Add tests for integration along 2d and 3d lines

tests/test_LineTransformation.cpp

 #include <catch2/catch_approx.hpp>
 #include <catch2/catch_test_macros.hpp>
 
+#include <analysis/GaussQuadratureDescriptor.hpp>
+#include <analysis/QuadratureManager.hpp>
 #include <geometry/LineTransformation.hpp>
 
 // clazy:excludeall=non-pod-global-static
@@ -40,6 +42,21 @@ TEST_CASE("LineTransformation", "[geometry]")
     REQUIRE(t(1)[1] == Catch::Approx(0.7));
 
     REQUIRE(t.velocityNorm() == Catch::Approx(l2Norm(0.5 * (b - a))));
+
+    auto p = [](const R2& X) {
+      const double x = X[0];
+      const double y = X[1];
+      return 2 * x * x + 3 * x - 3 * y * y + y + 2;
+    };
+
+    QuadratureFormula<1> qf = QuadratureManager::instance().getLineFormula(GaussQuadratureDescriptor(2));
+
+    double sum = 0;
+    for (size_t i = 0; i < qf.numberOfPoints(); ++i) {
+      sum += qf.weight(i) * t.velocityNorm() * p(t(qf.point(i)));
+    }
+
+    REQUIRE(sum == Catch::Approx(24.8585155630822));
   }
 
   SECTION("3D")
@@ -62,5 +79,21 @@ TEST_CASE("LineTransformation", "[geometry]")
     REQUIRE(t(1)[2] == Catch::Approx(0.3));
 
     REQUIRE(t.velocityNorm() == Catch::Approx(l2Norm(0.5 * (b - a))));
+
+    auto p = [](const R3& X) {
+      const double x = X[0];
+      const double y = X[1];
+      const double z = X[2];
+      return 2 * x * x + 3 * x - 3 * y * y + y + 2 * z * z - 0.5 * z + 2;
+    };
+
+    QuadratureFormula<1> qf = QuadratureManager::instance().getLineFormula(GaussQuadratureDescriptor(2));
+
+    double sum = 0;
+    for (size_t i = 0; i < qf.numberOfPoints(); ++i) {
+      sum += qf.weight(i) * t.velocityNorm() * p(t(qf.point(i)));
+    }
+
+    REQUIRE(sum == Catch::Approx(30.08440406681767));
   }
 }