[test] Add point-2d-simplex intersection test in 2d and 3d

test/common/geometry/CMakeLists.txt

 dumux_add_test(SOURCES test_0d1d_intersection.cc LABELS unit)
+dumux_add_test(SOURCES test_0d2d_intersection.cc LABELS unit)
 dumux_add_test(SOURCES test_0d3d_intersection.cc LABELS unit)
 dumux_add_test(SOURCES test_1d1d_intersection.cc LABELS unit)
 dumux_add_test(SOURCES test_1d3d_intersection.cc LABELS unit)

test/common/geometry/test_0d2d_intersection.cc

+#include <config.h>
+
+#include <iostream>
+#include <algorithm>
+#include <functional>
+#include <type_traits>
+
+#include <dune/common/classname.hh>
+#include <dune/common/exceptions.hh>
+#include <dune/common/fvector.hh>
+#include <dune/geometry/type.hh>
+#include <dune/geometry/multilineargeometry.hh>
+
+#include <dumux/common/math.hh>
+#include <dumux/common/geometry/intersectspointgeometry.hh>
+
+#ifndef DOXYGEN
+template<class Geometry>
+bool testIntersection(const Geometry& geo,
+                      const typename Geometry::GlobalCoordinate& p,
+                      bool foundExpected, bool verbose)
+{
+    bool found = Dumux::intersectsPointGeometry(p, geo);
+    if (!found && foundExpected)
+    {
+        std::cerr << "  Failed detecting intersection of " << geo.type();
+        for (int i = 0; i < geo.corners(); ++i)
+            std::cerr << " (" << geo.corner(i) << ")";
+        std::cerr << " with point: " << p << std::endl;
+    }
+    else if (found && !foundExpected)
+    {
+        std::cerr << "  Found false positive: intersection of " << geo.type();
+        for (int i = 0; i < geo.corners(); ++i)
+            std::cerr << " (" << geo.corner(i) << ")";
+        std::cerr << " with point: " << p << std::endl;
+    }
+    if (verbose)
+    {
+        if (found && foundExpected)
+            std::cout << "  Found intersection with " << p << std::endl;
+        else if (!found && !foundExpected)
+            std::cout << "  No intersection with " << p << std::endl;
+    }
+    return (found == foundExpected);
+}
+
+template<int dimworld, class Transformation>
+void runIntersectionTest(std::vector<bool>& returns, const Transformation& transform, bool verbose)
+{
+    using ctype = typename std::decay_t<decltype(transform({0.0}))>::value_type;
+    using Geo = Dune::MultiLinearGeometry<ctype, 2, dimworld>;
+    using Points = std::vector<typename Geo::GlobalCoordinate>;
+
+    // test triangle-point intersections
+    if (verbose) std::cout << "\n  -- Test triangle-point intersections" << std::endl;
+
+    if constexpr (dimworld == 2)
+    {
+        auto cornersTri = Points ({{0.0, 0.0}, {1.0, 0.0}, {0.0, 1.0}});
+        std::transform(cornersTri.begin(), cornersTri.end(), cornersTri.begin(),
+                       [&transform](const auto& p) { return transform(p); });
+        auto triangle = Geo(Dune::GeometryTypes::triangle, cornersTri);
+
+        for (const auto& corner : cornersTri)
+            returns.push_back(testIntersection(triangle, corner, true, verbose));
+
+        returns.push_back(testIntersection(triangle, transform({0.25, 0.25}), true, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.5, 0.5}), true, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.0, 0.5}), true, verbose));
+        returns.push_back(testIntersection(triangle, transform({1.01, 0.0}), false, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.5, 0.51}), false, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.0, -0.01}), false, verbose));
+    }
+
+    if constexpr (dimworld == 3)
+    {
+        auto cornersTri = Points ({{0.0, 0.0, 2.0}, {1.0, 0.0, 2.0}, {0.0, 1.0, 2.0}});
+        std::transform(cornersTri.begin(), cornersTri.end(), cornersTri.begin(),
+                       [&transform](const auto& p) { return transform(p); });
+        auto triangle = Geo(Dune::GeometryTypes::triangle, cornersTri);
+
+        for (const auto& corner : cornersTri)
+            returns.push_back(testIntersection(triangle, corner, true, verbose));
+
+        returns.push_back(testIntersection(triangle, transform({0.25, 0.25, 2.0}), true, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.5, 0.5, 2.0}), true, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.0, 0.5, 2.0}), true, verbose));
+        returns.push_back(testIntersection(triangle, transform({1.01, 0.0, 2.0}), false, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.5, 0.51, 2.0}), false, verbose));
+        returns.push_back(testIntersection(triangle, transform({0.0, -0.01, 2.0}), false, verbose));
+    }
+
+    // test quadrilateral-point intersections
+    if (verbose) std::cout << "\n  -- Test quadrilateral-point intersections" << std::endl;
+
+    if constexpr (dimworld == 2)
+    {
+        auto cornersQuad = Points ({{0.0, 0.0}, {1.0, 0.0}, {0.0, 1.0}, {1.0, 1.0}});
+        std::transform(cornersQuad.begin(), cornersQuad.end(), cornersQuad.begin(),
+                       [&transform](const auto& p) { return transform(p); });
+        auto quadrilateral = Geo(Dune::GeometryTypes::quadrilateral, cornersQuad);
+
+        for (const auto& corner : cornersQuad)
+            returns.push_back(testIntersection(quadrilateral, corner, true, verbose));
+
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 0.5}), true, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 0.0}), true, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 1.0}), true, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({1.01, 1.0}), false, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 1.01}), false, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.0, -0.01}), false, verbose));
+    }
+
+    if constexpr (dimworld == 3)
+    {
+        auto cornersQuad = Points ({{0.0, 0.0, 2.0}, {1.0, 0.0, 2.0}, {0.0, 1.0, 2.0}, {1.0, 1.0, 2.0}});
+        std::transform(cornersQuad.begin(), cornersQuad.end(), cornersQuad.begin(),
+                       [&transform](const auto& p) { return transform(p); });
+        auto quadrilateral = Geo(Dune::GeometryTypes::quadrilateral, cornersQuad);
+
+        for (const auto& corner : cornersQuad)
+            returns.push_back(testIntersection(quadrilateral, corner, true, verbose));
+
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 0.5, 2.0}), true, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 0.0, 2.0}), true, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 1.0, 2.0}), true, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({1.01, 1.0, 2.0}), false, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.5, 1.01, 2.0}), false, verbose));
+        returns.push_back(testIntersection(quadrilateral, transform({0.0, -0.01, 2.0}), false, verbose));
+    }
+}
+
+template<class ctype>
+auto create2DTransformation(const ctype scale,
+                          const Dune::FieldVector<ctype, 2>& translate,
+                          const ctype rotationAngle)
+{
+    std::cout << "Intersection test with transformation:"
+              << " ctype: " << Dune::className<ctype>()
+              << ", scaling: " << scale
+              << ", translation: " << translate
+              << ", rotationAngle: " << rotationAngle << std::endl;
+    // Rotation of a vector in two dimensions
+    // See rotation matrix (2d) at https://en.wikipedia.org/wiki/Rotation_matrix
+    const ctype sinAngle = std::sin(rotationAngle);
+    const ctype cosAngle = std::cos(rotationAngle);
+    return [=](Dune::FieldVector<ctype, 2> p){
+        p *= scale;
+        p.axpy(scale, translate);
+        auto tp = p;
+        tp[0] = p[0]*cosAngle-p[1]*sinAngle;
+        tp[1] = p[0]*sinAngle+p[1]*cosAngle;
+        return tp;
+    };
+}
+
+template<class ctype>
+auto create3DTransformation(const ctype scale,
+                          const Dune::FieldVector<ctype, 3>& translate,
+                          const Dune::FieldVector<ctype, 3>& rotationAxis,
+                          const ctype rotationAngle)
+{
+    std::cout << "Intersection test with transformation:"
+              << " ctype: " << Dune::className<ctype>()
+              << ", scaling: " << scale
+              << ", translation: " << translate
+              << ", rotationAxis: " << rotationAxis
+              << ", rotationAngle: " << rotationAngle << std::endl;
+    // Rotation of a vector in three dimensions
+    // See Rodrigues' rotation formular at https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
+    const ctype sinAngle = std::sin(rotationAngle);
+    const ctype cosAngle = std::cos(rotationAngle);
+    return [=](Dune::FieldVector<ctype, 3> p){
+        p *= scale;
+        p.axpy(scale, translate);
+        auto tp = p;
+        tp *= cosAngle;
+        tp.axpy(sinAngle, Dumux::crossProduct({rotationAxis}, p));
+        return tp.axpy((1.0-cosAngle)*(rotationAxis*p), rotationAxis);
+    };
+}
+
+#endif
+
+int main (int argc, char *argv[]) try
+{
+    // collect returns to determine exit code
+    std::vector<bool> returns;
+    constexpr bool verbose = false;
+
+    {
+        constexpr int dimworld = 2;
+        using Vec = Dune::FieldVector<double, dimworld>;
+
+        std::cout << "Test for point intersection with 2d geometries in 2d corddim" << std::endl;
+        for (const double scaling : {1.0, 1e3, 1e12, 1e-12})
+            for (const auto& translation : {0.0, 1.0})
+                for (const double angle : {0.0, 0.2*M_PI, 0.5*M_PI, 0.567576567*M_PI, M_PI})
+                    runIntersectionTest<dimworld>(returns, create2DTransformation<double>(scaling, Vec(translation), angle), verbose);
+    }
+
+    {
+        constexpr int dimworld = 3;
+        using Vec = Dune::FieldVector<double, dimworld>;
+
+        std::cout << "Test for point intersection with 2d geometries in 3d corddim" << std::endl;
+        for (const double scaling : {1.0, 1e3, 1e12, 1e-12})
+            for (const auto& translation : {0.0, 1.0})
+                for (const double angle : {0.0, 0.2*M_PI, 0.5*M_PI, 0.567576567*M_PI, M_PI})
+                    for (const auto& rotAxis : {Vec(std::sqrt(3.0)/3.0), Vec({std::sqrt(2.0)/2.0, std::sqrt(2.0)/2.0, 0.0})})
+                        runIntersectionTest<dimworld>(returns, create3DTransformation<double>(scaling, Vec(translation), rotAxis, angle), verbose);
+    }
+
+    // determine the exit code
+    if (std::any_of(returns.begin(), returns.end(), std::logical_not<bool>{}))
+        return 1;
+
+    std::cout << "\n++++++++++++++++++++++\n"
+              << "All tests passed!"
+              << "\n++++++++++++++++++++++" << std::endl;
+
+    return 0;
+}
+// //////////////////////////////////
+//   Error handler
+// /////////////////////////////////
+catch (const Dune::Exception& e) {
+    std::cout << e << std::endl;
+    return 1;
+}