diff --git a/dumux/common/geometry/boundingboxtreeintersection.hh b/dumux/common/geometry/boundingboxtreeintersection.hh
index d3f32aa2be58187c4f8ad5bf1356641d125ff464..b927070751f520fa1db6a48e0cd27a819952b3e2 100644
--- a/dumux/common/geometry/boundingboxtreeintersection.hh
+++ b/dumux/common/geometry/boundingboxtreeintersection.hh
@@ -45,12 +45,13 @@ class BoundingBoxTreeIntersection
using GlobalPosition = Dune::FieldVector<ctype, dimworld>;
public:
+ template<class Corners>
explicit BoundingBoxTreeIntersection(std::size_t a,
std::size_t b,
- std::vector<GlobalPosition>&& c)
+ Corners&& c)
: a_(a)
, b_(b)
- , corners_(std::move(c))
+ , corners_(c.begin(), c.end())
{
static_assert(int(EntitySet0::dimensionworld) == int(EntitySet1::dimensionworld),
"Can only store intersections of entity sets with the same world dimension");
diff --git a/dumux/common/geometry/geometryintersection.hh b/dumux/common/geometry/geometryintersection.hh
index f541a177583e18e29e613ef79de8b069ad4fb975..5e3afd3b41b191122e58fbad92f65004ab4b8bd3 100644
--- a/dumux/common/geometry/geometryintersection.hh
+++ b/dumux/common/geometry/geometryintersection.hh
@@ -23,14 +23,16 @@
#ifndef DUMUX_GEOMETRY_INTERSECTION_HH
#define DUMUX_GEOMETRY_INTERSECTION_HH
+#include <dune/common/version.hh>
#include <dune/common/exceptions.hh>
#include <dune/common/promotiontraits.hh>
#include <dune/geometry/referenceelements.hh>
#include <dumux/common/math.hh>
+#include <dumux/common/geometry/intersectspointgeometry.hh>
+#include <dumux/common/geometry/grahamconvexhull.hh>
-namespace Dumux
-{
+namespace Dumux {
/*!
* \ingroup Common
@@ -46,11 +48,8 @@ template
class GeometryIntersection
{
public:
- using ctype = typename Dune::PromotionTraits<typename Geometry1::ctype, typename Geometry2::ctype>::PromotedType;
- using GlobalPosition = Dune::FieldVector<ctype, dimworld>;
- using IntersectionType = std::vector<GlobalPosition>;
-
//! Determine if the two geometries intersect and compute the intersection corners
+ template<class IntersectionType>
static bool intersection(const Geometry1& geo1, const Geometry2& geo2, IntersectionType& intersection)
{
static_assert(dimworld == Geometry2::coorddimension, "Can only intersect geometries of same coordinate dimension");
@@ -59,19 +58,18 @@ public:
}
};
-//! Geometry collision detection with 3d and 1d geometry in 3d space
+//! polyhedron--segment intersection in 3d space
template <class Geometry1, class Geometry2>
class GeometryIntersection<Geometry1, Geometry2, 3, 3, 1>
{
enum { dimworld = 3 };
enum { dim1 = 3 };
enum { dim2 = 1 };
- enum { dimis = dim2 }; // the intersection dimension
public:
using ctype = typename Dune::PromotionTraits<typename Geometry1::ctype, typename Geometry2::ctype>::PromotedType;
- using GlobalPosition = Dune::FieldVector<ctype, dimworld>;
- using IntersectionType = std::vector<GlobalPosition>;
+ using Point = Dune::FieldVector<ctype, dimworld>;
+ using IntersectionType = std::array<std::vector<Point>, 1>;
private:
static constexpr ctype eps_ = 1.5e-7; // base epsilon for floating point comparisons
@@ -80,7 +78,8 @@ private:
public:
/*!
* \brief Colliding segment and convex polyhedron
- * \note Algorithm from "Real-Time Collision Detection" by Christer Ericson
+ * \note Algorithm based on the one from "Real-Time Collision Detection" by Christer Ericson,
+ * published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc.
* Basis is the theorem that for any two non-intersecting convex polyhedrons
* a separating plane exists.
* \param geo1/geo2 The geometries to intersect
@@ -116,7 +115,8 @@ public:
facets = {{1, 2, 0}, {0, 1, 3}, {0, 3, 2}, {1, 2, 3}};
break;
default:
- DUNE_THROW(Dune::NotImplemented, "Collision of segment and geometry of type " << geo1.type() << ", "<< geo1.corners() << " corners.");
+ DUNE_THROW(Dune::NotImplemented, "Collision of segment and geometry of type "
+ << geo1.type() << ", "<< geo1.corners() << " corners.");
}
return facets;
@@ -168,7 +168,258 @@ public:
}
// If we made it until here an intersection exists. We also export
// the intersections geometry now s(t) = a + t(b-a) in [tfirst, tlast]
- intersection = {geo2.global(tfirst), geo2.global(tlast)};
+ intersection = {std::vector<Point>({geo2.global(tfirst), geo2.global(tlast)})};
+ return true;
+ }
+};
+
+//! polyhedron--polygon intersection in 3d space
+template <class Geometry1, class Geometry2>
+class GeometryIntersection<Geometry1, Geometry2, 3, 3, 2>
+{
+ enum { dimworld = 3 };
+ enum { dim1 = 3 };
+ enum { dim2 = 2 };
+
+public:
+ using ctype = typename Dune::PromotionTraits<typename Geometry1::ctype, typename Geometry2::ctype>::PromotedType;
+ using Point = Dune::FieldVector<ctype, dimworld>;
+ using IntersectionType = std::vector<std::array<Point, 3>>;
+
+private:
+ static constexpr ctype eps_ = 1.5e-7; // base epsilon for floating point comparisons
+ using ReferenceElementsGeo1 = typename Dune::ReferenceElements<ctype, dim1>;
+ using ReferenceElementsGeo2 = typename Dune::ReferenceElements<ctype, dim2>;
+
+public:
+ /*!
+ * \brief Colliding segment and convex polyhedron
+ * \note First we find the vertex candidates for the intersection region as follows:
+ * Add triangle vertices that are inside the tetrahedron
+ * Add tetrahedron vertices that are inside the triangle
+ * Add all intersection points of tetrahedron edges (codim 2) with the triangle (codim 0) (6*1 tests)
+ * Add all intersection points of triangle edges (codim 1) with tetrahedron faces (codim 1) (3*4 tests)
+ * Remove duplicate points from the list
+ * Compute the convex hull polygon
+ * Return a triangulation of that polygon as intersection
+ * \param geo1/geo2 The geometries to intersect
+ * \param intersection A triangulation of the intersection polygon
+ */
+ static bool intersection(const Geometry1& geo1, const Geometry2& geo2, IntersectionType& intersection)
+ {
+ static_assert(int(dimworld) == int(Geometry2::coorddimension),
+ "Can only collide geometries of same coordinate dimension");
+
+ // the candidate intersection points
+ std::vector<Point> points; points.reserve(10);
+
+ // add 3d geometry corners that are inside the 2d geometry
+ for (int i = 0; i < geo1.corners(); ++i)
+ if (intersectsPointGeometry(geo1.corner(i), geo2))
+ points.emplace_back(geo1.corner(i));
+
+ // add 2d geometry corners that are inside the 3d geometry
+ for (int i = 0; i < geo2.corners(); ++i)
+ if (intersectsPointGeometry(geo2.corner(i), geo1))
+ points.emplace_back(geo2.corner(i));
+
+ // get some geometry types
+ using PolyhedronFaceGeometry = Dune::MultiLinearGeometry<ctype, 2, dimworld>;
+ using SegGeometry = Dune::MultiLinearGeometry<ctype, 1, dimworld>;
+
+#if DUNE_VERSION_NEWER(DUNE_COMMON,2,6)
+ const auto referenceElement1 = ReferenceElementsGeo1::general(geo1.type());
+ const auto referenceElement2 = ReferenceElementsGeo2::general(geo2.type());
+#else
+ const auto& referenceElement1 = ReferenceElementsGeo1::general(geo1.type());
+ const auto& referenceElement2 = ReferenceElementsGeo2::general(geo2.type());
+#endif
+
+ // add intersection points of all polyhedron edges (codim dim-1) with the polygon
+ for (int i = 0; i < referenceElement1.size(dim1-1); ++i)
+ {
+ const auto localEdgeGeom = referenceElement1.template geometry<dim1-1>(i);
+ const auto p = geo1.global(localEdgeGeom.corner(0));
+ const auto q = geo1.global(localEdgeGeom.corner(1));
+ const auto segGeo = SegGeometry(Dune::GeometryTypes::line, std::vector<Point>{p, q});
+
+ using PolySegTest = GeometryIntersection<Geometry2, SegGeometry>;
+ typename PolySegTest::IntersectionType intersection;
+ if (PolySegTest::template intersection<2>(geo2, segGeo, intersection))
+ points.emplace_back(intersection[0]);
+ }
+
+ // add intersection points of all polygon faces (codim 1) with the polyhedron faces
+ for (int i = 0; i < referenceElement1.size(1); ++i)
+ {
+ const auto faceGeo = [&]()
+ {
+ const auto localFaceGeo = referenceElement1.template geometry<1>(i);
+ if (localFaceGeo.corners() == 4)
+ {
+ const auto a = geo1.global(localFaceGeo.corner(0));
+ const auto b = geo1.global(localFaceGeo.corner(1));
+ const auto c = geo1.global(localFaceGeo.corner(2));
+ const auto d = geo1.global(localFaceGeo.corner(3));
+ return PolyhedronFaceGeometry(Dune::GeometryTypes::cube(2), std::vector<Point>{a, b, c, d});
+ }
+ else
+ {
+ const auto a = geo1.global(localFaceGeo.corner(0));
+ const auto b = geo1.global(localFaceGeo.corner(1));
+ const auto c = geo1.global(localFaceGeo.corner(2));
+ return PolyhedronFaceGeometry(Dune::GeometryTypes::simplex(2), std::vector<Point>{a, b, c});
+ }
+ }();
+
+ for (int j = 0; j < referenceElement2.size(1); ++j)
+ {
+ const auto localEdgeGeom = referenceElement2.template geometry<1>(j);
+ const auto p = geo2.global(localEdgeGeom.corner(0));
+ const auto q = geo2.global(localEdgeGeom.corner(1));
+ const auto segGeo = SegGeometry(Dune::GeometryTypes::line, std::vector<Point>{p, q});
+
+ using PolySegTest = GeometryIntersection<PolyhedronFaceGeometry, SegGeometry>;
+ typename PolySegTest::IntersectionType intersection;
+ if (PolySegTest::template intersection<2>(faceGeo, segGeo, intersection))
+ points.emplace_back(intersection[0]);
+ }
+ }
+
+ // return if no intersection points were found
+ if (points.empty()) return false;
+
+ // remove duplicates
+ const auto eps = (geo1.corner(0) - geo1.corner(1)).two_norm()*eps_;
+ std::sort(points.begin(), points.end(), [&eps](const auto& a, const auto& b) -> bool
+ {
+ return (abs(a[0]-b[0]) > eps ? a[0] < b[0] : (abs(a[1]-b[1]) > eps ? a[1] < b[1] : (a[2] < b[2])));
+ });
+
+ auto removeIt = std::unique(points.begin(), points.end(), [&eps](const auto& a, const auto&b)
+ {
+ return (b-a).two_norm() < eps;
+ });
+
+ points.erase(removeIt, points.end());
+
+ // return false if we don't have more than three unique points
+ if (points.size() < 3) return false;
+
+ // compute convex hull
+ const auto convexHull = grahamConvexHull2d3d(points);
+
+ // the intersections are the triangulation of the convex hull polygon
+ intersection = triangulateConvexHull(convexHull);
+ return true;
+ }
+};
+
+//! polygon--segment intersection in 3d space
+template <class Geometry1, class Geometry2>
+class GeometryIntersection<Geometry1, Geometry2, 3, 2, 1>
+{
+ enum { dimworld = 3 };
+ enum { dim1 = 2 };
+ enum { dim2 = 1 };
+
+public:
+ using ctype = typename Dune::PromotionTraits<typename Geometry1::ctype, typename Geometry2::ctype>::PromotedType;
+ using Point = Dune::FieldVector<ctype, dimworld>;
+ using IntersectionType = std::vector<Point>;
+
+private:
+ static constexpr ctype eps_ = 1.5e-7; // base epsilon for floating point comparisons
+ using ReferenceElements = typename Dune::ReferenceElements<ctype, dim1>;
+
+public:
+ /*!
+ * \brief Colliding segment and convex polyhedron
+ * \note Algorithm based on the one from "Real-Time Collision Detection" by Christer Ericson,
+ * published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc. (Chapter 5.3.6)
+ * \param geo1/geo2 The geometries to intersect
+ * \param intersection If the geometries collide intersection holds the corner points of
+ * the intersection object in global coordinates.
+ */
+ template<int dimIntersection>
+ static bool intersection(const Geometry1& geo1, const Geometry2& geo2, IntersectionType& is)
+ {
+ if (dimIntersection != 2)
+ DUNE_THROW(Dune::NotImplemented, "Only simplex intersections are currently implemented!");
+
+ static_assert(int(dimworld) == int(Geometry2::coorddimension), "Can only collide geometries of same coordinate dimension");
+
+ const auto p = geo2.corner(0);
+ const auto q = geo2.corner(1);
+
+ const auto a = geo1.corner(0);
+ const auto b = geo1.corner(1);
+ const auto c = geo1.corner(2);
+
+ if (geo1.corners() == 3)
+ return intersection<dimIntersection>(a, b, c, p, q, is);
+
+ else if (geo1.corners() == 4)
+ {
+ const auto d = geo1.corner(3);
+ if (intersection<dimIntersection>(a, b, d, p, q, is)) return true;
+ else if (intersection<dimIntersection>(a, d, c, p, q, is)) return true;
+ else return false;
+ }
+
+ else
+ DUNE_THROW(Dune::NotImplemented, "Collision of segment and geometry of type "
+ << geo1.type() << ", "<< geo1.corners() << " corners.");
+ }
+
+ // triangle--segment intersection with points as input
+ template<int dimIntersection>
+ static bool intersection(const Point& a, const Point& b, const Point& c,
+ const Point& p, const Point& q,
+ IntersectionType& is)
+ {
+ if (dimIntersection != 2)
+ DUNE_THROW(Dune::NotImplemented, "Only simplex intersections are currently implemented!");
+
+ const auto ab = b - a;
+ const auto ac = c - a;
+ const auto qp = p - q;
+
+ // compute the triangle normal that defines the triangle plane
+ const auto normal = crossProduct(ab, ac);
+
+ // compute the denominator
+ // if denom is 0 the segment is parallel and we can return
+ const auto denom = normal*qp;
+ const auto eps = eps_*ab.two_norm2()*qp.two_norm();
+ using std::abs;
+ if (abs(denom) < eps)
+ return false;
+
+ // compute intersection t value of pq with plane of triangle.
+ // a segment intersects if and only if 0 <= t <= 1.
+ const auto ap = p - a;
+ const auto t = (ap*normal)/denom;
+ if (t < 0.0 - eps_) return false;
+ if (t > 1.0 + eps_) return false;
+
+ // compute the barycentric coordinates and check if the intersection point
+ // is inside the bounds of the triangle
+ const auto e = crossProduct(qp, ap);
+ const auto v = (ac*e)/denom;
+ if (v < -eps_ || v > 1.0 + eps_) return false;
+ const auto w = -(ab*e)/denom;
+ if (w < -eps_ || v + w > 1.0 + eps_) return false;
+
+ // Now we are sure there is an intersection points
+ // Perform delayed division compute the last barycentric coordinate component
+ const auto u = 1.0 - v - w;
+
+ Point ip(0.0);
+ ip.axpy(u, a);
+ ip.axpy(v, b);
+ ip.axpy(w, c);
+ is = {ip};
return true;
}
};
diff --git a/dumux/common/geometry/intersectingentities.hh b/dumux/common/geometry/intersectingentities.hh
index 132e61f3b41ec2c70020e5ceb1131ac895521d93..d3bb24badb96672486da06f0338d0c68acbff435 100644
--- a/dumux/common/geometry/intersectingentities.hh
+++ b/dumux/common/geometry/intersectingentities.hh
@@ -145,7 +145,10 @@ void intersectingEntities(const BoundingBoxTree<EntitySet0>& treeA,
std::decay_t<decltype(geometryB)> >;
typename IntersectionAlgorithm::IntersectionType intersection;
if (IntersectionAlgorithm::intersection(geometryA, geometryB, intersection))
- intersections.emplace_back(eIdxA, eIdxB, std::move(intersection));
+ {
+ for (int i = 0; i < intersection.size(); ++i)
+ intersections.emplace_back(eIdxA, eIdxB, std::move(intersection[i]));
+ }
}
// if we reached the leaf in treeA, just continue in treeB