diff --git a/test/common/geometry/CMakeLists.txt b/test/common/geometry/CMakeLists.txt
index c2e2c5c6c713490e9ef35f6d98a3e371408db367..2ea2a16f3fd26996dfe23c4b74cff95d6c9a491e 100644
--- a/test/common/geometry/CMakeLists.txt
+++ b/test/common/geometry/CMakeLists.txt
@@ -1,4 +1,5 @@
dumux_add_test(SOURCES test_0d1d_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)
dumux_add_test(SOURCES test_1d2d_intersection.cc LABELS unit)
diff --git a/test/common/geometry/test_0d3d_intersection.cc b/test/common/geometry/test_0d3d_intersection.cc
new file mode 100644
index 0000000000000000000000000000000000000000..16c48998884fa06518e290ec3e4f0529f345fc52
--- /dev/null
+++ b/test/common/geometry/test_0d3d_intersection.cc
@@ -0,0 +1,183 @@
+#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<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, 3, 3>;
+ using Points = std::vector<typename Geo::GlobalCoordinate>;
+
+ // test tetrahedron-point intersections
+ if (verbose) std::cout << "\n -- Test tetrahedron-point intersections" << std::endl;
+
+ auto cornersTet = Points({{0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}, {0.0, 1.0, 0.0}, {0.0, 0.0, 1.0}});
+ std::transform(cornersTet.begin(), cornersTet.end(), cornersTet.begin(),
+ [&transform](const auto& p) { return transform(p); });
+ const auto tetrahedron = Geo(Dune::GeometryTypes::tetrahedron, cornersTet);
+
+ for (const auto& corner : cornersTet)
+ returns.push_back(testIntersection(tetrahedron, corner, true, verbose));
+ returns.push_back(testIntersection(tetrahedron, transform({0.0, 0.0, 0.5}), true, verbose));
+ returns.push_back(testIntersection(tetrahedron, transform({0.25, 0.25, 0.5}), true, verbose));
+ returns.push_back(testIntersection(tetrahedron, transform({0.5, 0.5, 0.5}), false, verbose));
+ returns.push_back(testIntersection(tetrahedron, transform({1.01, 0.0, 0.0}), false, verbose));
+ returns.push_back(testIntersection(tetrahedron, transform({0.5, 0.0, 0.51}), false, verbose));
+
+ // test hexahedron-point intersections
+ if (verbose) std::cout << "\n -- Test hexahedron-point intersections" << std::endl;
+
+ auto cornersHex = Points({{0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}, {0.0, 1.0, 0.0}, {1.0, 1.0, 0.0},
+ {0.0, 0.0, 1.0}, {1.0, 0.0, 1.0}, {0.0, 1.0, 1.0}, {1.0, 1.0, 1.0}});
+ std::transform(cornersHex.begin(), cornersHex.end(), cornersHex.begin(),
+ [&transform](const auto& p) { return transform(p); });
+ auto hexahedron = Geo(Dune::GeometryTypes::hexahedron, cornersHex);
+
+ for (const auto& corner : cornersHex)
+ returns.push_back(testIntersection(hexahedron, corner, true, verbose));
+ returns.push_back(testIntersection(hexahedron, transform({0.5, 0.5, 0.5}), true, verbose));
+ returns.push_back(testIntersection(hexahedron, transform({0.01, 0.01, 0.0001}), true, verbose));
+ returns.push_back(testIntersection(hexahedron, transform({1.01, 0.5, 0.5}), false, verbose));
+ returns.push_back(testIntersection(hexahedron, transform({2.0, 2.0, 2.0}), false, verbose));
+ returns.push_back(testIntersection(hexahedron, transform({-0.5, -0.0, -0.51}), false, verbose));
+
+ // test pyramid-point intersections
+ if (verbose) std::cout << "\n -- Test pyramid-point intersections" << std::endl;
+
+ auto cornersPyramid = Points({{0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}, {0.0, 1.0, 0.0},
+ {1.0, 1.0, 0.0}, {0.5, 0.5, 1.0}});
+ std::transform(cornersPyramid.begin(), cornersPyramid.end(), cornersPyramid.begin(),
+ [&transform](const auto& p) { return transform(p); });
+ auto pyramid = Geo(Dune::GeometryTypes::pyramid, cornersPyramid);
+
+ for (const auto& corner : cornersPyramid)
+ returns.push_back(testIntersection(pyramid, corner, true, verbose));
+ returns.push_back(testIntersection(pyramid, transform({0.5, 0.5, 0.0}), true, verbose));
+ returns.push_back(testIntersection(pyramid, transform({0.5, 0.5, 0.7}), true, verbose));
+ returns.push_back(testIntersection(pyramid, transform({0.5, 0.5, -0.0001}), false, verbose));
+ returns.push_back(testIntersection(pyramid, transform({0.25, 0.25, 0.5}), true, verbose));
+ returns.push_back(testIntersection(pyramid, transform({0.25, 0.75, 0.5}), true, verbose));
+ returns.push_back(testIntersection(pyramid, transform({0.75, 0.75, 0.5}), true, verbose));
+ returns.push_back(testIntersection(pyramid, transform({0.25, 0.25, 0.5001}), false, verbose));
+ returns.push_back(testIntersection(pyramid, transform({1.0, 1.0, 0.0001}), false, verbose));
+
+ // test prism-point intersections
+ if (verbose) std::cout << "\n -- Test prism-point intersections" << std::endl;
+
+ auto cornersPrism = Points({{0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}, {0.0, 1.0, 0.0},
+ {0.0, 0.0, 1.0}, {1.0, 0.0, 1.0}, {0.0, 1.0, 1.0}});
+ std::transform(cornersPrism.begin(), cornersPrism.end(), cornersPrism.begin(),
+ [&transform](const auto& p) { return transform(p); });
+ auto prism = Geo(Dune::GeometryTypes::prism, cornersPrism);
+
+ for (const auto& corner : cornersPrism)
+ returns.push_back(testIntersection(prism, corner, true, verbose));
+ returns.push_back(testIntersection(prism, transform({0.25, 0.0, 0.25}), true, verbose));
+ returns.push_back(testIntersection(prism, transform({0.0, 0.25, 0.25}), true, verbose));
+ returns.push_back(testIntersection(prism, transform({0.25, 0.25, 1.0}), true, verbose));
+ returns.push_back(testIntersection(prism, transform({0.25, 0.25, 0.0}), true, verbose));
+ returns.push_back(testIntersection(prism, transform({0.25, 0.25, -0.0001}), false, verbose));
+ returns.push_back(testIntersection(prism, transform({0.25, 0.25, 1.0001}), false, verbose));
+}
+
+template<class ctype>
+auto createTransformation(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;
+ 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;
+
+ using Vec = Dune::FieldVector<double, 3>;
+ for (const double scaling : {1.0, 1e3, 1e12, 1e-12})
+ for (const double 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(returns,
+ createTransformation<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;
+}