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namespace HMesh
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namespace HMesh
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{
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{
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	template<typename ITEM, typename ITEMID>
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	template<typename ITEM, typename ITEMID>
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	class AttributeVector;
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	class AttributeVector;
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	struct VertexTag {};
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    struct FaceTag {};
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    /** The ItemID class is simply a wrapper around an index. This class associates a type
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    struct HalfEdgeTag {};
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     with the index. */
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    template<typename T>
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    template<typename T>
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    class ItemID
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    class ItemID
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    {
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    {
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    public:
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    public:
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        ItemID();
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        ItemID(): index(INVALID_INDEX){}
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        bool operator ==(const ItemID& other) const;
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        bool operator ==(const ItemID& other) const { return index == other.index; }
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        bool operator !=(const ItemID& other) const;
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        bool operator !=(const ItemID& other) const { return index != other.index; }
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        bool operator <(const ItemID& other) const;
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        bool operator <(const ItemID& other) const { return index < other.index; }
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		template<typename X>
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		template<typename X>
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		friend std::ostream& operator<<(std::ostream& os, const ItemID<X>&);
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		friend std::ostream& operator<<(std::ostream& os, const ItemID<X>&);
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    private:
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    private:
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        typedef size_t IndexType;
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        typedef size_t IndexType;
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        static const IndexType INVALID_INDEX =  -1;
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        static const IndexType INVALID_INDEX =  -1;
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        ItemID(IndexType index);
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        explicit ItemID(IndexType _index): index(_index){}
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        friend class ConnectivityKernel;
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        friend class ConnectivityKernel;
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        template<typename ITEM, typename ITEMID>
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        template<typename ITEM> friend class ItemVector;
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        friend class AttributeVector;
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        template<typename ITEM, typename ITEMID> friend class AttributeVector;
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        IndexType index;
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        IndexType index;
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    };
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    };
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    typedef ItemID<VertexTag> VertexID;
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    typedef ItemID<FaceTag> FaceID;
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    typedef ItemID<HalfEdgeTag> HalfEdgeID;
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    static const VertexID InvalidVertexID;
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    static const FaceID InvalidFaceID;
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    static const HalfEdgeID InvalidHalfEdgeID;
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    template<typename T>
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    inline ItemID<T>::ItemID() : index(INVALID_INDEX){}
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    template<typename T>
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    inline ItemID<T>::ItemID(IndexType _index) : index(_index){}
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    template<typename T>
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    inline bool ItemID<T>::operator ==(const ItemID& other) const
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    { return index == other.index; }
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    template<typename T>
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    inline bool ItemID<T>::operator !=(const ItemID& other) const
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    { return index != other.index; }
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    template<typename T>
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    inline bool ItemID<T>::operator <(const ItemID& other) const
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    { return index < other.index; }
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	template<typename T>
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	template<typename T>
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	inline std::ostream& operator<<(std::ostream& os, const ItemID<T>& iid)
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	inline std::ostream& operator<<(std::ostream& os, const ItemID<T>& iid)
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	{
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	{
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		return (os << iid.index);
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		return (os << iid.index);
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	}
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	}