Improve deform: linear interpolation for twist and average local airfoil normal (#234)

* Lipo deform

* Exact middle twist

* Update default manifests

* Reduce relaxation factor

* Update default manifest

* Address copilot comments

* Use elliptic start

* Use smooth sqrt

Author: 1-Bart-1

Manifest-v1.11.toml.default

@@ -2,12 +2,12 @@
 
 julia_version = "1.11.9"
 manifest_format = "2.0"
-project_hash = "2208ea1100be74002e5a4dc77070f9be50832d18"
+project_hash = "1ad349ec1b7d8858e1bce3c1d99302d12b82e8e6"
 
 [[deps.ADTypes]]
-git-tree-sha1 = "f7304359109c768cf32dc5fa2d371565bb63b68a"
+git-tree-sha1 = "bbc22a9a08a0ef6460041086d8a7b27940ed4ffd"
 uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
-version = "1.21.0"
+version = "1.22.0"
 weakdeps = ["ChainRulesCore", "ConstructionBase", "EnzymeCore"]
 
     [deps.ADTypes.extensions]
@@ -229,9 +229,9 @@ version = "1.15.1"
 
 [[deps.DifferentiationInterface]]
 deps = ["ADTypes", "LinearAlgebra"]
-git-tree-sha1 = "7ae99144ea44715402c6c882bfef2adbeadbc4ce"
+git-tree-sha1 = "2147a95a217cc8a78ec96ee03581adf129468e49"
 uuid = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
-version = "0.7.16"
+version = "0.7.18"
 
     [deps.DifferentiationInterface.extensions]
     DifferentiationInterfaceChainRulesCoreExt = "ChainRulesCore"
@@ -241,8 +241,9 @@ version = "0.7.16"
     DifferentiationInterfaceFiniteDiffExt = "FiniteDiff"
     DifferentiationInterfaceFiniteDifferencesExt = "FiniteDifferences"
     DifferentiationInterfaceForwardDiffExt = ["ForwardDiff", "DiffResults"]
-    DifferentiationInterfaceGPUArraysCoreExt = "GPUArraysCore"
+    DifferentiationInterfaceGPUArraysCoreExt = ["GPUArraysCore", "Adapt"]
     DifferentiationInterfaceGTPSAExt = "GTPSA"
+    DifferentiationInterfaceHyperHessiansExt = "HyperHessians"
     DifferentiationInterfaceMooncakeExt = "Mooncake"
     DifferentiationInterfacePolyesterForwardDiffExt = ["PolyesterForwardDiff", "ForwardDiff", "DiffResults"]
     DifferentiationInterfaceReverseDiffExt = ["ReverseDiff", "DiffResults"]
@@ -255,6 +256,7 @@ version = "0.7.16"
     DifferentiationInterfaceZygoteExt = ["Zygote", "ForwardDiff"]
 
     [deps.DifferentiationInterface.weakdeps]
+    Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
     ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
     DiffResults = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
     Diffractor = "9f5e2b26-1114-432f-b630-d3fe2085c51c"
@@ -266,6 +268,7 @@ version = "0.7.16"
     ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
     GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
     GTPSA = "b27dd330-f138-47c5-815b-40db9dd9b6e8"
+    HyperHessians = "06b494a0-c8e0-40cc-ad32-d99506a00a6c"
     Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
     PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
     ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
@@ -298,9 +301,9 @@ uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
 version = "1.0.7"
 
 [[deps.EnzymeCore]]
-git-tree-sha1 = "24bbb6fc8fb87eb71c1f8d00184a60fc22c63903"
+git-tree-sha1 = "c6ee69ee502060982d12dbaaf3d8fcb4e835a0d1"
 uuid = "f151be2c-9106-41f4-ab19-57ee4f262869"
-version = "0.8.19"
+version = "0.8.20"
 weakdeps = ["Adapt", "ChainRulesCore"]
 
     [deps.EnzymeCore.extensions]
@@ -323,9 +326,9 @@ version = "1.11.0"
 
 [[deps.FiniteDiff]]
 deps = ["ArrayInterface", "LinearAlgebra", "Setfield"]
-git-tree-sha1 = "73e879af0e767bd6dfade7c5b09d7b05657a8284"
+git-tree-sha1 = "f7017a4f337f8df189fcce98e32b67a1298a2115"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
-version = "2.30.0"
+version = "2.31.0"
 
     [deps.FiniteDiff.extensions]
     FiniteDiffBandedMatricesExt = "BandedMatrices"
@@ -362,9 +365,9 @@ version = "1.1.3"
 
 [[deps.FunctionWrappersWrappers]]
 deps = ["FunctionWrappers", "PrecompileTools", "TruncatedStacktraces"]
-git-tree-sha1 = "ce6762f8f0e7542534f01523ae051e625cbf0468"
+git-tree-sha1 = "c1b0c3a166a2a393257aa888787ca817532e14ce"
 uuid = "77dc65aa-8811-40c2-897b-53d922fa7daf"
-version = "1.5.0"
+version = "1.8.0"
 
     [deps.FunctionWrappersWrappers.extensions]
     FunctionWrappersWrappersEnzymeExt = ["Enzyme", "EnzymeCore"]
@@ -436,9 +439,9 @@ version = "1.0.0"
 
 [[deps.JLLWrappers]]
 deps = ["Artifacts", "Preferences"]
-git-tree-sha1 = "0533e564aae234aff59ab625543145446d8b6ec2"
+git-tree-sha1 = "7204148362dafe5fe6a273f855b8ccbe4df8173e"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
-version = "1.7.1"
+version = "1.8.0"
 
 [[deps.Krylov]]
 deps = ["LinearAlgebra", "Printf", "SparseArrays"]
@@ -493,9 +496,9 @@ version = "1.18.0+0"
 
 [[deps.LineSearch]]
 deps = ["ADTypes", "CommonSolve", "ConcreteStructs", "FastClosures", "LinearAlgebra", "MaybeInplace", "PrecompileTools", "SciMLBase", "SciMLJacobianOperators", "StaticArraysCore"]
-git-tree-sha1 = "69da095e4c24ed3c4a168bb76dc9c620a6d7239c"
+git-tree-sha1 = "fd58a77c92e7c8f1db25c9839127d52943a49349"
 uuid = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
-version = "0.1.7"
+version = "0.1.9"
 
     [deps.LineSearch.extensions]
     LineSearchLineSearchesExt = "LineSearches"
@@ -510,9 +513,9 @@ version = "1.11.0"
 
 [[deps.LinearSolve]]
 deps = ["ArrayInterface", "ConcreteStructs", "DocStringExtensions", "EnumX", "GPUArraysCore", "InteractiveUtils", "Krylov", "Libdl", "LinearAlgebra", "MKL_jll", "Markdown", "OpenBLAS_jll", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLLogging", "SciMLOperators", "Setfield", "StaticArraysCore"]
-git-tree-sha1 = "42b5cb44317e89ef75dd841c9c8eba9045bf9ff0"
+git-tree-sha1 = "04940e970234c6ac650eec9adfc62677cca2328d"
 uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
-version = "3.75.0"
+version = "3.76.0"
 
     [deps.LinearSolve.extensions]
     LinearSolveAMDGPUExt = "AMDGPU"
@@ -537,12 +540,12 @@ version = "3.75.0"
     LinearSolveKrylovKitExt = "KrylovKit"
     LinearSolveMetalExt = "Metal"
     LinearSolveMooncakeExt = "Mooncake"
-    LinearSolvePETScCSRExt = ["PETSc", "SparseArrays", "SparseMatricesCSR"]
-    LinearSolvePETScExt = ["PETSc", "SparseArrays"]
+    LinearSolvePETScExt = ["PETSc", "SparseArrays", "SparseMatricesCSR"]
     LinearSolvePETScMPIExt = ["PETSc", "PartitionedArrays", "SparseArrays", "SparseMatricesCSR"]
     LinearSolveParUExt = ["ParU_jll", "SparseArrays"]
     LinearSolvePardisoExt = ["Pardiso", "SparseArrays"]
     LinearSolveRecursiveFactorizationExt = "RecursiveFactorization"
+    LinearSolveSTRUMPACKExt = ["SparseArrays", "STRUMPACK_jll"]
     LinearSolveSparseArraysExt = "SparseArrays"
     LinearSolveSparspakExt = ["SparseArrays", "Sparspak"]
 
@@ -574,6 +577,7 @@ version = "3.75.0"
     Pardiso = "46dd5b70-b6fb-5a00-ae2d-e8fea33afaf2"
     PartitionedArrays = "5a9dfac6-5c52-46f7-8278-5e2210713be9"
     RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
+    STRUMPACK_jll = "86fbd0b9-476f-557c-b766-62c724b42d8c"
     SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
     SparseMatricesCSR = "a0a7dd2c-ebf4-11e9-1f05-cf50bc540ca1"
     Sparspak = "e56a9233-b9d6-4f03-8d0f-1825330902ac"
@@ -661,9 +665,9 @@ version = "1.2.0"
 
 [[deps.NonlinearSolve]]
 deps = ["ADTypes", "ArrayInterface", "BracketingNonlinearSolve", "CommonSolve", "ConcreteStructs", "DifferentiationInterface", "FastClosures", "FiniteDiff", "ForwardDiff", "LineSearch", "LinearAlgebra", "LinearSolve", "NonlinearSolveBase", "NonlinearSolveFirstOrder", "NonlinearSolveQuasiNewton", "NonlinearSolveSpectralMethods", "PrecompileTools", "Preferences", "Reexport", "SciMLBase", "SciMLLogging", "Setfield", "SimpleNonlinearSolve", "StaticArraysCore", "SymbolicIndexingInterface"]
-git-tree-sha1 = "e88921859836899abe94d08ea0fd42137067280e"
+git-tree-sha1 = "ae0b0f875e4dfda538ab6977ec7939126ee9a1fe"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
-version = "4.17.1"
+version = "4.19.0"
 
     [deps.NonlinearSolve.extensions]
     NonlinearSolveFastLevenbergMarquardtExt = "FastLevenbergMarquardt"
@@ -853,9 +857,9 @@ version = "1.3.4"
 
 [[deps.RecursiveArrayTools]]
 deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "LinearAlgebra", "PrecompileTools", "RecipesBase", "StaticArraysCore", "SymbolicIndexingInterface"]
-git-tree-sha1 = "79a5a1a5b6294c54602d18a59026ec0b07471054"
+git-tree-sha1 = "57b6fb3932fc8d1fc911f840d2c9de5fe3ba5008"
 uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
-version = "4.2.0"
+version = "4.3.0"
 
     [deps.RecursiveArrayTools.extensions]
     RecursiveArrayToolsCUDAExt = "CUDA"
@@ -912,11 +916,16 @@ version = "0.5.18"
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
 
+[[deps.SafeTestsets]]
+git-tree-sha1 = "81ec49d645af090901120a1542e67ecbbe044db3"
+uuid = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+version = "0.1.0"
+
 [[deps.SciMLBase]]
 deps = ["ADTypes", "Accessors", "Adapt", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "PreallocationTools", "PrecompileTools", "Preferences", "Printf", "Random", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLLogging", "SciMLOperators", "SciMLPublic", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface"]
-git-tree-sha1 = "4fdad3606c60fbbd52424737c31ec4141672c809"
+git-tree-sha1 = "fed3c3d9781685d982256f94ac85ad4ddf8ee78f"
 uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-version = "3.3.0"
+version = "3.10.0"
 
     [deps.SciMLBase.extensions]
     SciMLBaseChainRulesCoreExt = "ChainRulesCore"
@@ -963,9 +972,9 @@ version = "0.1.13"
 
 [[deps.SciMLLogging]]
 deps = ["Logging", "LoggingExtras", "Preferences"]
-git-tree-sha1 = "0161be062570af4042cf6f69e3d5d0b0555b6927"
+git-tree-sha1 = "35bdd8e578af78030d98b262461e8eedc045d943"
 uuid = "a6db7da4-7206-11f0-1eab-35f2a5dbe1d1"
-version = "1.9.1"
+version = "1.10.0"
 
     [deps.SciMLLogging.extensions]
     SciMLLoggingTracyExt = "Tracy"
@@ -974,16 +983,21 @@ version = "1.9.1"
     Tracy = "e689c965-62c8-4b79-b2c5-8359227902fd"
 
 [[deps.SciMLOperators]]
-deps = ["Accessors", "ArrayInterface", "DocStringExtensions", "LinearAlgebra"]
-git-tree-sha1 = "234869cf9fee9258a95464b7a7065cc7be84db00"
+deps = ["Accessors", "Adapt", "ArrayInterface", "DocStringExtensions", "LinearAlgebra", "SafeTestsets"]
+git-tree-sha1 = "ef54b9bcfc6694b11aea8458619d1416885bec1e"
 uuid = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
-version = "1.16.0"
-weakdeps = ["SparseArrays", "StaticArraysCore"]
+version = "1.20.0"
 
     [deps.SciMLOperators.extensions]
+    SciMLOperatorsLoopVectorizationExt = "LoopVectorization"
     SciMLOperatorsSparseArraysExt = "SparseArrays"
     SciMLOperatorsStaticArraysCoreExt = "StaticArraysCore"
 
+    [deps.SciMLOperators.weakdeps]
+    LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+
 [[deps.SciMLPublic]]
 git-tree-sha1 = "0ba076dbdce87ba230fff48ca9bca62e1f345c9b"
 uuid = "431bcebd-1456-4ced-9d72-93c2757fff0b"
@@ -1089,9 +1103,9 @@ version = "7.7.0+0"
 
 [[deps.SymbolicIndexingInterface]]
 deps = ["Accessors", "ArrayInterface", "RuntimeGeneratedFunctions", "StaticArraysCore"]
-git-tree-sha1 = "94c58884e013efff548002e8dc2fdd1cb74dfce5"
+git-tree-sha1 = "173ecfe5f7c5a36043b5f2b8cecaa30a4fc958ef"
 uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
-version = "0.3.46"
+version = "0.3.47"
 
     [deps.SymbolicIndexingInterface.extensions]
     SymbolicIndexingInterfacePrettyTablesExt = "PrettyTables"
@@ -1182,9 +1196,9 @@ version = "1.59.0+0"
 
 [[deps.oneTBB_jll]]
 deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
-git-tree-sha1 = "1350188a69a6e46f799d3945beef36435ed7262f"
+git-tree-sha1 = "da8c1f6eee04831f14edcfa5dae611d309807e57"
 uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
-version = "2022.0.0+1"
+version = "2022.3.0+0"
 
 [[deps.p7zip_jll]]
 deps = ["Artifacts", "Libdl"]