--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/Grids/manifolds_test.jl	Thu May 01 15:05:11 2025 +0200
@@ -0,0 +1,217 @@
+using Test
+
+using Diffinitive.Grids
+using Diffinitive.RegionIndices
+using Diffinitive.LazyTensors
+
+using StaticArrays
+
+west = CartesianBoundary{1,LowerBoundary}
+east = CartesianBoundary{1,UpperBoundary}
+south = CartesianBoundary{2,LowerBoundary}
+north = CartesianBoundary{2,UpperBoundary}
+bottom = CartesianBoundary{3, LowerBoundary}
+top = CartesianBoundary{3, UpperBoundary}
+
+@testset "Chart" begin
+    X(ξ) = 2ξ
+    Grids.jacobian(::typeof(X), ξ) = @SMatrix[2 0; 0 2]
+    c = Chart(X, unitsquare())
+    @test c isa Chart{2}
+    @test parameterspace(c) == unitsquare()
+    @test ndims(c) == 2
+
+    @testset "Calling" begin
+        c = Chart(X, unitsquare())
+        @test c([.3,.2]) == [.6,.4]
+        @test_throws DomainError c([3,2])
+    end
+
+    @testset "jacobian(::Chart, ⋅)" begin
+        c = Chart(X, unitsquare())
+        @test_throws DomainError jacobian(c, [3,2])
+        @test jacobian(c, [.3,.2]) == [2 0; 0 2]
+    end
+
+    @test Set(boundary_identifiers(Chart(X,unitsquare()))) == Set([east(),west(),south(),north()])
+end
+
+@testset "CartesianAtlas" begin
+    @testset "Constructors" begin
+        c = Chart(identity, unitsquare())
+        @test CartesianAtlas([c c; c c]) isa Atlas
+
+        c2 = Chart(x->2x, unitsquare())
+        @test CartesianAtlas([c c2; c2 c]) isa CartesianAtlas
+        @test CartesianAtlas(@SMatrix[c c; c c]) isa CartesianAtlas
+        @test CartesianAtlas(@SMatrix[c c2; c2 c]) isa CartesianAtlas
+    end
+
+    @testset "Getters" begin
+        c = Chart(identity, unitsquare())
+        a = CartesianAtlas([c c; c c])
+        @test charts(a) == [c c; c c]
+    end
+
+    @testset "connections" begin
+        # 2D
+        a = CartesianAtlas(fill(Chart(identity, unitsquare()), 2,3))
+
+        @test Set(connections(a)) == Set([
+            (MultiBlockBoundary{(1,1), east}(), MultiBlockBoundary{(2,1), west}()),
+            (MultiBlockBoundary{(1,1), north}(), MultiBlockBoundary{(1,2), south}()),
+            (MultiBlockBoundary{(2,1), north}(), MultiBlockBoundary{(2,2), south}()),
+            (MultiBlockBoundary{(1,2), east}(), MultiBlockBoundary{(2,2), west}()),
+            (MultiBlockBoundary{(1,2), north}(), MultiBlockBoundary{(1,3), south}()),
+            (MultiBlockBoundary{(2,2), north}(), MultiBlockBoundary{(2,3), south}()),
+            (MultiBlockBoundary{(1,3), east}(), MultiBlockBoundary{(2,3), west}()),
+        ])
+
+        # 3D
+        a = CartesianAtlas(fill(Chart(identity, unitcube()), 2,2,3))
+        @test Set(connections(a)) == Set([
+            (MultiBlockBoundary{(1,1,1), east}(),  MultiBlockBoundary{(2,1,1), west}()),
+            (MultiBlockBoundary{(1,1,1), north}(), MultiBlockBoundary{(1,2,1), south}()),
+            (MultiBlockBoundary{(2,1,1), north}(), MultiBlockBoundary{(2,2,1), south}()),
+            (MultiBlockBoundary{(1,2,1), east}(),  MultiBlockBoundary{(2,2,1), west}()),
+
+            (MultiBlockBoundary{(1,1,2), east}(),  MultiBlockBoundary{(2,1,2), west}()),
+            (MultiBlockBoundary{(1,1,2), north}(), MultiBlockBoundary{(1,2,2), south}()),
+            (MultiBlockBoundary{(2,1,2), north}(), MultiBlockBoundary{(2,2,2), south}()),
+            (MultiBlockBoundary{(1,2,2), east}(),  MultiBlockBoundary{(2,2,2), west}()),
+
+            (MultiBlockBoundary{(1,1,3), east}(),  MultiBlockBoundary{(2,1,3), west}()),
+            (MultiBlockBoundary{(1,1,3), north}(), MultiBlockBoundary{(1,2,3), south}()),
+            (MultiBlockBoundary{(2,1,3), north}(), MultiBlockBoundary{(2,2,3), south}()),
+            (MultiBlockBoundary{(1,2,3), east}(),  MultiBlockBoundary{(2,2,3), west}()),
+
+            (MultiBlockBoundary{(1,1,1), top}(), MultiBlockBoundary{(1,1,2), bottom}()),
+            (MultiBlockBoundary{(2,1,1), top}(), MultiBlockBoundary{(2,1,2), bottom}()),
+            (MultiBlockBoundary{(1,2,1), top}(), MultiBlockBoundary{(1,2,2), bottom}()),
+            (MultiBlockBoundary{(2,2,1), top}(), MultiBlockBoundary{(2,2,2), bottom}()),
+
+            (MultiBlockBoundary{(1,1,2), top}(), MultiBlockBoundary{(1,1,3), bottom}()),
+            (MultiBlockBoundary{(2,1,2), top}(), MultiBlockBoundary{(2,1,3), bottom}()),
+            (MultiBlockBoundary{(1,2,2), top}(), MultiBlockBoundary{(1,2,3), bottom}()),
+            (MultiBlockBoundary{(2,2,2), top}(), MultiBlockBoundary{(2,2,3), bottom}()),
+        ])
+    end
+
+    @testset "boundary_identifiers" begin
+        # 2D
+        a = CartesianAtlas(fill(Chart(identity, unitcube()), 2,3))
+        @test Set(boundary_identifiers(a)) == Set([
+            MultiBlockBoundary{(1,1), south}(),
+            MultiBlockBoundary{(2,1), south}(),
+            MultiBlockBoundary{(2,1), east}(),
+            MultiBlockBoundary{(2,2), east}(),
+            MultiBlockBoundary{(2,3), east}(),
+            MultiBlockBoundary{(1,3), north}(),
+            MultiBlockBoundary{(2,3), north}(),
+            MultiBlockBoundary{(1,1), west}(),
+            MultiBlockBoundary{(1,2), west}(),
+            MultiBlockBoundary{(1,3), west}(),
+        ])
+
+        # 3D
+        a = CartesianAtlas(fill(Chart(identity, unitsquare()), 2,2,3))
+        @test Set(boundary_identifiers(a)) == Set([
+            MultiBlockBoundary{(1,1,1), bottom}(),
+            MultiBlockBoundary{(2,1,1), bottom}(),
+            MultiBlockBoundary{(1,2,1), bottom}(),
+            MultiBlockBoundary{(2,2,1), bottom}(),
+
+            MultiBlockBoundary{(1,1,3), top}(),
+            MultiBlockBoundary{(2,1,3), top}(),
+            MultiBlockBoundary{(1,2,3), top}(),
+            MultiBlockBoundary{(2,2,3), top}(),
+
+            MultiBlockBoundary{(1,1,1), west}(),
+            MultiBlockBoundary{(1,2,1), west}(),
+            MultiBlockBoundary{(1,1,2), west}(),
+            MultiBlockBoundary{(1,2,2), west}(),
+            MultiBlockBoundary{(1,1,3), west}(),
+            MultiBlockBoundary{(1,2,3), west}(),
+
+            MultiBlockBoundary{(2,1,1), east}(),
+            MultiBlockBoundary{(2,2,1), east}(),
+            MultiBlockBoundary{(2,1,2), east}(),
+            MultiBlockBoundary{(2,2,2), east}(),
+            MultiBlockBoundary{(2,1,3), east}(),
+            MultiBlockBoundary{(2,2,3), east}(),
+
+            MultiBlockBoundary{(1,1,1), south}(),
+            MultiBlockBoundary{(2,1,1), south}(),
+            MultiBlockBoundary{(1,1,2), south}(),
+            MultiBlockBoundary{(2,1,2), south}(),
+            MultiBlockBoundary{(1,1,3), south}(),
+            MultiBlockBoundary{(2,1,3), south}(),
+
+            MultiBlockBoundary{(1,2,1), north}(),
+            MultiBlockBoundary{(2,2,1), north}(),
+            MultiBlockBoundary{(1,2,2), north}(),
+            MultiBlockBoundary{(2,2,2), north}(),
+            MultiBlockBoundary{(1,2,3), north}(),
+            MultiBlockBoundary{(2,2,3), north}(),
+        ])
+    end
+end
+
+@testset "UnstructuredAtlas" begin
+    @testset "Constructors" begin
+        c1 = Chart(identity, unitsquare())
+        c2 = Chart(x->2x, unitsquare())
+        cn = [
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+
+        @test UnstructuredAtlas([c1, c1, c1], cn) isa UnstructuredAtlas
+        @test UnstructuredAtlas([c1, c2, c1, c2], cn) isa UnstructuredAtlas
+
+
+        cn = @SVector[
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+        @test UnstructuredAtlas(@SVector[c1, c1, c1], cn) isa UnstructuredAtlas
+        @test UnstructuredAtlas(@SVector[c1, c2, c1, c2], cn) isa UnstructuredAtlas
+    end
+
+    @testset "Getters" begin
+        c = Chart(identity, unitsquare())
+        cn = [
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+
+        a = UnstructuredAtlas([c, c, c], cn)
+
+        @test charts(a) == [c,c,c]
+        @test connections(a) == cn
+    end
+
+    @testset "boundary_identifiers" begin
+        c = Chart(identity, unitsquare())
+        cn = [
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+
+        a = UnstructuredAtlas([c, c, c], cn)
+
+        @test Set(boundary_identifiers(a)) == Set([
+            MultiBlockBoundary{1, west}(),
+            MultiBlockBoundary{1, south}(),
+            MultiBlockBoundary{2, south}(),
+            MultiBlockBoundary{2, east}(),
+            MultiBlockBoundary{3, north}(),
+            MultiBlockBoundary{3, east}(),
+        ])
+
+    end
+end