diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt index 22326e51da2..b147cf1f81f 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt @@ -695,14 +695,17 @@ as follows: @@ -2876,27 +2878,29 @@ can be used to represent a 2D arrangement embedded in a 3D surface. The template is parameterized by template parameters geometry traits and topology traits. The topology-traits type deals with the topology of the parametric -surface. As explained in the previous section, a parametric surface -\f$S \f$ is given by a continuous function \f$\phi_S: \Phi \rightarrow -\mathbb{R}^3\f$, where the domain \f$\Phi = X \times Y\f$ is a -rectangular two-dimensional parameter space; \f$S = -\phi_S(\Phi)\f$. \f$X\f$ and \f$Y\f$ are open, half-open, or closed -intervals with endpoints in \f$\overline{\mathbb{R}}\f$. +surface; see Section \ref aos_sec-topol_traits. As explained in the +previous section, a parametric surface \f$S \f$ is given by a +continuous function \f$\phi_S: \Phi \rightarrow \mathbb{R}^3\f$, where +the domain \f$\Phi = X \times Y\f$ is a rectangular two-dimensional +parameter space; \f$S = \phi_S(\Phi)\f$. \f$X\f$ and \f$Y\f$ are open, +half-open, or closed intervals with endpoints in +\f$\overline{\mathbb{R}}\f$. The geometry-traits type introduces the type names of the basic geometric objects (i.e., point, curve, and \f$u \f$-monotone curve) and the set of operations on objects of these types required to construct and maintain the arrangement and to operate on it. The traits-concept hierarchy described in Section \ref aos_sec-geom_traits -accurately defines the requirements imposed on a model of a -geometry traits class. Recall that requirements apply to the parameter -space \f$\Phi = X \times Y\f$; thus, they are defined in terms of -\f$x\f$ and \f$y\f$ coordinates. Most requirements apply to all type -of arrangements regardless of the embedding surface. However, several +accurately defines the requirements imposed on a model of a geometry +traits class. Recall that requirements apply to the parameter space +\f$\Phi = X \times Y\f$; thus, they are defined in terms of \f$x\f$ +and \f$y\f$ coordinates. Most requirements apply to all type of +arrangements regardless of the embedding surface. However, several refined concepts apply only to arrangements on surfaces that are not -the plane, that is, modeled with \f$\phi_S\f$ not being the identity -mapping. They differ according to the type of the side boundaries of -the parameter space being open, closed, contracted, or identified. +in the plane, that is, modeled with \f$\phi_S\f$ not being the +identity mapping. They differ according to the type of the side +boundaries of the parameter space being open, closed, contracted, or +identified. At this point only one type of arrangements on non planar surfaces is supported, namely, arrangements embedded in the sphere and induced by @@ -2931,6 +2935,127 @@ Sites are drawn in red and Voronoi edges are drawn in blue. (d) A degenerate power diagram of 14 sites on the sphere. \cgalFigureCaptionEnd + +\subsection aos_ssec-curved_surfaces-basic Basic Manipulation and Traversal Methods + + +The types \link Arrangement_on_surface_2::Vertex `Vertex`\endlink, +\link Arrangement_on_surface_2::Halfedge `Halfedge`\endlink, and \link +Arrangement_on_surface_2::Face `Face`\endlink nested in the +`Arrangement_on_surface_2` class template support the methods listed +in Section \ref arr_ssectraverse and in Section \ref +arr_sssecunb_basic. Let \f$v\f$, \f$e\f$, and \f$f\f$ be handles to a +vertex of type \link Arrangement_on_surface_2::Vertex +`Vertex`\endlink, a halfedge of type \link +Arrangement_on_surface_2::Halfedge `Halfedge`\endlink, and a face of +type \link Arrangement_on_surface_2::Face `Face`\endlink, +respectively. + + + +The template function `is_in_x_range()` listed below, and defined in the +file `is_in_x_range.h`, checks whether a given point \f$p\f$ is in the +$x$-range of the curve associated with a given halfedge \f$e\f$. The +function template also exemplifies how some of the above functions can +be used. + +\code +bool is_in_x_range(const X_monotone_curve_2& xcv, const Point_2& point) const { + typedef Arr_geodesic_arc_on_sphere_traits_2 Traits; + + Direction_2 p = project_xy(point); + if (xcv.is_vertical()) { + const Direction_3& normal = xcv.normal(); + Direction_2 q = (xcv.is_directed_right()) ? + Direction_2(-(normal.dy()), normal.dx()) : + Direction_2(normal.dy(), -(normal.dx())); + const Kernel& kernel = *this; + return kernel.equal_2_object()(p, q); + } + + // The curve is not vertical: + Direction_2 r = project_xy(xcv.right()); + const Kernel& kernel = *this; + if (kernel.equal_2_object()(p, r)) return true; + Direction_2 l = Traits::project_xy(xcv.left()); + if (kernel.equal_2_object()(p, l)) return true; + return kernel.counterclockwise_in_between_2_object()(p, l, r); +} +\endcode + \section aos_sec-geom_traits The Geometry Traits @@ -5250,9 +5375,17 @@ instantiate the curve-data traits: \section aos_sec-topol_traits The Topology Traits - -At this point we do not expose the topology traits concept. The -package contains one topology traits, namely, +A topology traits class encapsulates the definitions of the +topological entities and the implementation of the functions that +handle these topological entities, used by the +`Arrangement_on_surface_2` class +template and by the peripheral modules. Every topology traits class +must model the basic concept `ArrangementBasicTopologyTraits`. A model +of this basic concept holds the (\sc{Dcel}) data structure used to +represent the arrangement cells (i.e., vertices, edges, and facets) +and the incident * relations between them. At this point we do not +expose the concepts that refine the basic concept. The package +contains one topology traits, namely, `Arr_spherical_topology_traits_2`. It can serve as a topology traits for an arrangement embedded on a sphere. More precisely, for an arrangement embedded on a sphere defined over a parameter space the diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_segment_traits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_segment_traits_2.h index dc104a10619..244fdb67252 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_segment_traits_2.h +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_segment_traits_2.h @@ -60,11 +60,11 @@ supports the merging of curves of opposite directions. \cgalModels `ArrangementDirectionalXMonotoneTraits_2` */ -template< typename Kernel > -class Arr_segment_traits_2 { +template +class Arr_segment_traits_2 : public Kernel { public: -Class Trim_2{ +Class Trim_2 { public: /// \name Creation /// @{ diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h index eeed2041379..3969c0a92cc 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h @@ -21,6 +21,8 @@ namespace CGAL { * `Arr_default_dcel`. * * + * \cgalModels `ArrangementBasicTopologyTraits` + * * \sa `Arr_default_dcel` * \sa `CGAL::Arr_geodesic_arc_on_sphere_traits_2` */ diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h index 68b15923796..0bb487d18bd 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h @@ -76,20 +76,20 @@ public: typedef typename Topology_traits::Dcel Dcel; /*! the point type, as defined by the traits class. */ - typedef typename Geometry__traits_2::Point_2 Point_2; + typedef typename Geometry_traits_2::Point_2 Point_2; /*! the \f$ x\f$-monotone curve type, as defined by the traits class. */ typedef typename Geometry_traits_2::X_monotone_curve_2 X_monotone_curve_2; /*! the size type (equivalent to `size_t`). */ - typedef typename Dcel::Size Size; + typedef typename Dcel::Size Size; /*! \ingroup PkgArrangementOnSurface2DCEL * An object \f$ v\f$ of the class `Vertex` represents an arrangement vertex, * that is a \f$ 0\f$-dimensional cell, associated with a point on the * ambient surface. */ - class Vertex : public Dcel::Vertex { + class Vertex : public typename Dcel::Vertex { public: /// \name Creation /// @{ @@ -162,7 +162,7 @@ public: * Halfedges are stored in doubly-connected lists and form chains. These * chains define the inner and outer boundaries of connected components. */ - class Halfedge : public Dcel::Halfedge { + class Halfedge : public typename Dcel::Halfedge { public: /// \name Creation /// @{ @@ -226,8 +226,8 @@ public: /*! \ingroup PkgArrangementOnSurface2DCEL * - * An object of the class `Face` represents an arrangement face, namely, a \f$ - * 2\f$-dimensional arrangement cell. An arrangement that supports only + * An object of the class `Face` represents an arrangement face, namely, a + * \f$2\f$-dimensional arrangement cell. An arrangement that supports only * bounded curves contains exactly one unbounded face, and a number of * bounded faces. An arrangement that supports also unbounded curves has one * or more unbounded faces. Such an arrangement has also exactly one @@ -241,8 +241,37 @@ public: * do not correspond to real curves. A face may also contain holes, which are * defined by clockwise-oriented halfedge chains, and isolated vertices. */ - class Face : public Dcel::Face { + class Face : public typename Dcel::Face { + private: + typedef Dcel::Face Base; + public: + + /// \name Types inherited from the base Dcel::Face + /// @{ + + /*! a bidirectional iterator over the inner CCBs of the face. + * Its value type is `Ccb_halfedge_circulator`. + */ + typedef typename Base::Inner_ccb_iterator Inner_ccb_iterator; + + /*! a bidirectional iterator over the outer CCBs of the face. + * Its value type is `Ccb_halfedge_circulator`. + */ + typedef typename Base::Outer_ccb_iterator Outer_ccb_iterator; + + /*! a bidirectional iterator over the holes (i.e., inner CCBs) contained + * inside the face. Its value type is `Ccb_halfedge_circulator`. + */ + typedef typename Base::Hole_iterator Hole_iterator; + + /*! a bidirectional iterator over the isolated vertices contained inside + * the face. Its value type is `Vertex`. + */ + typedef typename Base::Isolated_vertex_iterator Isolated_vertex_iterator; + + /// @} + /// \name Creation /// @{ diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBasicTopologyTraits.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBasicTopologyTraits.h new file mode 100644 index 00000000000..750182554c3 --- /dev/null +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBasicTopologyTraits.h @@ -0,0 +1,51 @@ +/*! \ingroup PkgArrangementOnSurface2ConceptsTopologyTraits + * \cgalConcept + * + * The concept `ArrangementBasicTopologyTraits` defines the minimal + * functionality needed for a model of a topology traits, which can substitutes + * the `TopolTraits` template parameters when the class template + * `Arrangement_on_surface_2` is instantiated. In + * particular. a model of this concept holds the Dcel data structure used to + * represent the arrangement cells (i.e., vertices, edges, and facets) and the + * incident relations between them. + * + * \cgalHasModel `CGAL::Arr_spherical_topology_traits_2` + */ + +class ArrangementBasicTopologyTraits { +public: + /// \name Types + /// @{ + + //! models the concept `ArrTraits::Point_2`. + typedef unspecified_type Point_2; + + //! models the concept `ArrTraits::XMonotoneCurve_2`. + typedef unspecified_type X_monotone_curve_2; + + //! models the concept `ArrangementDcel`. + typedef unspecified_type Dcel; + + /// @} + + /// \name Creation + /// @{ + + /// @} + + /// \name Access Functions + /// @{ + + /*! Obtain the DCEL (const version). */ + const Dcel& dcel() const; + + /*! Obtain the DCEL (non-const version). */ + Dcel& dcel(); + + /// @} + + /// \name Modifiers + /// @{ + /// @} + +}; diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBasicTraits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBasicTraits_2.h index 7680e9f6601..90399a98211 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBasicTraits_2.h +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBasicTraits_2.h @@ -103,7 +103,7 @@ public: /*! models the concept `ArrTraits::ConstructMaxVertex_2`. */ -typedef unspecified_type Construct_max_vertex_2; + typedef unspecified_type Construct_max_vertex_2; /*! models the concept `ArrTraits::IsVertical_2`. */ diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt index d82ada01e9d..3d2336b6ee4 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt @@ -114,6 +114,7 @@ implemented as peripheral classes or as free (global) functions. - `ArrangementDcelOuterCcb` - `ArrangementDcelInnerCcb` - `ArrangementDcelIsolatedVertex` +- `ArrangementBasicTopologyTraits` - `ArrangementBasicTraits_2` - `ArrangementConstructXMonotoneCurveTraits_2` - `ArrangementLandmarkTraits_2` diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp index 729f720a404..b0293f6051d 100644 --- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp +++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp @@ -31,10 +31,10 @@ int main() { for (auto it = arr.unbounded_faces_begin(); it != arr.unbounded_faces_end(); ++it) { - std::cout << "Face no. " << k++ << "(" << it->number_of_outer_ccbs() - << "," << it->number_of_inner_ccbs() << ")" << ": "; - Arrangement::Ccb_halfedge_const_circulator first, curr; - curr = first = it->outer_ccb(); + std::cout << "Face no. " << k++ << "(" << it->is_unbounded() << "," + << it->number_of_holes() << ")" << ": "; + Arrangement::Ccb_halfedge_const_circulator first = it->outer_ccb(); + auto curr = first; if (! curr->source()->is_at_open_boundary()) std::cout << "(" << curr->source()->point() << ")";