[CORE] Fixed issue with projection onto 2D2 line when input does not lie exactly on the line.

kratos/geometries/line_2d_2.h

@@ -1066,26 +1066,13 @@ class Line2D2 : public Geometry<TPointType>
         const TPointType& r_first_point  = BaseType::GetPoint(0);
         const TPointType& r_second_point = BaseType::GetPoint(1);
 
-        // Project point
-        const double tolerance = 1e-14; // Tolerance
+        // Project the point on the line in global space
+        const auto vector_from_first_point_to_input = rPoint - r_first_point;
+        const auto unity_line_direction             = (r_second_point - r_first_point) / Length();
+        const auto projection_on_line               = inner_prod(vector_from_first_point_to_input, unity_line_direction);
 
-        const double length = Length();
-
-        const double length_1 = std::sqrt( std::pow(rPoint[0] - r_first_point[0], 2)
-                    + std::pow(rPoint[1] - r_first_point[1], 2));
-
-        const double length_2 = std::sqrt( std::pow(rPoint[0] - r_second_point[0], 2)
-                    + std::pow(rPoint[1] - r_second_point[1], 2));
-
-        if (length_1 <= (length + tolerance) && length_2 <= (length + tolerance)) {
-            rResult[0] = 2.0 * length_1/(length + tolerance) - 1.0;
-        } else {
-            if (length_1 > length_2) {
-                rResult[0] = 2.0 * length_1/(length + tolerance) - 1.0;
-            } else {
-                rResult[0] = -2.0 * length_1/(length + tolerance) - 1.0;
-            }
-        }
+        // Conversion to local space 
+        rResult[0] = 2.0 * projection_on_line/Length() - 1.0;
 
         return rResult ;
     }
@@ -1409,4 +1396,4 @@ const GeometryData Line2D2<TPointType>::msGeometryData(
 template<class TPointType>
 const GeometryDimension Line2D2<TPointType>::msGeometryDimension(2, 1);
 
-}  // namespace Kratos.
+}  // namespace Kratos.

kratos/tests/cpp_tests/geometries/test_line_2d_2.cpp

@@ -270,6 +270,48 @@ namespace Testing {
         KRATOS_EXPECT_NEAR(test_point_local_coords(2), 0.0, TOLERANCE);
     }
 
+    /** Checks the point local coordinates for a given point respect to the line.
+    * A point 'above' the line is selected (meaning it moved a bit in the direction normal to the line).
+    */
+    KRATOS_TEST_CASE_IN_SUITE(Line2D2PointLocalCoordinates_NotAligned, KratosCoreGeometriesFastSuite)
+    {
+        // Create the test line
+        auto geom = GeneratePointsDiagonalLine2D2();
+
+        // Set the point to be checked, starting at the center and move it in the normal direction
+        Point test_point(0.5 - 0.1,0.5 + 0.1,0.0);
+
+        // Compute the centre local coordinates
+        array_1d<double, 3> test_point_local_coords;
+        geom->PointLocalCoordinates(test_point_local_coords, test_point);
+
+        // Since we started at the center and moved in the normal direction, we expect the local
+        // coordinate to be (0, 0, 0)
+        KRATOS_EXPECT_NEAR(test_point_local_coords(0), 0.0, TOLERANCE);
+        KRATOS_EXPECT_NEAR(test_point_local_coords(1), 0.0, TOLERANCE);
+        KRATOS_EXPECT_NEAR(test_point_local_coords(2), 0.0, TOLERANCE);
+    }
+
+    /** Checks the point local coordinates for a given point respect to the line.
+    * A point outside and not aligned with the line is selected. In this case the distance from first node is larger than the length
+    */
+    KRATOS_TEST_CASE_IN_SUITE(Line2D2PointLocalCoordinatesOutsidePointNotAligned, KratosCoreGeometriesFastSuite)
+    {
+        // Create the test line
+        auto geom = GeneratePointsDiagonalLine2D2();
+
+        // Set the point to be checked (moved in the normal direction)
+        Point test_point(-1.5 - 0.1,-1.5 + 0.1,0.0);
+
+        // Compute the centre local coordinates
+        array_1d<double, 3> test_point_local_coords;
+        geom->PointLocalCoordinates(test_point_local_coords, test_point);
+
+        KRATOS_EXPECT_NEAR(test_point_local_coords(0), -4.0, TOLERANCE);
+        KRATOS_EXPECT_NEAR(test_point_local_coords(1), 0.0, TOLERANCE);
+        KRATOS_EXPECT_NEAR(test_point_local_coords(2), 0.0, TOLERANCE);
+    }
+
     /** Tests the Jacobian determinants using 'GI_GAUSS_1' integration method.
     * Tests the Jacobian determinants using 'GI_GAUSS_1' integration method.
     */