[Extend] Add a test for the minimisation logic

See if our alternating Gauss-Seidel scheme can really minimise distances

dune/tectonic/CMakeLists.txt

+add_subdirectory(test)
+
 install(FILES
   body.hh
   frictiondata.hh

dune/tectonic/test/CMakeLists.txt

+set(TESTS test-polyhedral-minimisation)
+foreach(_test ${TESTS})
+  add_executable(${_test} EXCLUDE_FROM_ALL ${_test}.cc)
+  target_link_dune_default_libraries(${_test})
+  add_test(${_test} ${_test})
+endforeach()
+
+add_directory_test_target(_test_target)
+add_dependencies(${_test_target} ${TESTS})

dune/tectonic/test/test-polyhedral-minimisation.cc

+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#include <dune/common/fvector.hh>
+
+#include <dune/tectonic/polyhedrondistance.hh>
+
+int main() {
+  using LocalVector = Dune::FieldVector<double, 2>;
+
+  auto const test =
+      [&](ConvexPolyhedron<LocalVector> const &p1,
+          ConvexPolyhedron<LocalVector> const &p2, double analyticalDistance) {
+        LocalVector target;
+        {
+          double const error =
+              std::abs(analyticalDistance - distance(p1, p2, 1e-12));
+          std::cout << "error: " << error << std::endl;
+          assert(error < 1e-12);
+        }
+      };
+  {
+    /*
+     * Calculate the distance between two triangles, where it is attained at a
+     * face-vertex pair
+     *
+     *    O
+     *    |\
+     *    | \
+     * O  O--O
+     * |\
+     * | \
+     * O--O
+     */
+    double const analyticalDistance = std::sqrt(2.0);
+    LocalVector tmp;
+
+    ConvexPolyhedron<LocalVector> bs1;
+    bs1.vertices.resize(3);
+    tmp[0] = 0;
+    tmp[1] = 0;
+    bs1.vertices[0] = tmp;
+    tmp[0] = 0;
+    tmp[1] = 2;
+    bs1.vertices[1] = tmp;
+    tmp[0] = 2;
+    tmp[1] = 0;
+    bs1.vertices[2] = tmp;
+
+    ConvexPolyhedron<LocalVector> bs2;
+    bs2.vertices.resize(3);
+    tmp[0] = 2;
+    tmp[1] = 2;
+    bs2.vertices[0] = tmp;
+    tmp[0] = 2;
+    tmp[1] = 4;
+    bs2.vertices[1] = tmp;
+    tmp[0] = 4;
+    tmp[1] = 2;
+    bs2.vertices[2] = tmp;
+
+    test(bs1, bs2, analyticalDistance);
+  }
+
+  {
+    /*
+     * Calculate the distance between two triangles, where it is
+     * attained in a face-face pair
+     *
+     *    O--O
+     *     \ |
+     *      \|
+     * O     O
+     * |\
+     * | \
+     * O--O
+     */
+    double const analyticalDistance = 2.0 * std::sqrt(2.0);
+    LocalVector tmp;
+
+    ConvexPolyhedron<LocalVector> bs1;
+    bs1.vertices.resize(3);
+    tmp[0] = 0;
+    tmp[1] = 0;
+    bs1.vertices[0] = tmp;
+    tmp[0] = 0;
+    tmp[1] = 2;
+    bs1.vertices[1] = tmp;
+    tmp[0] = 2;
+    tmp[1] = 0;
+    bs1.vertices[2] = tmp;
+
+    ConvexPolyhedron<LocalVector> bs2;
+    bs2.vertices.resize(3);
+    tmp[0] = 4;
+    tmp[1] = 4;
+    bs2.vertices[0] = tmp;
+    tmp[0] = 2;
+    tmp[1] = 4;
+    bs2.vertices[1] = tmp;
+    tmp[0] = 4;
+    tmp[1] = 2;
+    bs2.vertices[2] = tmp;
+
+    test(bs1, bs2, analyticalDistance);
+  }
+
+  {
+    /*
+     * Calculate the distance between two triangles, where it is
+     * attained in a vertex-vertex pair
+     *
+     *       O
+     *       |\
+     *       | \
+     * O--O  O--O
+     *  \ |
+     *   \|
+     *    O
+     */
+    double analyticalDistance = 2.0;
+    LocalVector tmp;
+
+    ConvexPolyhedron<LocalVector> bs1;
+    bs1.vertices.resize(3);
+    tmp[0] = 2;
+    tmp[1] = 2;
+    bs1.vertices[0] = tmp;
+    tmp[0] = 0;
+    tmp[1] = 2;
+    bs1.vertices[1] = tmp;
+    tmp[0] = 2;
+    tmp[1] = 0;
+    bs1.vertices[2] = tmp;
+
+    ConvexPolyhedron<LocalVector> bs2;
+    bs2.vertices.resize(3);
+    tmp[0] = 4;
+    tmp[1] = 2;
+    bs2.vertices[0] = tmp;
+    tmp[0] = 4;
+    tmp[1] = 4;
+    bs2.vertices[1] = tmp;
+    tmp[0] = 6;
+    tmp[1] = 2;
+    bs2.vertices[2] = tmp;
+
+    test(bs1, bs2, analyticalDistance);
+  }
+}