//=======================================================================
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// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
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// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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//=======================================================================
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#ifndef BOOST_SELF_AVOIDING_WALK_HPP
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#define BOOST_SELF_AVOIDING_WALK_HPP
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/*
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This file defines necessary components for SAW.
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mesh language: (defined by myself to clearify what is what)
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A triangle in mesh is called an triangle.
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An edge in mesh is called an line.
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A vertex in mesh is called a point.
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A triangular mesh corresponds to a graph in which a vertex is a
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triangle and an edge(u, v) stands for triangle u and triangle v
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share an line.
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After this point, a vertex always refers to vertex in graph,
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therefore it is a traingle in mesh.
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*/
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#include <utility>
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#include <boost/config.hpp>
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#include <boost/graph/graph_traits.hpp>
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#include <boost/property_map/property_map.hpp>
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#define SAW_SENTINAL -1
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namespace boost
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{
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template < class T1, class T2, class T3 > struct triple
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{
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T1 first;
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T2 second;
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T3 third;
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triple(const T1& a, const T2& b, const T3& c)
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: first(a), second(b), third(c)
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{
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}
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triple() : first(SAW_SENTINAL), second(SAW_SENTINAL), third(SAW_SENTINAL) {}
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};
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typedef triple< int, int, int > Triple;
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/* Define a vertex property which has a triangle inside. Triangle is
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represented by a triple. */
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struct triangle_tag
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{
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enum
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{
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num = 100
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};
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};
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typedef property< triangle_tag, Triple > triangle_property;
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/* Define an edge property with a line. A line is represented by a
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pair. This is not required for SAW though.
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*/
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struct line_tag
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{
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enum
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{
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num = 101
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};
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};
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template < class T >
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struct line_property : public property< line_tag, std::pair< T, T > >
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{
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};
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/*Precondition: Points in a Triangle are in order */
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template < class Triangle, class Line >
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inline void get_sharing(const Triangle& a, const Triangle& b, Line& l)
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{
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l.first = SAW_SENTINAL;
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l.second = SAW_SENTINAL;
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if (a.first == b.first)
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{
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l.first = a.first;
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if (a.second == b.second || a.second == b.third)
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l.second = a.second;
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else if (a.third == b.second || a.third == b.third)
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l.second = a.third;
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}
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else if (a.first == b.second)
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{
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l.first = a.first;
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if (a.second == b.third)
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l.second = a.second;
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else if (a.third == b.third)
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l.second = a.third;
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}
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else if (a.first == b.third)
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{
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l.first = a.first;
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}
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else if (a.second == b.first)
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{
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l.first = a.second;
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if (a.third == b.second || a.third == b.third)
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l.second = a.third;
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}
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else if (a.second == b.second)
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{
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l.first = a.second;
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if (a.third == b.third)
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l.second = a.third;
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}
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else if (a.second == b.third)
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{
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l.first = a.second;
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}
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else if (a.third == b.first || a.third == b.second || a.third == b.third)
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l.first = a.third;
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/*Make it in order*/
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if (l.first > l.second)
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{
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typename Line::first_type i = l.first;
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l.first = l.second;
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l.second = i;
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}
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}
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template < class TriangleDecorator, class Vertex, class Line >
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struct get_vertex_sharing
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{
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typedef std::pair< Vertex, Line > Pair;
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get_vertex_sharing(const TriangleDecorator& _td) : td(_td) {}
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inline Line operator()(const Vertex& u, const Vertex& v) const
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{
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Line l;
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get_sharing(td[u], td[v], l);
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return l;
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}
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inline Line operator()(const Pair& u, const Vertex& v) const
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{
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Line l;
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get_sharing(td[u.first], td[v], l);
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return l;
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}
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inline Line operator()(const Pair& u, const Pair& v) const
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{
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Line l;
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get_sharing(td[u.first], td[v.first], l);
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return l;
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}
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TriangleDecorator td;
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};
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/* HList has to be a handle of data holder so that pass-by-value is
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* in right logic.
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*
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* The element of HList is a pair of vertex and line. (remember a
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* line is a pair of two ints.). That indicates the walk w from
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* current vertex is across line. (If the first of line is -1, it is
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* a point though.
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*/
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template < class TriangleDecorator, class HList, class IteratorD >
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class SAW_visitor : public bfs_visitor<>, public dfs_visitor<>
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{
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typedef typename boost::property_traits< IteratorD >::value_type iter;
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/*use boost shared_ptr*/
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typedef typename HList::element_type::value_type::second_type Line;
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public:
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typedef tree_edge_tag category;
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inline SAW_visitor(TriangleDecorator _td, HList _hlist, IteratorD ia)
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: td(_td), hlist(_hlist), iter_d(ia)
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{
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}
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template < class Vertex, class Graph >
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inline void start_vertex(Vertex v, Graph&)
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{
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Line l1;
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l1.first = SAW_SENTINAL;
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l1.second = SAW_SENTINAL;
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hlist->push_front(std::make_pair(v, l1));
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iter_d[v] = hlist->begin();
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}
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/*Several symbols:
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w(i): i-th triangle in walk w
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w(i) |- w(i+1): w enter w(i+1) from w(i) over a line
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w(i) ~> w(i+1): w enter w(i+1) from w(i) over a point
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w(i) -> w(i+1): w enter w(i+1) from w(i)
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w(i) ^ w(i+1): the line or point w go over from w(i) to w(i+1)
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*/
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template < class Edge, class Graph > bool tree_edge(Edge e, Graph& G)
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{
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using std::make_pair;
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typedef typename boost::graph_traits< Graph >::vertex_descriptor Vertex;
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Vertex tau = target(e, G);
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Vertex i = source(e, G);
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get_vertex_sharing< TriangleDecorator, Vertex, Line > get_sharing_line(
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td);
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Line tau_i = get_sharing_line(tau, i);
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iter w_end = hlist->end();
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iter w_i = iter_d[i];
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iter w_i_m_1 = w_i;
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iter w_i_p_1 = w_i;
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/*----------------------------------------------------------
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* true false
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*==========================================================
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*a w(i-1) |- w(i) w(i-1) ~> w(i) or w(i-1) is null
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*----------------------------------------------------------
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*b w(i) |- w(i+1) w(i) ~> w(i+1) or no w(i+1) yet
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*----------------------------------------------------------
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*/
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bool a = false, b = false;
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--w_i_m_1;
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++w_i_p_1;
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b = (w_i->second.first != SAW_SENTINAL);
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if (w_i_m_1 != w_end)
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{
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a = (w_i_m_1->second.first != SAW_SENTINAL);
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}
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if (a)
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{
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if (b)
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{
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/*Case 1:
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w(i-1) |- w(i) |- w(i+1)
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*/
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Line l1 = get_sharing_line(*w_i_m_1, tau);
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iter w_i_m_2 = w_i_m_1;
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--w_i_m_2;
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bool c = true;
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if (w_i_m_2 != w_end)
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{
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c = w_i_m_2->second != l1;
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}
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if (c)
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{ /* w(i-1) ^ tau != w(i-2) ^ w(i-1) */
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/*extension: w(i-1) -> tau |- w(i) */
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w_i_m_1->second = l1;
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/*insert(pos, const T&) is to insert before pos*/
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iter_d[tau] = hlist->insert(w_i, make_pair(tau, tau_i));
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}
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else
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{ /* w(i-1) ^ tau == w(i-2) ^ w(i-1) */
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/*must be w(i-2) ~> w(i-1) */
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bool d = true;
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// need to handle the case when w_i_p_1 is null
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Line l3 = get_sharing_line(*w_i_p_1, tau);
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if (w_i_p_1 != w_end)
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d = w_i_p_1->second != l3;
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if (d)
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{ /* w(i+1) ^ tau != w(i+1) ^ w(i+2) */
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/*extension: w(i) |- tau -> w(i+1) */
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w_i->second = tau_i;
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iter_d[tau]
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= hlist->insert(w_i_p_1, make_pair(tau, l3));
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}
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else
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{ /* w(i+1) ^ tau == w(i+1) ^ w(i+2) */
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/*must be w(1+1) ~> w(i+2) */
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Line l5 = get_sharing_line(*w_i_m_1, *w_i_p_1);
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if (l5 != w_i_p_1->second)
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{ /* w(i-1) ^ w(i+1) != w(i+1) ^ w(i+2) */
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/*extension: w(i-2) -> tau |- w(i) |- w(i-1) ->
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* w(i+1) */
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w_i_m_2->second = get_sharing_line(*w_i_m_2, tau);
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iter_d[tau]
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= hlist->insert(w_i, make_pair(tau, tau_i));
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w_i->second = w_i_m_1->second;
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w_i_m_1->second = l5;
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iter_d[w_i_m_1->first]
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= hlist->insert(w_i_p_1, *w_i_m_1);
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hlist->erase(w_i_m_1);
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}
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else
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{
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/*mesh is tetrahedral*/
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// dont know what that means.
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;
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}
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}
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}
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}
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else
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{
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/*Case 2:
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w(i-1) |- w(i) ~> w(1+1)
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*/
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if (w_i->second.second == tau_i.first
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|| w_i->second.second == tau_i.second)
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{ /*w(i) ^ w(i+1) < w(i) ^ tau*/
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/*extension: w(i) |- tau -> w(i+1) */
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w_i->second = tau_i;
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Line l1 = get_sharing_line(*w_i_p_1, tau);
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iter_d[tau] = hlist->insert(w_i_p_1, make_pair(tau, l1));
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}
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else
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{ /*w(i) ^ w(i+1) !< w(i) ^ tau*/
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Line l1 = get_sharing_line(*w_i_m_1, tau);
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bool c = true;
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iter w_i_m_2 = w_i_m_1;
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--w_i_m_2;
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if (w_i_m_2 != w_end)
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c = l1 != w_i_m_2->second;
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if (c)
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{ /*w(i-1) ^ tau != w(i-2) ^ w(i-1)*/
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/*extension: w(i-1) -> tau |- w(i)*/
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w_i_m_1->second = l1;
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iter_d[tau] = hlist->insert(w_i, make_pair(tau, tau_i));
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}
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else
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{ /*w(i-1) ^ tau == w(i-2) ^ w(i-1)*/
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/*must be w(i-2)~>w(i-1)*/
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/*extension: w(i-2) -> tau |- w(i) |- w(i-1) -> w(i+1)*/
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w_i_m_2->second = get_sharing_line(*w_i_m_2, tau);
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iter_d[tau] = hlist->insert(w_i, make_pair(tau, tau_i));
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w_i->second = w_i_m_1->second;
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w_i_m_1->second = get_sharing_line(*w_i_m_1, *w_i_p_1);
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iter_d[w_i_m_1->first]
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= hlist->insert(w_i_p_1, *w_i_m_1);
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hlist->erase(w_i_m_1);
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}
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}
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}
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}
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else
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{
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if (b)
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{
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/*Case 3:
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w(i-1) ~> w(i) |- w(i+1)
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*/
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bool c = false;
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if (w_i_m_1 != w_end)
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c = (w_i_m_1->second.second == tau_i.first)
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|| (w_i_m_1->second.second == tau_i.second);
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if (c)
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{ /*w(i-1) ^ w(i) < w(i) ^ tau*/
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/* extension: w(i-1) -> tau |- w(i) */
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if (w_i_m_1 != w_end)
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w_i_m_1->second = get_sharing_line(*w_i_m_1, tau);
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iter_d[tau] = hlist->insert(w_i, make_pair(tau, tau_i));
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}
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else
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{
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bool d = true;
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Line l1;
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l1.first = SAW_SENTINAL;
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l1.second = SAW_SENTINAL;
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if (w_i_p_1 != w_end)
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{
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l1 = get_sharing_line(*w_i_p_1, tau);
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d = l1 != w_i_p_1->second;
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}
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if (d)
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{ /*w(i+1) ^ tau != w(i+1) ^ w(i+2)*/
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/*extension: w(i) |- tau -> w(i+1) */
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w_i->second = tau_i;
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iter_d[tau]
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= hlist->insert(w_i_p_1, make_pair(tau, l1));
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}
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else
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{
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/*must be w(i+1) ~> w(i+2)*/
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/*extension: w(i-1) -> w(i+1) |- w(i) |- tau -> w(i+2)
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*/
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iter w_i_p_2 = w_i_p_1;
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++w_i_p_2;
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w_i_p_1->second = w_i->second;
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iter_d[i] = hlist->insert(w_i_p_2, make_pair(i, tau_i));
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hlist->erase(w_i);
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Line l2 = get_sharing_line(*w_i_p_2, tau);
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iter_d[tau]
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= hlist->insert(w_i_p_2, make_pair(tau, l2));
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}
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}
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}
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else
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{
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/*Case 4:
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w(i-1) ~> w(i) ~> w(i+1)
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*/
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bool c = false;
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if (w_i_m_1 != w_end)
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{
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c = (w_i_m_1->second.second == tau_i.first)
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|| (w_i_m_1->second.second == tau_i.second);
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}
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if (c)
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{ /*w(i-1) ^ w(i) < w(i) ^ tau */
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/*extension: w(i-1) -> tau |- w(i) */
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if (w_i_m_1 != w_end)
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w_i_m_1->second = get_sharing_line(*w_i_m_1, tau);
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iter_d[tau] = hlist->insert(w_i, make_pair(tau, tau_i));
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}
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else
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{
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/*extension: w(i) |- tau -> w(i+1) */
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w_i->second = tau_i;
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Line l1;
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l1.first = SAW_SENTINAL;
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l1.second = SAW_SENTINAL;
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if (w_i_p_1 != w_end)
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l1 = get_sharing_line(*w_i_p_1, tau);
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iter_d[tau] = hlist->insert(w_i_p_1, make_pair(tau, l1));
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}
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}
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}
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return true;
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}
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protected:
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TriangleDecorator td; /*a decorator for vertex*/
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HList hlist;
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/*This must be a handle of list to record the SAW
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The element type of the list is pair<Vertex, Line>
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*/
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IteratorD iter_d;
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/*Problem statement: Need a fast access to w for triangle i.
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*Possible solution: mantain an array to record.
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iter_d[i] will return an iterator
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which points to w(i), where i is a vertex
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representing triangle i.
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*/
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};
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template < class Triangle, class HList, class Iterator >
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inline SAW_visitor< Triangle, HList, Iterator > visit_SAW(
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Triangle t, HList hl, Iterator i)
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{
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return SAW_visitor< Triangle, HList, Iterator >(t, hl, i);
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}
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template < class Tri, class HList, class Iter >
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inline SAW_visitor< random_access_iterator_property_map< Tri*, Tri, Tri& >,
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HList, random_access_iterator_property_map< Iter*, Iter, Iter& > >
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visit_SAW_ptr(Tri* t, HList hl, Iter* i)
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{
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typedef random_access_iterator_property_map< Tri*, Tri, Tri& > TriD;
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typedef random_access_iterator_property_map< Iter*, Iter, Iter& > IterD;
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return SAW_visitor< TriD, HList, IterD >(t, hl, i);
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}
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// should also have combo's of pointers, and also const :(
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}
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#endif /*BOOST_SAW_H*/
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