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| | NormalToMeshProjectionManifold (const TopoDS_Shape &sh, const double tolerance=1e-7) |
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| virtual std::unique_ptr< Manifold< dim, spacedim > > | clone () const override |
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| virtual Point< spacedim > | project_to_manifold (const ArrayView< const Point< spacedim > > &surrounding_points, const Point< spacedim > &candidate) const override |
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| virtual Point< spacedim > | get_new_point (const ArrayView< const Point< spacedim > > &surrounding_points, const ArrayView< const double > &weights) const override |
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| virtual void | get_new_points (const ArrayView< const Point< spacedim > > &surrounding_points, const Table< 2, double > &weights, ArrayView< Point< spacedim > > new_points) const override |
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| virtual Tensor< 1, spacedim > | get_tangent_vector (const Point< spacedim > &x1, const Point< spacedim > &x2) const override |
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| virtual Tensor< 1, spacedim > | normal_vector (const typename Triangulation< dim, spacedim >::face_iterator &face, const Point< spacedim > &p) const override |
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| Tensor< 1, 1 > | normal_vector (const Triangulation< 1, 1 >::face_iterator &, const Point< 1 > &) const |
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| Tensor< 1, 2 > | normal_vector (const Triangulation< 1, 2 >::face_iterator &, const Point< 2 > &) const |
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| Tensor< 1, 3 > | normal_vector (const Triangulation< 1, 3 >::face_iterator &, const Point< 3 > &) const |
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| Tensor< 1, 2 > | normal_vector (const Triangulation< 2, 2 >::face_iterator &face, const Point< 2 > &p) const |
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| Tensor< 1, 3 > | normal_vector (const Triangulation< 3, 3 >::face_iterator &face, const Point< 3 > &p) const |
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| virtual void | get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, typename Manifold< dim, spacedim >::FaceVertexNormals &face_vertex_normals) const override |
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| void | get_normals_at_vertices (const Triangulation< 1 >::face_iterator &, Manifold< 1, 1 >::FaceVertexNormals &) const |
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| void | get_normals_at_vertices (const Triangulation< 1, 2 >::face_iterator &, Manifold< 1, 2 >::FaceVertexNormals &) const |
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| void | get_normals_at_vertices (const Triangulation< 1, 3 >::face_iterator &, Manifold< 1, 3 >::FaceVertexNormals &) const |
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| void | get_normals_at_vertices (const Triangulation< 2 >::face_iterator &face, Manifold< 2, 2 >::FaceVertexNormals &face_vertex_normals) const |
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| void | get_normals_at_vertices (const Triangulation< 2, 3 >::face_iterator &, Manifold< 2, 3 >::FaceVertexNormals &) const |
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| void | get_normals_at_vertices (const Triangulation< 3 >::face_iterator &face, Manifold< 3, 3 >::FaceVertexNormals &face_vertex_normals) const |
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| void | get_normals_at_vertices (const Triangulation< 2, 2 >::face_iterator &face, FaceVertexNormals &n) const |
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| void | get_normals_at_vertices (const Triangulation< 3, 3 >::face_iterator &face, FaceVertexNormals &n) const |
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| const Tensor< 1, spacedim > & | get_periodicity () const |
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| Point< 1 > | get_new_point_on_quad (const Triangulation< 1, 1 >::quad_iterator &) const |
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| Point< 2 > | get_new_point_on_quad (const Triangulation< 1, 2 >::quad_iterator &) const |
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| Point< 3 > | get_new_point_on_quad (const Triangulation< 1, 3 >::quad_iterator &) const |
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| Point< 3 > | get_new_point_on_hex (const Triangulation< 3, 3 >::hex_iterator &hex) const |
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| Point< 1 > | get_new_point_on_face (const Triangulation< 1, 1 >::face_iterator &) const |
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| Point< 2 > | get_new_point_on_face (const Triangulation< 1, 2 >::face_iterator &) const |
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| Point< 3 > | get_new_point_on_face (const Triangulation< 1, 3 >::face_iterator &) const |
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| virtual void | get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, FaceVertexNormals &face_vertex_normals) const |
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| virtual Point< spacedim > | get_intermediate_point (const Point< spacedim > &p1, const Point< spacedim > &p2, const double w) const |
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| virtual Point< spacedim > | get_new_point_on_line (const typename Triangulation< dim, spacedim >::line_iterator &line) const |
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| virtual Point< spacedim > | get_new_point_on_quad (const typename Triangulation< dim, spacedim >::quad_iterator &quad) const |
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| virtual Point< spacedim > | get_new_point_on_hex (const typename Triangulation< dim, spacedim >::hex_iterator &hex) const |
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| Point< spacedim > | get_new_point_on_face (const typename Triangulation< dim, spacedim >::face_iterator &face) const |
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| Point< spacedim > | get_new_point_on_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const |
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template<
int dim,
int spacedim>
class OpenCASCADE::NormalToMeshProjectionManifold< dim, spacedim >
A Manifold object based on OpenCASCADE TopoDS_Shape where new points are first computed by averaging the surrounding points in the same way as FlatManifold does, and then projecting them using OpenCASCADE utilities onto the manifold along a direction which is an estimation of the surrounding points (hence mesh cell) normal.
The direction normal to the mesh is particularly useful because it is the direction in which the mesh is missing nodes. For instance, during the refinement of a cell a new node is initially created around the baricenter of the cell. This location somehow ensures a uniform distance from the nodes of the old cell. Projecting such cell baricenter onto the CAD surface in the direction normal to the original cell will then retain uniform distance from the points of the original cell. Of course, at the stage of mesh generation, no dof handler nor finite element are defined, and such direction has to be estimated. For the case in which 8 surrounding points are present, 4 different triangles are identified with the points assigned, and the normals of such triangles are averaged to obtain the approximation of the normal to the cell.
The case in which 2 surrounding points are present (i.e.:a cell edge is being refined) is of course more tricky. The average of the CAD surface normals at the 2 surrounding points is first computed, and then projected onto the plane normal to the segment linking the surrounding points. This again is an attempt to have the new point with equal distance with respect to the surrounding points
This class only operates with CAD faces and makes the assumption that the shape you pass to it contains at least one face. If that is not the case, an Exception is thrown. In debug mode there is a sanity check to make sure that the surrounding points (the ones used in project_to_manifold()) actually live on the Manifold, i.e., calling OpenCASCADE::closest_point() on those points leaves them untouched. If this is not the case, an ExcPointNotOnManifold is thrown.
Notice that this type of Manifold descriptor may fail to give results if the triangulation to be refined is close to the boundary of the given TopoDS_Shape, or when the normal direction estimated from the surrounding points does not intersect the shape. An exception is thrown when this happens.
Definition at line 230 of file manifold_lib.h.
Let the new point be the average sum of surrounding vertices.
This particular implementation constructs the weighted average of the surrounding points, and then calls internally the function project_to_manifold(). The reason why we do it this way, is to allow lazy programmers to implement only the project_to_manifold() function for their own Manifold classes which are small (or trivial) perturbations of a flat manifold. This is the case whenever the coarse mesh is a decent approximation of the manifold geometry. In this case, the middle point of a cell is close to true middle point of the manifold, and a projection may suffice.
For most simple geometries, it is possible to get reasonable results by deriving your own Manifold class from FlatManifold, and write a new interface only for the project_to_manifold function. You will have good approximations also with large deformations, as long as in the coarsest mesh size you are trying to refine, the middle point is not too far from the manifold mid point, i.e., as long as the coarse mesh size is small enough.
Reimplemented from Manifold< dim, spacedim >.
| virtual Point< spacedim > Manifold< dim, spacedim >::get_intermediate_point |
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const Point< spacedim > & |
p1, |
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const Point< spacedim > & |
p2, |
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const double |
w |
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virtualinherited |
Return an intermediate point between two given points. Overloading this function allows the default pair-wise reduction implementation of the method get_new_point() that takes a Quadrature object as input to work properly.
An implementation of this function should returns a parametric curve on the manifold, joining the points p1 and p2, with parameter w in the interval [0,1]. In particular get_intermediate_point(p1, p2, 0.0) should return p1 and get_intermediate_point(p1, p2, 1.0) should return p2.
In its default implementation, this function calls the project_to_manifold() method with the convex combination of p1 and p2. User classes can get away by simply implementing the project_to_manifold() method.
Reimplemented in ChartManifold< dim, dim, dim >, ChartManifold< dim, dim, 3 >, ChartManifold< dim, spacedim, 1 >, ChartManifold< dim, spacedim, 2 >, ChartManifold< dim, spacedim_A+spacedim_B, chartdim_A+chartdim_B >, ChartManifold< dim, 3, 3 >, ChartManifold< dim_A, spacedim_A, chartdim_A >, and ChartManifold< dim_B, spacedim_B, chartdim_B >.
The periodicity of this Manifold. Periodicity affects the way a middle point is computed. It is assumed that if two points are more than half period distant, then the distance should be computed by crossing the periodicity boundary, i.e., the average is computed by adding a full period to the sum of the two. For example, if along direction 0 we have 2*pi periodicity, then the average of (2*pi-eps) and (eps) is not pi, but 2*pi (or zero), since, on a periodic manifold, these two points are at distance 2*eps and not (2*pi-eps).
A periodicity 0 along one direction means no periodicity. This is the default value for all directions.
Definition at line 794 of file manifold.h.
1.9.5