Add helper utilities for reference elements

dune/fu-tutorial/CMakeLists.txt

 #install headers
-install(FILES fu-tutorial.hh DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dune/fu-tutorial)
+install(FILES
+    fu-tutorial.hh
+    referenceelementutility.hh
+    DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dune/fu-tutorial)

dune/fu-tutorial/referenceelementutility.hh

+// -*- tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*-
+// vi: set ts=8 sw=2 et sts=2:
+#ifndef DUNE_FU_TUTORIAL_REFERENCEELEMENTUTILITY_hh
+#define DUNE_FU_TUTORIAL_REFERENCEELEMENTUTILITY_hh
+
+#include <dune/common/reservedvector.hh>
+#include <dune/common/power.hh>
+#include <dune/geometry/referenceelements.hh>
+#include <dune/geometry/dimension.hh>
+
+namespace Dune {
+namespace FuTutorial {
+
+
+
+/**
+ * \brief Encapsulate dynamic codim value
+ */
+class DynamicCodim
+{
+public:
+  constexpr DynamicCodim():
+    value_(0)
+  {}
+
+  constexpr explicit DynamicCodim(std::size_t value) :
+    value_(value)
+  {}
+
+  /**
+   * \brief Allow conversion from static Codim value
+   */
+  template<int value>
+  constexpr DynamicCodim(Dune::Codim<value> staticCodim):
+    value_(value)
+  {}
+
+  constexpr operator std::size_t() const
+  {
+    return value_;
+  }
+
+private:
+  std::size_t value_;
+};
+
+
+
+/**
+ * \brief Generate dynamic codim from dynamic raw value
+ */
+auto codim(std::size_t i)
+{
+  return DynamicCodim(i);
+}
+
+
+
+/**
+ * \brief Encapsulate dynamic subentity information
+ *
+ * This is a strongly typed pair of codimension and index
+ */
+class DynamicSubEntity
+{
+public:
+
+  constexpr DynamicSubEntity():
+    codim_(0),
+    index_(0)
+  {}
+
+  constexpr DynamicSubEntity(DynamicCodim codim, std::size_t index):
+    codim_(codim),
+    index_(index)
+  {}
+
+  constexpr DynamicCodim codim() const
+  {
+    return codim_;
+  }
+
+  constexpr std::size_t index() const
+  {
+    return index_;
+  }
+
+  constexpr operator std::size_t() const
+  {
+    return index_;
+  }
+
+private:
+  DynamicCodim codim_;
+  std::size_t index_;
+};
+
+
+
+/**
+ * \brief Create subentity identifier for given codim and index
+ */
+auto subEntity(DynamicCodim codim, std::size_t index)
+{
+  return DynamicSubEntity(codim, index);
+}
+
+
+
+/**
+ * \brief Create subentity identifier for facet of given index
+ */
+auto facet(std::size_t index)
+{
+  return subEntity(codim(1), index);
+}
+
+
+
+/**
+ * \brief Create subentity identifier for inside facet
+ */
+template<class Intersection>
+auto insideFacet(const Intersection& intersection)
+{
+  return subEntity(codim(1), intersection.indexInInside());
+}
+
+
+
+/**
+ * \brief Get reference element for given entity
+ */
+template<class FieldType, class Entity>
+const auto& referenceElement(const Entity& entity)
+{
+  return Dune::ReferenceElements<FieldType, Entity::dimension>::general(entity.type());
+}
+
+
+/**
+ * \brief Get reference element for given entity
+ */
+template<class Entity>
+const auto& referenceElement(const Entity& entity)
+{
+  return Dune::ReferenceElements<double, Entity::dimension>::general(entity.type());
+}
+
+
+/**
+ * \brief Get number of subentities of given codim
+ *
+ * This should (maybe) be a member of ReferenceElement.
+ */
+template<class ctype, int dim>
+std::size_t size(const Dune::ReferenceElement<ctype, dim>& referenceElement, DynamicCodim codim)
+{
+  return referenceElement.size(codim);
+}
+
+
+
+/**
+ * \brief Get GeometryType of subentity
+ *
+ * This should (maybe) be a member of ReferenceElement.
+ */
+template<class ctype, int dim>
+Dun::GeometryType type(const Dune::ReferenceElement<ctype, dim>& referenceElement, DynamicSubEntity subEntity)
+{
+  return referenceElement.type(subEntity.index(), subEntity.codim());
+}
+
+
+
+/**
+ * \brief Get number of subsubentities of given codim for a subentity
+ *
+ * This should (maybe) be a member of ReferenceElement.
+ */
+template<class ctype, int dim>
+std::size_t size(const Dune::ReferenceElement<ctype, dim>& referenceElement, DynamicSubEntity subEntity, DynamicCodim subSubEntityCodim)
+{
+  return referenceElement.size(subEntity.index(), subEntity.codim(), subSubEntityCodim);
+}
+
+
+
+/**
+ * \brief Get index of a subsubentity for a subentity within the ReferenceElement
+ *
+ * This should (maybe) be a member of ReferenceElement.
+ * However, this could also be hidden, because the
+ * functionality is often misunderstood and you normaly
+ * need all subsubentities anyway.
+ */
+template<class ctype, int dim>
+auto subEntity(const Dune::ReferenceElement<ctype, dim>& referenceElement, DynamicSubEntity se, DynamicSubEntity subSubEntity)
+{
+  return subEntity(subSubEntity.codim(), referenceElement.subEntity(se.index(), se.codim(), subSubEntity.index(), subSubEntity.codim()));
+}
+
+
+
+/**
+ * \brief Get index-range of subsubentities of given codim for a subentity within the ReferenceElement
+ *
+ * This should (maybe) be a member of ReferenceElement.
+ */
+template<class ctype, int dim>
+auto subEntities(const Dune::ReferenceElement<ctype, dim>& referenceElement, const DynamicSubEntity subEntityTag, DynamicCodim codim)
+{
+  static const std::size_t maxSubEntityCount = Dune::StaticPower<2,dim>::power;
+  std::size_t subEntityCount = size(referenceElement, subEntityTag, codim);
+
+  // Todo: This could be replaced by an on-the fly range by doing a
+  // transformation to an index range. Unfortunately these range tools
+  // have not arrived in std yet.
+  Dune::ReservedVector<DynamicSubEntity, maxSubEntityCount > indices;
+  indices.resize(subEntityCount);
+  for(std::size_t i=0; i<subEntityCount; ++i)
+    indices[i] = subEntity(referenceElement, subEntityTag, subEntity(codim, i));
+
+  return indices;
+}
+
+
+
+/**
+ * \brief Get index-range of subentities of given codim
+ *
+ * This should (maybe) be a member of ReferenceElement.
+ */
+template<class ctype, int dim>
+auto subEntities(const Dune::ReferenceElement<ctype, dim>& referenceElement, DynamicCodim cd)
+{
+  return subEntities(referenceElement, subEntity(codim(0), 0), cd);
+}
+
+
+
+/**
+ * \brief Get index-range of vertices of given subentity within the ReferenceElement
+ */
+template<class ctype, int dim>
+auto subVertices(const Dune::ReferenceElement<ctype, dim>& referenceElement, const DynamicSubEntity subEntityTag)
+{
+  return subEntities(referenceElement, subEntityTag, codim(dim));
+}
+
+
+
+/**
+ * \brief Get index of subentity
+ *
+ * This should (maybe) be a member of IndexSet
+ */
+template<class IndexSet, class Entity>
+auto subIndex(const IndexSet& indexSet, const Entity& entity, DynamicSubEntity subEntity)
+{
+  return indexSet.subIndex(entity, subEntity.index(), subEntity.codim());
+}
+
+
+
+/**
+ * \brief Get id of subentity
+ *
+ * This should (maybe) be a member of IdSet.
+ */
+template<class IdSet, class Entity>
+auto subId(const IdSet& idSet, const Entity& entity, DynamicSubEntity subEntity)
+{
+  return idSet.subId(entity, subEntity.index(), subEntity.codim());
+}
+
+
+
+} // end namespace FuTutorial
+} // end namespace Dune
+
+
+
+#endif // DUNE_FU_TUTORIAL_REFERENCEELEMENTUTILITY_hh