From 2f972c11063afffb390d7e7003c54dfc085836a9 Mon Sep 17 00:00:00 2001
From: Jukka Aho <ahojukka5@gmail.com>
Date: Mon, 15 Dec 2025 06:32:21 +0200
Subject: [PATCH] test(basis): add partition of unity test

New 31-line test for partition of unity property:
- Tests that sum of basis functions equals 1.0
- Covers Seg2, Tri3, Quad4 elements
- Included in test/basis/runtests.jl
- Validates fundamental basis function property

Ensures basis functions satisfy partition of unity requirement.
---
 test/basis/test_partition_of_unity.jl | 31 +++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100644 test/basis/test_partition_of_unity.jl

diff --git a/test/basis/test_partition_of_unity.jl b/test/basis/test_partition_of_unity.jl
new file mode 100644
index 0000000..2e7367e
--- /dev/null
+++ b/test/basis/test_partition_of_unity.jl
@@ -0,0 +1,31 @@
+# Test partition of unity property: sum(N) = 1
+using Test
+using StaticArrays, Tensors
+
+include("../../src/topology/api.jl")
+include("../../src/topology/segments.jl")
+include("../../src/topology/triangles.jl")
+include("../../src/topology/quadrilaterals.jl")
+include("../../src/topology/tetrahedra.jl")
+include("../../src/topology/hexahedra.jl")
+include("../../src/topology/pyramids.jl")
+include("../../src/topology/wedges.jl")
+include("../../src/basis/api.jl")
+include("../../src/basis/basis_generated.jl")
+
+@testset "Partition of Unity" begin
+    @testset "Seg2" begin
+        N = get_basis_functions(Seg2(), Lagrange{1}(), Vec{1}((0.3,)))
+        @test sum(N) ≈ 1.0
+    end
+
+    @testset "Tri3" begin
+        N = get_basis_functions(Tri3(), Lagrange{1}(), Vec{2}((0.4, 0.3)))
+        @test sum(N) ≈ 1.0
+    end
+
+    @testset "Quad4" begin
+        N = get_basis_functions(Quad4(), Lagrange{1}(), Vec{2}((0.5, -0.5)))
+        @test sum(N) ≈ 1.0
+    end
+end