Fix face node ordering for Tetrahedron{3} (#475)

This commit fixes the ordering for Ferrite.faces(...) s.t. they are
counter clockwise from the outside. Also adjust the face order for
Lagrange{3,RefCube,2}() to match Lagrange{3,RefCube,1}().

src/Grid/grid.jl

@@ -727,7 +727,7 @@ faces(c::Union{Quadrilateral,QuadraticQuadrilateral}) = ((c.nodes[1],c.nodes[2])
 edges(c::Line3D) = ((c.nodes[1],c.nodes[2]),)
 vertices(c::Union{Tetrahedron,QuadraticTetrahedron}) = (c.nodes[1], c.nodes[2], c.nodes[3], c.nodes[4])
 edges(c::Union{Tetrahedron,QuadraticTetrahedron}) = ((c.nodes[1],c.nodes[2]), (c.nodes[2],c.nodes[3]), (c.nodes[3],c.nodes[1]), (c.nodes[1],c.nodes[4]), (c.nodes[2],c.nodes[4]), (c.nodes[3],c.nodes[4]))
-faces(c::Union{Tetrahedron,QuadraticTetrahedron}) = ((c.nodes[1],c.nodes[2],c.nodes[3]), (c.nodes[1],c.nodes[2],c.nodes[4]), (c.nodes[2],c.nodes[3],c.nodes[4]), (c.nodes[1],c.nodes[4],c.nodes[3]))
+faces(c::Union{Tetrahedron,QuadraticTetrahedron}) = ((c.nodes[1],c.nodes[3],c.nodes[2]), (c.nodes[1],c.nodes[2],c.nodes[4]), (c.nodes[2],c.nodes[3],c.nodes[4]), (c.nodes[1],c.nodes[4],c.nodes[3]))
 vertices(c::Union{Hexahedron,Cell{3,20,6}}) = (c.nodes[1], c.nodes[2], c.nodes[3], c.nodes[4], c.nodes[5], c.nodes[6], c.nodes[7], c.nodes[8])
 edges(c::Union{Hexahedron,Cell{3,20,6}}) = ((c.nodes[1],c.nodes[2]), (c.nodes[2],c.nodes[3]), (c.nodes[3],c.nodes[4]), (c.nodes[4],c.nodes[1]), (c.nodes[5],c.nodes[6]), (c.nodes[6],c.nodes[7]), (c.nodes[7],c.nodes[8]), (c.nodes[8],c.nodes[5]), (c.nodes[1],c.nodes[5]), (c.nodes[2],c.nodes[6]), (c.nodes[3],c.nodes[7]), (c.nodes[4],c.nodes[8]))
 faces(c::Union{Hexahedron,Cell{3,20,6}}) = ((c.nodes[1],c.nodes[4],c.nodes[3],c.nodes[2]), (c.nodes[1],c.nodes[2],c.nodes[6],c.nodes[5]), (c.nodes[2],c.nodes[3],c.nodes[7],c.nodes[6]), (c.nodes[3],c.nodes[4],c.nodes[8],c.nodes[7]), (c.nodes[1],c.nodes[5],c.nodes[8],c.nodes[4]), (c.nodes[5],c.nodes[6],c.nodes[7],c.nodes[8]))

src/interpolations.jl

@@ -337,7 +337,7 @@ end
 getnbasefunctions(::Lagrange{3,RefTetrahedron,1}) = 4
 nvertexdofs(::Lagrange{3,RefTetrahedron,1}) = 1
 
-faces(::Lagrange{3,RefTetrahedron,1}) = ((1,2,3), (1,2,4), (2,3,4), (1,4,3))
+faces(::Lagrange{3,RefTetrahedron,1}) = ((1,3,2), (1,2,4), (2,3,4), (1,4,3))
 edges(::Lagrange{3,RefTetrahedron,1}) = ((1,2), (2,3), (3,1), (1,4), (2,4), (3,4))
 
 function reference_coordinates(::Lagrange{3,RefTetrahedron,1})
@@ -365,7 +365,7 @@ getnbasefunctions(::Lagrange{3,RefTetrahedron,2}) = 10
 nvertexdofs(::Lagrange{3,RefTetrahedron,2}) = 1
 nedgedofs(::Lagrange{3,RefTetrahedron,2}) = 1
 
-faces(::Lagrange{3,RefTetrahedron,2}) = ((1,2,3,5,6,7), (1,2,4,5,9,8), (2,3,4,6,10,9), (1,4,3,8,10,7))
+faces(::Lagrange{3,RefTetrahedron,2}) = ((1,3,2,7,6,5), (1,2,4,5,9,8), (2,3,4,6,10,9), (1,4,3,8,10,7))
 edges(::Lagrange{3,RefTetrahedron,2}) = ((1,5,2), (2,6,3), (3,7,1), (1,8,4), (2,9,4), (3,10,4))
 
 function reference_coordinates(::Lagrange{3,RefTetrahedron,2})
@@ -446,7 +446,14 @@ nedgedofs(::Lagrange{3,RefCube,2}) = 1
 nfacedofs(::Lagrange{3,RefCube,2}) = 1
 ncelldofs(::Lagrange{3,RefCube,2}) = 1
 
-faces(::Lagrange{3,RefCube,2}) = ((1,2,6,5, 9,18,13,17, 23), (2,3,7,6, 10,19,14,18, 22), (3,4,8,7, 11,20,15,19, 24), (1,5,8,4, 12,17,16,20, 21), (1,4,3,2, 9,10,11,12, 25), (5,6,7,8, 13,14,15,16, 26))
+faces(::Lagrange{3,RefCube,2}) = (
+    (1,4,3,2, 9,10,11,12, 25),
+    (1,2,6,5, 9,18,13,17, 23),
+    (2,3,7,6, 10,19,14,18, 22),
+    (3,4,8,7, 11,20,15,19, 24),
+    (1,5,8,4, 12,17,16,20, 21),
+    (5,6,7,8, 13,14,15,16, 26),
+)
 edges(::Lagrange{3,RefCube,2}) = ((1,2, 9), (2,3, 10), (3,4, 11), (4,1, 12), (1,5, 16), (2,6, 19), (3,7, 18), (4,8, 19), (5,6, 13), (6,7, 14), (7,8, 15), (8,5, 16))
 
 function reference_coordinates(::Lagrange{3,RefCube,2})

test/test_interpolations.jl

@@ -51,6 +51,30 @@ for interpolation in (Lagrange{1, RefCube, 1}(),
             end
         end
     end
+
+    # Test that faces(...) return in counter clockwise order (viewing from the outside)
+    if interpolation isa Lagrange
+        function __outward_normal(coords::Vector{<:Vec{1}}, nodes)
+            n = coords[nodes[1]]
+            return n / norm(n)
+        end
+        function __outward_normal(coords::Vector{<:Vec{2}}, nodes)
+            p1 = coords[nodes[1]]
+            p2 = coords[nodes[2]]
+            n = Vec{2}((p2[2] - p1[2], - p2[1] + p1[1]))
+            return n / norm(n)
+        end
+        function __outward_normal(coords::Vector{<:Vec{3}}, nodes)
+            p1 = coords[nodes[1]]
+            p2 = coords[nodes[2]]
+            p3 = coords[nodes[3]]
+            n = (p3 - p2) × (p1 - p2)
+            return n / norm(n)
+        end
+        for (facenodes, normal) in zip(Ferrite.faces(interpolation), reference_normals(interpolation))
+            @test __outward_normal(coords, facenodes) ≈ normal
+        end
+    end
 end
 
 end

test/test_utils.jl

@@ -44,7 +44,7 @@ function reference_normals(::Lagrange{3, RefTetrahedron})
 end
 
 # Lagrange{3, Cube}
-function reference_normals(::Lagrange{3, RefCube, 1})
+function reference_normals(::Lagrange{3, RefCube})
     return [Vec{3, Float64}(( 0.0,  0.0, -1.0)),
             Vec{3, Float64}(( 0.0, -1.0,  0.0)),
             Vec{3, Float64}(( 1.0,  0.0,  0.0)),