points
 
-    function InterfaceCellValues(ip::IP, here::CV; use_same_cv) where {IP<:InterfaceCellInterpolation, CV<:CellValues}
-        sides_and_baseindices = Tuple( get_side_and_baseindex(ip, i) for i in 1:getnbasefunctions(ip) )
-        base_indices_here  = collect( get_interface_index(ip, :here,  i) for i in 1:getnbasefunctions(ip.base) )
-        base_indices_there = collect( get_interface_index(ip, :there, i) for i in 1:getnbasefunctions(ip.base) )
+    function InterfaceCellValues(ip::IP, here::CV; use_same_cv::Bool, include_R::Bool) where {
+            sdim, shape<:AbstractRefShape{sdim}, 
+            IP<:Union{InterfaceCellInterpolation{shape}, VectorizedInterpolation{<:Any,<:Any,<:Any,<:InterfaceCellInterpolation{shape}}},
+            CV<:CellValues}
+        sides_and_baseindices, base_indices_here, base_indices_there = _prepare_baseindices(ip)
         there = use_same_cv ? here : deepcopy(here)
-        return new{CV}(here, there, base_indices_here, base_indices_there, sides_and_baseindices)
+        
+        if include_R
+            T = eltype(here.detJdV)
+            TR = Vector{Tensor{2, sdim, T}}
+            R = TR(undef, length(getnquadpoints(here)))
+        else
+            TR = Nothing
+            R = nothing
+        end
+        return new{CV,TR}(here, there, base_indices_here, base_indices_there, sides_and_baseindices, R)
     end
+end
 
-    function InterfaceCellValues(ip::IP, here::CV; use_same_cv) where {IP<:VectorizedInterpolation{<:Any,<:Any,<:Any,<:InterfaceCellInterpolation}, CV<:CellValues}
-        sides_and_baseindices = Tuple( get_side_and_baseindex(ip, i) for i in 1:getnbasefunctions(ip) )
-        ip = ip.ip
-        base_indices_here  = collect( get_interface_index(ip, :here,  i) for i in 1:getnbasefunctions(ip.base) )
-        base_indices_there = collect( get_interface_index(ip, :there, i) for i in 1:getnbasefunctions(ip.base) )
-        there = use_same_cv ? here : deepcopy(here)
-        return new{CV}(here, there, base_indices_here, base_indices_there, sides_and_baseindices)
-    end
+function _prepare_baseindices(ip::IP) where {IP<:InterfaceCellInterpolation}
+    sides_and_baseindices = Tuple( get_side_and_baseindex(ip, i) for i in 1:getnbasefunctions(ip) )
+    base_indices_here  = collect( get_interface_index(ip, :here,  i) for i in 1:getnbasefunctions(ip.base) )
+    base_indices_there = collect( get_interface_index(ip, :there, i) for i in 1:getnbasefunctions(ip.base) )
+    return sides_and_baseindices, base_indices_here, base_indices_there
+end
+function _prepare_baseindices(ip::IP) where {IP<:VectorizedInterpolation{<:Any,<:Any,<:Any,<:InterfaceCellInterpolation}}
+    sides_and_baseindices = Tuple( get_side_and_baseindex(ip, i) for i in 1:getnbasefunctions(ip) )
+    ip = ip.ip
+    base_indices_here  = collect( get_interface_index(ip, :here,  i) for i in 1:getnbasefunctions(ip.base) )
+    base_indices_there = collect( get_interface_index(ip, :there, i) for i in 1:getnbasefunctions(ip.base) )
+    return sides_and_baseindices, base_indices_here, base_indices_there
 end
 
 InterfaceCellValues(qr::QuadratureRule, args...; kwargs...) = InterfaceCellValues(Float64, qr, args...; kwargs...)
@@ -43,17 +62,17 @@ InterfaceCellValues(qr::QuadratureRule, args...; kwargs...) = InterfaceCellValue
 function InterfaceCellValues(::Type{T}, qr::QuadratureRule, 
             ip::InterfaceCellInterpolation, 
             ip_geo::VectorizedInterpolation{sdim,<:Any,<:Any,<:InterfaceCellInterpolation} = default_geometric_interpolation(ip); 
-            use_same_cv=true, kwargs...) where {T, sdim}
+            use_same_cv=true, include_R=false, kwargs...) where {T, sdim}
     cv = CellValues(T, qr, ip.base, VectorizedInterpolation{sdim}(ip_geo.ip.base); kwargs...)
-    return InterfaceCellValues(ip, cv; use_same_cv=use_same_cv)
+    return InterfaceCellValues(ip, cv; use_same_cv=use_same_cv, include_R=include_R)
 end
 function InterfaceCellValues(::Type{T}, qr::QuadratureRule, 
             ip::VectorizedInterpolation{vdim,<:Any,<:Any,<:InterfaceCellInterpolation}, 
             ip_geo::VectorizedInterpolation{sdim,<:Any,<:Any,<:InterfaceCellInterpolation} = default_geometric_interpolation(ip); 
-            use_same_cv=true, kwargs...) where {T, vdim, sdim}
+            use_same_cv=true, include_R=false, kwargs...) where {T, vdim, sdim}
     cv = CellValues(T, qr, VectorizedInterpolation{vdim}(ip.ip.base), 
                            VectorizedInterpolation{sdim}(ip_geo.ip.base); kwargs...)
-    return InterfaceCellValues(ip, cv; use_same_cv=use_same_cv)
+    return InterfaceCellValues(ip, cv; use_same_cv=use_same_cv, include_R=include_R)
 end
 
 function InterfaceCellValues(::Type{T}, qr::QuadratureRule, 
@@ -90,13 +109,39 @@ Ferrite.shape_gradient_type(cv::InterfaceCellValues) = shape_gradient_type(cv.he
 
 Ferrite.reinit!(cv::InterfaceCellValues, cc::CellCache) = reinit!(cv, cc.coords) # TODO: Needed?
 
-function Ferrite.reinit!(cv::InterfaceCellValues, x::AbstractVector{Vec{sdim,T}}) where {sdim, T}
-    reinit!(cv.here, @view x[cv.base_indices_here])
-    if cv.here === cv.there
-        reinit!(cv.there, @view x[cv.base_indices_there])
+function Ferrite.reinit!(cv::InterfaceCellValues{CV,TR}, x::AbstractVector{Vec{sdim,T}}) where {sdim, T, CV, TR}
+    x_here  = @view x[cv.base_indices_here]
+    reinit!(cv.here, x_here)
+
+    if ! (cv.here === cv.there)
+        x_there = @view x[cv.base_indices_there]
+        reinit!(cv.there, x_there)
+    end
+
+    if ! isnothing(cv.R)
+        x_there = @view x[cv.base_indices_there]
+        for qp in 1:getnquadpoints(cv.here)
+            mapping_here  = Ferrite.calculate_mapping(cv.here.geo_mapping,  qp, x_here)
+            mapping_there = Ferrite.calculate_mapping(cv.there.geo_mapping, qp, x_there)
+            J_here  = Ferrite.getjacobian(mapping_here)
+            J_there = Ferrite.getjacobian(mapping_there)
+            J = (J_here + J_there) / 2
+            cv.R[qp] = _get_R_from_J(J)
+        end
     end
     return nothing
 end
+function _get_R_from_J(J::SMatrix{2,1,T}) where T 
+    v1 = J[:, 1]
+    v2 = SVector{2,T}((-v[2], v[1]))
+    return Tensor{2,2,T}(((v1/norm(v1))..., (v2/norm(v2))...))
+end
+function _get_R_from_J(J::SMatrix{3,2,T}) where T 
+    v1 = J[:, 1]
+    v3 = v1 × J[:, 2]
+    v2 = v3 × v1
+    return Tensor{2,3,T}(((v1/norm(v1))..., (v2/norm(v2))..., (v3/norm(v3))...))
+end
 
 get_side_and_baseindex(cv::InterfaceCellValues, i::Integer) = cv.sides_and_baseindices[i]
 
@@ -277,6 +322,15 @@ function Ferrite.function_gradient_jump(cv::InterfaceCellValues, qp::Int, u::Abs
     return function_gradient(cv, qp, u, false) - function_gradient(cv, qp, u, true)
 end
 
+"""
+    midplane_rotation(cv::InterfaceCellValues, qp::Int)
+
+Compute the rotation matrix of the midplane in quadrature point.
+"""
+function midplane_rotation(cv::InterfaceCellValues, qp::Int)
+    return cv.R[qp]
+end
+
 function Base.show(io::IO, d::MIME"text/plain", cv::InterfaceCellValues)
     if cv.here === cv.there
         print(io, "InterfaceCellValues based on a single CellValues:\n"); show(io, d, cv.here)
diff --git a/test/test_cellvalues.jl b/test/test_cellvalues.jl
index 7f52e17..bc0da37 100644
--- a/test/test_cellvalues.jl
+++ b/test/test_cellvalues.jl
@@ -36,4 +36,18 @@
         @test all(abs.(function_gradient_jump(cv, qp, u)) .≤ 1e-14)
         @test getdetJdV_average(cv, qp) == (getdetJdV(cv.here, qp) + getdetJdV(cv.there, qp)) / 2
     end
+
+    cv = InterfaceCellValues(qr, ip; include_R=true)
+    x  = repeat([Vec{3}((1.0,0.0,0.0)), Vec{3}((0.0,1.0,0.0)), Vec{3}((0.0,0.0,1.0))], 2)
+    n  = Vec{3}(( sqrt(1/3),  sqrt(1/3),   sqrt(1/3)))
+    t₁ = Vec{3}(( sqrt(1/2),  0.0,        -sqrt(1/2)))
+    t₂ = Vec{3}((-sqrt(1/6), 2*sqrt(1/6), -sqrt(1/6)))
+    reinit!(cv, x)
+    for qp in 1:getnquadpoints(cv)
+        R = midplane_rotation(cv, qp)
+        @test tdot(R) ≈ one(R) # Fails e.g. when dx/dξ₁ not perpendicular to dx/ξ₂
+        @test R⋅Vec{3}((1.0,0.0,0.0)) ≈ t₁
+        @test R⋅Vec{3}((0.0,1.0,0.0)) ≈ t₂
+        @test R⋅Vec{3}((0.0,0.0,1.0)) ≈ n
+    end
 end
\ No newline at end of file