CGAL几何库 半边网格数据结构 模板类 设计核心思想

    CGAL是一个优秀的几何处理库,对于三维网格采用半边格式存储。

      其实对于网格而言,无外乎定义它的边,顶点,面,数据存储。

      问题是用户可能会有不同的需求,比如做模型简化,需要对每个顶点加一个cost域,而对其它应用则不需要,

也许你会说可以给基本的定点数据结构加一个指针,用户自己定义其它的数据都由该指针指向,但这种设计并不好。

 显然模板化处理是更好的方法,不要把顶点类型定死。

      这样一来我们可以通过让一个网格类,拥有不同的顶点类型,边类型,面类型,具体类型由用户决定,用户可以通过

继承底层提供的基本类型,加入自己 的需要的属性,方法,生成新的类型,作为template参数,并传给网格类。从而实现

了网格的灵活设计。 

       CGAL就是采用了这一方法,但是它有大量的模板技巧,wrapper class 包装等等,从而对于想要了解底层具体实现的而言

显得比较复杂难于理解,虽然它的使用还是很简单方便的。 下面我将根据参考文献 Using Generic Programming for Designing a Data Structure for Polyhedral Surface

介绍其模板类设计的非常简洁的核心的思想,并给出代码实例,注意和实际CGAL实现代码是有出入的,这里做了简化

(比如CGAL对顶点,边,面数据结构进行了wrapper class封装,使得wrapper class没有任何模板参数),但是思想是一致的。 


      这里为了简单,去掉面,仅仅考虑边和顶点,对于顶点我们要记录它的对应的半边信息,对于半边我们也要记录顶点信息,

      问题是对于特定的item type,比如顶点,它不知道其相关联的其它item的具体类型,如半边的具体类型 。 

 

      在CGAL的设计中,vertex顶点,通过一个placeholder来获得其它item的类型信息。(在下面的小程序演示中,HalfedgeDS作为那个placeholder,存储所有iterm的类型信息)

 

     CGAL将所有的局部类型信息,如顶点,半边,面放在一个单一的模板参数Refs中。

     在顶点中仅仅用到 Halfedge_handel作为对应的halfedge的引用。

     其他如半边,面的设计类似。

     对于整体的半边数据结构,它将会由如顶点,半边,面的类型来模板化,(parameterized with the item types)

     但是item types如顶点,已经是 class template模板类了,所以我们需要 template as template arguments 即模板参数本身是模板类

 

这种方法还是很常见的,比如考虑二叉树的设计,允许二叉树类装配不同类型的节点,即节点是模板参数

而节点类本身允许有不同的存储数据类型,也就是说节点本身就是模板类。 

可以采用下面的设计 

二叉树节点类

template <typename ElemType>
class Node {
       private:
            ElemType m_data; 
}; 

 二叉树类

template  <template<type Elem> class Node, typename U>
class BinaryTree {
 
       private:
            Node<U>  *m_root; 
}; 

 具体使用

BinaryTree< Node, int> MyBinaryTree;

即可。 

 

好回到CGAL中,这 里的类型依赖构成了一个循环,半边数据结构需要vertex,halfedge类型参数的实化,而半边数据结构类halfedge ds知道 handle 类型,可以用做Refs 参数的实际类型, 尽管当前handles还没有被声明(vertex,halfedge同样需要半边数据结构类来实化)。声明和定义的不同使得这一切成为可能。

struct Edge;
struct Node {
Edge * edge;
// .... maybe more than one edge ....
};
struct Edge {
Node * source;
Node * dest;
};
//最简单的一个示例
template <class Graph>
struct Node {
typedef typename Graph::Edge Edge;
Edge* edge;
// .... maybe some more edges ....
};
template <class Graph>
struct Edge {
typedef typename Graph::Node Node;
Node* node;
};
template < template <class G> class T_Node,
template <class G> class T_Edge>
struct Graph {
typedef Graph< T_Node, T_Edge>       Self;
typedef T_Node<Self>                 Node;
typedef T_Edge<Self>                 Edge;
};
int main() {
typedef Graph< Node, Edge> G;
G::Node node;
G::Edge edge;
node.edge = &edge;
edge.node = &node;
}

template <class Graph>
struct Colored_node : public Node<Graph> {
int color;
};
int main() {
typedef Graph< Colored_node, Edge> G;
G::Node node;
G::Edge edge;
node.edge = &edge;
edge.node = &node;
node.color = 3;
}

 注意上面代码用的是指针,本质上还是利用前置声明,如果改为Edge edge,就不行了,因为那样编译器需要知道Edge的定义,前置声明不行。

It is important to understand that these cyclic definitions work -- as for the C example -- because we can make use of a declared type to define pointers and references to this type before this type is defined itself. For example, we cannot change the pointer member Edge * edge  of the node class to a value Edge edge .


 好了,说了这么多看实际的代码吧。

我写了个小程序测试了一下,为了测试加入了显示PrintName的代码。

 //simple_cgal.h
#include <list>
#include <string>
#include <iostream>
using std::list;
using std::string;
using std::cout;
using std::endl;
template <typename Refs>
struct Vertex {
      typedef typename Refs::Halfedge_handle Halfedge_handle;
      Vertex(string name = "vertex0") { m_name = name;}
      void PrintName() const {
         cout << "This is " << m_name << endl;
       }
      Halfedge_handle halfedge() const { return h; }
      void set_halfedge (Halfedge_handle g) { h = g; }
private:
      Halfedge_handle h;
      string m_name;
};
template <typename Refs>
struct Halfedge {
      typedef typename Refs::Vertex_handle Vertex_handle;
      Halfedge(string name = "halfedge0") { m_name = name;}
      void PrintName() const {
            cout << "This is " << m_name << endl;
      }
      Vertex_handle vertex() const { return v;}
      void set_vertex (Vertex_handle vv) { v = vv;}
private:
      Vertex_handle v;
      string m_name;
};
template < template <typename Ref> class Vertex, template <typename Ref> class Halfedge>
struct HalfedgeDS {
      typedef HalfedgeDS< Vertex, Halfedge> Self;
      typedef Vertex<Self>                  V;
      typedef Halfedge<Self>                H;
      typedef list<V>                       Vlist;
      typedef list<H>                       Hlist;
      typedef typename Vlist::iterator Vertex_handle;
      typedef typename Hlist::iterator Halfedge_handle;
};
 //test_simple_cgal.cc
#include "simple_cgal.h"
#include <iostream>
using namespace std;
int main(int argc, char *argv[])
{
    typedef HalfedgeDS< Vertex, Halfedge> HDS;
    typedef HDS::V Vert;
    typedef HDS::H HalfEdge;
    typedef HDS::Vlist Vlist;
    typedef HDS::Hlist Hlist;
    Vert v("vertex a");
    HalfEdge h("Halfedge b");
    Vlist vlist;
    Hlist hlist;
    vlist.push_back(v);
    hlist.push_back(h);
    v.set_halfedge(hlist.begin());
    h.set_vertex(vlist.begin());
    v.halfedge()->PrintName();
    h.vertex()->PrintName();
    return 0;
}
运行结果:

      
      
      
      
This is Halfedge b This is vertex a CGAL中实际的定义对于顶点,边和面元素进行了封装,将他们放在同一个不带模板参数的类里面,类似下面代码模仿的HalfedgeDS_iems, 从而将他们集中到一起并且最外层去掉模板参数,里面通过wrapper将他们的定义包装。用户可以定义不同的顶点类,只要 在传给HalfedgeDS的HalfedgeItesms参数的类中typedef 自己定义的顶点类为Vertex即可。 //简单模拟vertex,halfedge wrapper用法演示 //simple_cgal2.h
#include <list>
#include <string>
#include <iostream>
using std::list;
using std::string;
using std::cout;
using std::endl;
template <typename Refs>
struct Vertex {
      typedef typename Refs::Halfedge_handle Halfedge_handle;
      Vertex(string name = "vertex0") { m_name = name;}
      void PrintName() const {
            cout << "This is " << m_name << endl;
      }
      Halfedge_handle halfedge() const { return h; }
      void set_halfedge (Halfedge_handle g) { h = g; }
   private:
      Halfedge_handle h;
      string m_name;
};
template <typename Refs>
struct Halfedge {
      typedef typename Refs::Vertex_handle Vertex_handle;
      Halfedge(string name = "halfedge0") { m_name = name;}
      void PrintName() const {
            cout << "This is " << m_name << endl;
      }
      Vertex_handle vertex() const { return v;}
      void set_vertex (Vertex_handle vv) { v = vv;}
   private:
      Vertex_handle v;
      string m_name;
};
struct HalfedgeDS_iems {
      template <class Refs>
      struct Vertex_wrapper {
            typedef Vertex<Refs> Vertex;
      };
      template <class Refs>
      struct Halfedge_wrapper {
            typedef Halfedge<Refs> Halfedge;
            };
};
template < typename HalfedgeDSItems>
struct HalfedgeDS {
      typedef HalfedgeDS< HalfedgeDSItems> Self;
      typedef HalfedgeDSItems                            Items;
      typedef typename Items::template Vertex_wrapper<Self>                                                                                                            Vertex_wrapper;
            typedef typename Items::template Halfedge_wrapper<Self>
Halfedge_wrapper;
            typedef typename Vertex_wrapper::Vertex            Vertex;
            typedef typename Halfedge_wrapper::Halfedge        Halfedge;
            typedef list<Vertex>                       Vlist;
            typedef list<Halfedge>                       Hlist;
            typedef typename Vlist::iterator Vertex_handle;
            typedef typename Hlist::iterator Halfedge_handle;
};

//test_simgple_cgal2.cc
#include "simple_cgal2.h"
#include <iostream>

using namespace std;

int main(int argc, char *argv[])

{

      typedef HalfedgeDS<HalfedgeDS_iems> HDS;

      typedef HDS::Vertex Vert;

      typedef HDS::Halfedge HalfEdge;

      typedef HDS::Vlist Vlist;

      typedef HDS::Hlist Hlist;

      Vert v("vertex a");

      HalfEdge h("Halfedge b");

      Vlist vlist;

      Hlist hlist;

      vlist.push_back(v);

      hlist.push_back(h);

      v.set_halfedge(hlist.begin());

      h.set_vertex(vlist.begin());

      v.halfedge()->PrintName();

      h.vertex()->PrintName();

      return 0;

}


运行结果和上面程序一致。多了一个HalfedgeDS_iems包装的一个好处是由于HalfedgeDS_iems没有模板参数,所以下面的定义是可能的,CGAL中定义有Polyhedron它的一个模板参数是HDS,即半边结构,考虑上面没有封装到HalfedgeItesms的方案,
template < template <typename Ref> class Vertex, template <typename Ref> class Halfedge>
struct HalfedgeDS
HalfedgeDS的定义已经有两级模板参数了,如果再被传递会有三级模板参数,C++是不允许这样的,所以HalfedgeDS_iems方法不失为一种绕过的技巧。关于Polyhedron_items<Items>下面给予介绍。先看一个用户自己扩充面的例子,完全继承已有的边和顶点,用户当然也可以全部扩充,总之通过wrapper是很灵活的。
template < class Traits,

           class Items = Items_default,

           template < class, class> calss HDS = HalfedgeDS_default>

struct Polyhedron {

      typedef Polyhedron_items<Items> Deerived_items;

      typedef HDS< Traits, Derived_items> HDS;

      typedef typename HDS::Vertex                  Vertex;

      typedef typename HDS::Halfedge                Halfedge;

      typedef typename HDS::Face                    Face;



.....

};
template <class Refs, class Triats>

class My_facet : public CGAL_HalfedgeDS_facet_base<Refs> {

      int face_cost;  // we need to sore addtional info 

    public:

       typename Traits::Vector_3 normal;  

};

struct My_items : public CGAL_Polyhedron_items_3 {

      template <class Refs, class Traits>

      struct Face_wrapper {

            typedef My_facet< Refs, Traits> Facet;

      };

};

typedef CGAL_Polyhedron_3<Traits, My_items> Polyhedron;
OK,用户使用起来就是这么简单,这样我们的Polyhedron就是应用用户定义的facet了同时保留了CGAL_Polyhedron_items_3中定义的facet的所以属性函数,如set_handle.由于用户没有定义Vertex和Halfedge所以它们完全用CGAL_Polyhedron_items_3中提供的Vertex和Halfege不加任何扩充。//CGAL源代码
class Polyhedron_items_3 {

public:

    template < class Refs, class Traits>

    struct Vertex_wrapper {

        typedef typename Traits::Point_3 Point;

        typedef HalfedgeDS_vertex_base< Refs, Tag_true, Point> Vertex;

    };

    template < class Refs, class Traits>

    struct Halfedge_wrapper {

        typedef HalfedgeDS_halfedge_base< Refs>                Halfedge;

    };

    template < class Refs, class Traits>

    struct Face_wrapper {

        typedef typename Traits::Plane_3 Plane;

        typedef HalfedgeDS_face_base< Refs, Tag_true, Plane>   Face;

    };

};

template < class Refs >

class HalfedgeDS_face_base< Refs, Tag_true, Tag_false> {

public:

    typedef Refs                                 HalfedgeDS;

    typedef HalfedgeDS_face_base< Refs, Tag_true, Tag_false>   Base;

    typedef Tag_true                             Supports_face_halfedge;

    typedef typename Refs::Vertex_handle         Vertex_handle;

    typedef typename Refs::Vertex_const_handle   Vertex_const_handle;

    typedef typename Refs::Halfedge_handle       Halfedge_handle;

    typedef typename Refs::Halfedge_const_handle Halfedge_const_handle;

    typedef typename Refs::Face_handle           Face_handle;

    typedef typename Refs::Face_const_handle     Face_const_handle;

    typedef typename Refs::Vertex                Vertex;

    typedef typename Refs::Halfedge              Halfedge;

    // Additional tags required by Polyhedron.

    typedef Tag_false                            Supports_face_plane;

    struct Plane_not_supported {};

    typedef Plane_not_supported                  Plane;

    // No longer required.

    //typedef Tag_false                            Supports_face_normal;

private:

    Halfedge_handle hdg;

public:

    Halfedge_handle       halfedge()                        { return hdg; }

    Halfedge_const_handle halfedge() const                  { return hdg; }

    void                  set_halfedge( Halfedge_handle h)  { hdg = h; }

};
这里面实现还是有另外的技巧,原文章中又以vertex举例了,就按照vertex继续吧。
template <class Vertex_base>

struct Polyhedron_vertex : public Vertex_base {

      typedef Vertex_base Base;

private:

      void set_halfedge(typename Base::Halfedge_handle g) {

            Base::set_halfedge(g);

      }

};

template <class Items>

struct Polyhderon_items {

      template <class Refs, class Traits>

      struct Vertex_wrapper {

            typedef typename Items::Vertex_wrapper<Refs, Traits> Wrapper;

            typedef typename Wrapper::Vertex Vertex_base;

            typedef Polyhedron_vertex<Vertex_base> Vertex;

      };

      //similar for facet and halfedge

};



template < class Traits,

           class Items = Items_default,

           template < class, class> calss HDS = HalfedgeDS_default>

struct Polyhedron {

      typedef Polyhedron_items<Items> Deerived_items;

      typedef HDS< Traits, Derived_items> HDS;

      typedef typename HDS::Vertex                  Vertex;

      typedef typename HDS::Halfedge                Halfedge;

      typedef typename HDS::Face                    Face;



.....

};

用户自定义的Items,Vetex会被当作模板参数传递如下。也就是说最后实际用的是Polyhedron_items<Items> 中定义的Vertex Polyhedron_vertex<Vertex_base>而 Items即为用户定义并传递的点面边数据类型类。Vertex_base是用户定义的Vertex类型。下面看一下CGAL实际的代码,这里的I_Polyhedron_vertex其实就是上面的Polyhedron_vertex。

template <class VertexBase>

class I_Polyhedron_vertex  : public VertexBase  {

public:

    typedef VertexBase                            Base;

    //typedef typename Base::HalfedgeDS              HDS;

    typedef typename Base::Point                   Point;

    typedef Point                                  Point_3;



    // Handles have to explicitly repeated, although they are derived

    typedef typename Base::Vertex_handle           Vertex_handle;

    typedef typename Base::Halfedge_handle         Halfedge_handle;

    typedef typename Base::Face_handle             Face_handle;

    typedef typename Base::Face_handle             Facet_handle;

    typedef typename Base::Vertex_const_handle     Vertex_const_handle;

    typedef typename Base::Halfedge_const_handle   Halfedge_const_handle;

    typedef typename Base::Face_const_handle       Face_const_handle;

    typedef typename Base::Face_const_handle       Facet_const_handle;

    typedef typename Base::Halfedge                Halfedge;

    typedef typename Base::Face                    Face;

    typedef typename Base::Face                    Facet;



    // Supported options by HDS.

    typedef typename Base::Supports_vertex_halfedge

                                                  Supports_vertex_halfedge;

    typedef typename Base::Supports_vertex_point  Supports_vertex_point;



    // Circulator category.

    typedef typename Halfedge::Supports_halfedge_prev  Supports_prev;



public:

    // Circulator category.

    typedef HalfedgeDS_circulator_traits<Supports_prev> Ctr;

    typedef typename Ctr::iterator_category circulator_category;



    // Circulators around a vertex and around a facet.

    typedef I_HalfedgeDS_facet_circ< Halfedge_handle, circulator_category>

                                         Halfedge_around_facet_circulator;



    typedef I_HalfedgeDS_vertex_circ< Halfedge_handle, circulator_category>

                                        Halfedge_around_vertex_circulator;



    typedef I_HalfedgeDS_facet_circ<

        Halfedge_const_handle,

        circulator_category>       Halfedge_around_facet_const_circulator;



    typedef I_HalfedgeDS_vertex_circ<

        Halfedge_const_handle,

        circulator_category>      Halfedge_around_vertex_const_circulator;







    typedef typename Halfedge_around_vertex_circulator::size_type

        size_type;

    typedef typename Halfedge_around_vertex_circulator::difference_type

        difference_type;



public:

    // We need to repeat the constructors here.

    I_Polyhedron_vertex() {}

    I_Polyhedron_vertex( const VertexBase& b) : VertexBase(b) {}

    I_Polyhedron_vertex( const Point_3& p) : VertexBase(p) {}



// New Access Functions (not provided in VertexBase).



    Halfedge_around_vertex_circulator vertex_begin() {

        // a circulator of halfedges around the vertex (clockwise).

        return Halfedge_around_vertex_circulator( this->halfedge());

    }

    Halfedge_around_vertex_const_circulator vertex_begin() const {

        // a circulator of halfedges around the vertex (clockwise).

        return Halfedge_around_vertex_const_circulator( this->halfedge());

    }



    // the degree of the vertex, i.e., edges emanating from this vertex 

    std::size_t vertex_degree() const { 

        return this->halfedge()->vertex_degree(); 

    }

    size_type degree() const { return vertex_degree(); } //backwards compatible



    // returns true if the vertex has exactly two incident edges

    bool is_bivalent() const { return  this->halfedge()->is_bivalent(); }



    // returns true if the vertex has exactly three incident edges

    bool is_trivalent() const { return  this->halfedge()->is_trivalent(); }



    // No longer hidden. Now the restricted version with precondition.

    // sets incident halfedge to h. Precondition: h is incident, i.e.,

    // h->vertex() == v.

    void  set_halfedge( Halfedge_handle hh) {

        CGAL_assertion( &*(hh->vertex()) == this);

        Base::set_halfedge(hh);

    }

};
//所有这些内容对应的具体CGAL源代码参照/usr/local/include/CGAL 
Polyhedron_3.h
HalfedgeDS_vector.h //vecotor和list思路一致不过是采用不同的内部数据组织,vector或者listHalfedgeDS_list.hPolyhedron_items_3.hHalfedgeDS_halfedge_base.h


       
       
       
       


       
       
       
       


       
       
       
       

   

      
      
      
      
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