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Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
#include "tcenterlinevectP.h"
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//==========================================================================
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//============================================
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//      Sequence conversion into TStroke
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//============================================
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//Globals
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namespace
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{
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const double Polyg_eps_max = 1;	//Sequence simplification max error
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const double Polyg_eps_mul = 0.75; //Sequence simpl. thickness-multiplier error
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const double Quad_eps_max = infinity; //As above, for sequence conversion into strokes
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									  //const double Quad_eps_mul= 0.2;     //NOTE: Substituted by globals->currConfig->m_penalty
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}
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//--------------------------------------------------------------------------
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//-------------------------------
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//      Simplify Sequences
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//-------------------------------
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//EXPLANATION:  Before converting sequences in strokes, we simplify them
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//by eliminating sequence of points which lie on the same straight line,
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//leaving the extremities only.
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class SequenceSimplifier
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{
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	const Sequence *m_s;
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	const SkeletonGraph *m_graph;
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private:
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	class Length
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	{
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	public:
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		int n;
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		double l;
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		UINT firstNode, secondNode;
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		Length() : n(0), l(0) {}
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		Length(int n_, double l_) : n(n_), l(l_) {}
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		inline void infty(void)
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		{
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			n = infinity;
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			l = infinity;
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		}
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		inline bool operator<(Length sl)
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		{
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			return n < sl.n ? 1 : n > sl.n ? 0 : l < sl.l ? 1 : 0;
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		}
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		inline Length operator+(Length sl)
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		{
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			return Length(n + sl.n, l + sl.l);
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		}
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	};
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	Length lengthOf(UINT a, UINT aLink, UINT b);
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public:
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	//Methods
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	SequenceSimplifier(const Sequence *s)
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		: m_s(s), m_graph(m_s->m_graphHolder) {}
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	void simplify(std::vector<unsigned int=""> &result);</unsigned>
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};
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//--------------------------------------------------------------------------
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//Bellman algorithm for Sequences
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//NOTE: Circular Sequences are dealt.
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void SequenceSimplifier::simplify(std::vector<unsigned int=""> &result)</unsigned>
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{
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	//Initialize variables
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	unsigned int n;
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	unsigned int i, j, iLink, jLink;
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	//NOTE: If s is circular, we have to protect
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	i = m_s->m_head;
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	iLink = m_s->m_headLink;
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	//NOTE: If m_head==m_tail then we have to force the first step by "|| n==1"
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	for (n = 1; i != m_s->m_tail || n == 1; ++n, m_s->next(i, iLink))
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		;
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	Length L_att, L_min, l_min, l_ji;
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	unsigned int p_i, a, b;
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	std::vector<length> M(n);</length>
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	std::vector<length> K(n);</length>
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	std::vector<unsigned int=""> P(n);</unsigned>
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	//Search for minimal path
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	i = m_s->m_head;
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	iLink = m_s->m_headLink;
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	for (a = 1; i != m_s->m_tail || a == 1; m_s->next(i, iLink), ++a) {
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		L_min.infty();
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		l_min.infty();
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		p_i = 0;
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		j = m_s->m_head;
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		jLink = m_s->m_headLink;
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		unsigned int iNext = m_graph->getNode(i).getLink(iLink).getNext();
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		for (b = 0; j != iNext || b == 0; m_s->next(j, jLink), ++b) {
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			if ((L_att = M[b] + (l_ji = lengthOf(j, jLink, iNext))) < L_min) {
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				L_min = L_att;
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				p_i = b;
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				l_min = l_ji;
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			}
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		}
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		M[a] = L_min;
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		K[a] = l_min;
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		P[a] = p_i;
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	}
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	//Copies minimal path found to the output reducedIndices vector
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	//NOTE: size() is added due to circular sequences case handling
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	unsigned int redSize = result.size();
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	result.resize(redSize + M[n - 1].n + 1);
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	result[redSize + M[n - 1].n] = K[n - 1].secondNode;
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	for (b = n - 1, a = redSize + M[n - 1].n - 1; b > 0; b = P[b], --a)
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		result[a] = K[b].firstNode;
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}
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//--------------------------------------------------------------------------
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//Length between two sequence points
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SequenceSimplifier::Length
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SequenceSimplifier::lengthOf(UINT a, UINT aLink, UINT b)
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{
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	UINT curr, old;
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	T3DPointD v;
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	double d, vv;
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	Length res;
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	res.n = 1;
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	res.firstNode = a;
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	res.secondNode = b;
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	v = *m_graph->getNode(b) - *m_graph->getNode(a);
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	vv = norm(v);
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	curr = m_graph->getNode(a).getLink(aLink).getNext();
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	old = a;
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	//If the distance between extremities is small, check if the same holds
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	//for internal points; if so, ok - otherwise set infty().
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	if (vv < 0.1) {
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		for (; curr != b; m_s->advance(old, curr)) {
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			d = tdistance(*m_graph->getNode(curr), *m_graph->getNode(a));
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			if (d > 0.1)
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				res.infty();
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		}
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		return res;
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	}
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	//Otherwise, check distances from line passing from a and b
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	v = v * (1 / vv);
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	for (; curr != b; m_s->advance(old, curr)) {
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		d = tdistance2(*m_graph->getNode(curr), v, *m_graph->getNode(a));
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		if (d > tmin(m_graph->getNode(curr)->z * Polyg_eps_mul, Polyg_eps_max)) {
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			res.infty();
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			return res;
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		} else
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			res.l += d;
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	}
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	return res;
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}
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//==========================================================================
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//===============================
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//      Sequence conversion
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//===============================
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//EXPLANATION: Sequences convert into TStrokes by applying a SequenceConverter
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//  class. A graph minimal-path algorithm is run by using a lexicographic-ordered
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//  (number of quadratics, error) length.
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class SequenceConverter
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{
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	const Sequence *m_s;
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	const SkeletonGraph *m_graph;
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	double m_penalty;
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public:
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	//Length construction globals (see 'lengthOf' method)
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	unsigned int middle;
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	std::vector<double> pars;</double>
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	class Length
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	{
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	public:
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		int n;
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		double l;
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		std::vector<t3dpointd> CPs;</t3dpointd>
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		Length() : n(0), l(0) {}
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		Length(int n_, double l_) : n(n_), l(l_) {}
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		inline void infty(void)
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		{
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			n = infinity;
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			l = infinity;
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		}
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		inline bool operator<(Length sl)
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		{
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			return n < sl.n ? 1 : n > sl.n ? 0 : l < sl.l ? 1 : 0;
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		}
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		inline Length operator+(Length sl)
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		{
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			return Length(n + sl.n, l + sl.l);
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		}
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		void set_CPs(const T3DPointD &a, const T3DPointD &b, const T3DPointD &c)
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		{
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			CPs.resize(3);
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			CPs[0] = a;
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			CPs[1] = b;
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			CPs[2] = c;
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		}
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		void set_CPs(const T3DPointD &a, const T3DPointD &b, const T3DPointD &c,
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					 const T3DPointD &d, const T3DPointD &e)
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		{
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			CPs.resize(5);
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			CPs[0] = a;
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			CPs[1] = b;
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			CPs[2] = c;
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			CPs[3] = d;
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			CPs[4] = e;
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		}
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	};
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	//Intermediate Sequence form
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	std::vector<t3dpointd> middleAddedSequence;</t3dpointd>
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	std::vector<unsigned int=""> *inputIndices;</unsigned>
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	//Methods
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	SequenceConverter(const Sequence *s, double penalty)
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		: m_s(s), m_graph(m_s->m_graphHolder), m_penalty(penalty) {}
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	Length lengthOf(unsigned int a, unsigned int b);
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	void addMiddlePoints();
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	TStroke *operator()(std::vector<unsigned int=""> *indices);</unsigned>
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	//Length construction methods
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	bool parametrize(unsigned int a, unsigned int b);
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	void lengthOfTriplet(unsigned int i, Length &len);
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	bool calculateCPs(unsigned int i, unsigned int j, Length &len);
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	bool penalty(unsigned int a, unsigned int b, Length &len);
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};
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//--------------------------------------------------------------------------
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//Changes in stroke thickness are considered more penalizating
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inline double ellProd(const T3DPointD &a, const T3DPointD &b)
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{
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	return a.x * b.x + a.y * b.y + 5 * a.z * b.z;
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}
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//--------------------------------------------------------------------------
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//EXPLANATION:  After simplification, we receive a vector<uint> of indices</uint>
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//corresponding to the vertices of the simplified current sequence.
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//Before beginning conversion, we need to add middle points between the
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//above vertex points.
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inline void SequenceConverter::addMiddlePoints()
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{
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	unsigned int i, j, n;
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	n = inputIndices->size();
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	middleAddedSequence.clear();
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	if (n == 2) {
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		middleAddedSequence.resize(3);
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		middleAddedSequence[0] = *m_graph->getNode((*inputIndices)[0]);
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		middleAddedSequence[1] =
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			(*m_graph->getNode((*inputIndices)[0]) +
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			 *m_graph->getNode((*inputIndices)[1])) *
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			0.5;
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		middleAddedSequence[2] = *m_graph->getNode((*inputIndices)[1]);
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	} else {
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		middleAddedSequence.resize(2 * n - 3);
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		middleAddedSequence[0] = *m_graph->getNode((*inputIndices)[0]);
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		for (i = j = 1; i < n - 2; ++i, j += 2) {
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			middleAddedSequence[j] = *m_graph->getNode((*inputIndices)[i]);
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			middleAddedSequence[j + 1] =
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				(*m_graph->getNode((*inputIndices)[i]) +
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				 *m_graph->getNode((*inputIndices)[i + 1])) *
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				0.5;
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		}
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		middleAddedSequence[j] = *m_graph->getNode((*inputIndices)[n - 2]);
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		middleAddedSequence[j + 1] = *m_graph->getNode((*inputIndices)[n - 1]);
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	}
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}
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//--------------------------------------------------------------------------
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TStroke *SequenceConverter::operator()(std::vector<unsigned int=""> *indices)</unsigned>
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{
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	//Prepare Sequence
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	inputIndices = indices;
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	addMiddlePoints();
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	//Initialize local variables
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	unsigned int n = (middleAddedSequence.size() + 1) / 2; //Number of middle points
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	//unsigned int i, j;
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	unsigned int i;
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	int j;
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	Length L_att, L_min, l_min, l_ji;
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	unsigned int p_i, a, b;
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	std::vector<length> M(n);</length>
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	std::vector<length> K(n);</length>
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	std::vector<unsigned int=""> P(n);</unsigned>
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	//Bellman algorithm
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	for (i = 2, a = 1; i < middleAddedSequence.size(); i += 2, ++a) {
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		L_min.infty();
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		l_min.infty();
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		p_i = 0;
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		//for(j=0, b=0; j
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		for (j = i - 2, b = j / 2; j >= 0; j -= 2, --b) {
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			if ((L_att = M[b] + (l_ji = lengthOf(j, i))) < L_min) {
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				L_min = L_att;
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				p_i = b;
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				l_min = l_ji;
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			}
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			//NOTE: The following else may be taken out to perform a deeper
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			//search for optimal result. However, it prevents quadratic complexities
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			//on large-scale images.
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			else if (l_ji.n == infinity)
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				break; //Stops searching for current i
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		}
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		M[a] = L_min;
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		K[a] = l_min;
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		P[a] = p_i;
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Read off the output
Toshihiro Shimizu 890ddd
	std::vector<tthickpoint> controlPoints(2 * M[n - 1].n + 1);</tthickpoint>
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	for (b = n - 1, a = 2 * M[n - 1].n; b > 0; b = P[b]) {
Toshihiro Shimizu 890ddd
		for (i = K[b].CPs.size() - 1; i > 0; --i, --a)
Toshihiro Shimizu 890ddd
			controlPoints[a] = K[b].CPs[i];
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
	controlPoints[0] = middleAddedSequence[0];
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	TStroke *res = new TStroke(controlPoints);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	return res;
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------
Toshihiro Shimizu 890ddd
//      Conversion Length build-up
Toshihiro Shimizu 890ddd
//--------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
SequenceConverter::Length SequenceConverter::lengthOf(unsigned int a, unsigned int b)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	Length l;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//If we have a triplet, apply a specific procedure
Toshihiro Shimizu 890ddd
	if (b == a + 2) {
Toshihiro Shimizu 890ddd
		lengthOfTriplet(a, l);
Toshihiro Shimizu 890ddd
		return l;
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
	//otherwise
Toshihiro Shimizu 890ddd
	if (!parametrize(a, b) || !calculateCPs(a, b, l) || !penalty(a, b, l))
Toshihiro Shimizu 890ddd
		l.infty();
Toshihiro Shimizu 890ddd
	return l;
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
void SequenceConverter::lengthOfTriplet(unsigned int i, Length &len)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	T3DPointD A = middleAddedSequence[i];
Toshihiro Shimizu 890ddd
	T3DPointD B = middleAddedSequence[i + 1];
Toshihiro Shimizu 890ddd
	T3DPointD C = middleAddedSequence[i + 2];
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//We assume that this convertion is faithful, avoiding length penalty
Toshihiro Shimizu 890ddd
	len.l = 0;
Toshihiro Shimizu 890ddd
	double d = tdistance(B, C - A, A);
Toshihiro Shimizu 890ddd
	if (d <= 2) {
Toshihiro Shimizu 890ddd
		len.n = 1;
Toshihiro Shimizu 890ddd
		len.set_CPs(A, B, C);
Toshihiro Shimizu 890ddd
	} else if (d <= 6) {
Toshihiro Shimizu 890ddd
		len.n = 2;
Toshihiro Shimizu 890ddd
		d = (d - 1) / d;
Toshihiro Shimizu 890ddd
		T3DPointD U = A + d * (B - A), V = C + d * (B - C);
Toshihiro Shimizu 890ddd
		len.set_CPs(A, U, (U + V) * 0.5, V, C);
Toshihiro Shimizu 890ddd
	} else {
Toshihiro Shimizu 890ddd
		len.n = 2;
Toshihiro Shimizu 890ddd
		len.set_CPs(A, (A + B) * 0.5, B, (B + C) * 0.5, C);
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
bool SequenceConverter::parametrize(unsigned int a, unsigned int b)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	unsigned int curr, old;
Toshihiro Shimizu 890ddd
	unsigned int i;
Toshihiro Shimizu 890ddd
	double w, t;
Toshihiro Shimizu 890ddd
	double den;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	pars.clear();
Toshihiro Shimizu 890ddd
	pars.push_back(0);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	for (old = a, curr = a + 1, den = 0; curr < b; old = curr, curr += 2) {
Toshihiro Shimizu 890ddd
		w = norm(middleAddedSequence[curr] - middleAddedSequence[old]);
Toshihiro Shimizu 890ddd
		den += w;
Toshihiro Shimizu 890ddd
		pars.push_back(w);
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
	w = norm(middleAddedSequence[b] - middleAddedSequence[old]);
Toshihiro Shimizu 890ddd
	den += w;
Toshihiro Shimizu 890ddd
	pars.push_back(w);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	if (den < 0.1)
Toshihiro Shimizu 890ddd
		return 0;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	for (i = 1, t = 0; i < pars.size(); ++i) {
Toshihiro Shimizu 890ddd
		t += 2 * pars[i] / den;
Toshihiro Shimizu 890ddd
		pars[i] = t;
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Seek the interval which holds 1 - the middle interval
Toshihiro Shimizu 890ddd
	for (middle = 0; middle < pars.size() && pars[middle + 1] <= 1; ++middle)
Toshihiro Shimizu 890ddd
		;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	return 1;
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//==========================================================================
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//------------------------
Toshihiro Shimizu 890ddd
//    CP construcion
Toshihiro Shimizu 890ddd
//------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//NOTE: Check my thesis for variable meanings (int_ stands for 'integral').
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//Some integrals (int_) for the CP linear system resolution
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
inline T3DPointD int_H(const T3DPointD &A, const T3DPointD &B, double t1, double t2)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	return -(0.375 * (pow(t2, 4) - pow(t1, 4))) * B + (pow(t2, 3) - pow(t1, 3)) * (B * 0.6667 - A * 0.5) + (pow(t2, 2) - pow(t1, 2)) * A;
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
inline T3DPointD int_K(const T3DPointD &A, const T3DPointD &B, double t1, double t2)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	return (pow(t2, 4) - pow(t1, 4)) * (B * 0.125) + (pow(t2, 3) - pow(t1, 3)) * (A * 0.1667);
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
bool SequenceConverter::calculateCPs(unsigned int i, unsigned int j, Length &len)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	unsigned int curr, old;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	TAffine M;
Toshihiro Shimizu 890ddd
	TPointD l;
Toshihiro Shimizu 890ddd
	T3DPointD a, e, x, y, A, B;
Toshihiro Shimizu 890ddd
	T3DPointD IH, IK, IM, IN_; //"IN" seems to be reserved word
Toshihiro Shimizu 890ddd
	double HxL, KyL, MxO, NyO;
Toshihiro Shimizu 890ddd
	unsigned int k;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	a = middleAddedSequence[i];
Toshihiro Shimizu 890ddd
	e = middleAddedSequence[j];
Toshihiro Shimizu 890ddd
	x = middleAddedSequence[i + 1] - a;
Toshihiro Shimizu 890ddd
	y = middleAddedSequence[j - 1] - e;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Build TAffine M
Toshihiro Shimizu 890ddd
	double par = ellProd(x, y) / 5;
Toshihiro Shimizu 890ddd
	M = TAffine(ellProd(x, x) / 3, par, 0, par, ellProd(y, y) / 3, 0);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Costruisco il termine noto b:
Toshihiro Shimizu 890ddd
	//Calculate polygonal integrals
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Integral from 0.0 to 1.0
Toshihiro Shimizu 890ddd
	for (k = 0, old = i, curr = i + 1; k < middle; ++k, old = curr, curr += 2) {
Toshihiro Shimizu 890ddd
		B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k + 1] - pars[k]));
Toshihiro Shimizu 890ddd
		A = middleAddedSequence[old] - pars[k] * B;
Toshihiro Shimizu 890ddd
		IH += int_H(A, B, pars[k], pars[k + 1]);
Toshihiro Shimizu 890ddd
		IK += int_K(A, B, pars[k], pars[k + 1]);
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	if (curr == j + 1)
Toshihiro Shimizu 890ddd
		curr = j;
Toshihiro Shimizu 890ddd
	B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k + 1] - pars[k]));
Toshihiro Shimizu 890ddd
	A = middleAddedSequence[old] - pars[k] * B;
Toshihiro Shimizu 890ddd
	IH += int_H(A, B, pars[k], 1.0);
Toshihiro Shimizu 890ddd
	IK += int_K(A, B, pars[k], 1.0);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Integral from 1.0 to 2.0
Toshihiro Shimizu 890ddd
	for (k = pars.size() - 1, old = j, curr = j - 1; k > middle + 1; --k, old = curr, curr -= 2) {
Toshihiro Shimizu 890ddd
		B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k] - pars[k - 1]));
Toshihiro Shimizu 890ddd
		A = middleAddedSequence[curr] - (2 - pars[k - 1]) * B;
Toshihiro Shimizu 890ddd
		IM += int_K(A, B, 2 - pars[k], 2 - pars[k - 1]);
Toshihiro Shimizu 890ddd
		IN_ += int_H(A, B, 2 - pars[k], 2 - pars[k - 1]);
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	if (old == i + 1)
Toshihiro Shimizu 890ddd
		curr = i;
Toshihiro Shimizu 890ddd
	B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k] - pars[k - 1]));
Toshihiro Shimizu 890ddd
	A = middleAddedSequence[curr] - (2 - pars[k - 1]) * B;
Toshihiro Shimizu 890ddd
	IM += int_K(A, B, 2 - pars[k], 1.0);
Toshihiro Shimizu 890ddd
	IN_ += int_H(A, B, 2 - pars[k], 1.0);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Polygonal-free integrals
Toshihiro Shimizu 890ddd
	T3DPointD f = (a + e) * 0.5;
Toshihiro Shimizu 890ddd
	HxL = (ellProd(a, x) * 0.3) + (ellProd(f, x) / 5.0);
Toshihiro Shimizu 890ddd
	NyO = (ellProd(e, y) * 0.3) + (ellProd(f, y) / 5.0);
Toshihiro Shimizu 890ddd
	KyL = (ellProd(a, y) / 15.0) + (ellProd(f, y) / 10.0);
Toshihiro Shimizu 890ddd
	MxO = ((e * x) / 15.0) + (ellProd(f, x) / 10.0);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Infine, ho il termine noto
Toshihiro Shimizu 890ddd
	l = TPointD(ellProd(IH, x) - HxL + ellProd(IM, x) - MxO,
Toshihiro Shimizu 890ddd
				ellProd(IK, y) - KyL + ellProd(IN_, y) - NyO);
Toshihiro Shimizu 890ddd
	M.a13 = -l.x;
Toshihiro Shimizu 890ddd
	M.a23 = -l.y;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Check validity conditions:
Toshihiro Shimizu 890ddd
	//  a) System is not singular
Toshihiro Shimizu 890ddd
	if (fabs(M.det()) < 0.01)
Toshihiro Shimizu 890ddd
		return 0;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	M = M.inv();
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//  b) Shift (solution) is positive
Toshihiro Shimizu 890ddd
	if (M.a13 < 0 || M.a23 < 0)
Toshihiro Shimizu 890ddd
		return 0;
Toshihiro Shimizu 890ddd
	T3DPointD b = a + M.a13 * x;
Toshihiro Shimizu 890ddd
	T3DPointD d = e + M.a23 * y;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//  c) The height of every CP must be >=0
Toshihiro Shimizu 890ddd
	if (b.z < 0 || d.z < 0)
Toshihiro Shimizu 890ddd
		return 0;
Toshihiro Shimizu 890ddd
	len.set_CPs(a, b, (b + d) * 0.5, d, e);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	return 1;
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//==========================================================================
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//------------------------
Toshihiro Shimizu 890ddd
//      Penalties
Toshihiro Shimizu 890ddd
//------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
inline T3DPointD int_B0a(const T3DPointD &A, const T3DPointD &B, double t1, double t2)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	return (0.25 * (pow(t2, 4) - pow(t1, 4))) * B + ((pow(t2, 3) - pow(t1, 3)) / 3.0) * (A - 2.0 * B) + (0.5 * (pow(t2, 2) - pow(t1, 2))) * (B - 2.0 * A) + (t2 - t1) * A;
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
inline T3DPointD int_B1a(const T3DPointD &A, const T3DPointD &B, double t1, double t2)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	return -(0.5 * (pow(t2, 4) - pow(t1, 4))) * B + (2.0 * ((pow(t2, 3) - pow(t1, 3)) / 3.0) * (B - A) + (pow(t2, 2) - pow(t1, 2)) * A);
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
inline T3DPointD int_B2a(const T3DPointD &A, const T3DPointD &B, double t1, double t2)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	return (0.25 * (pow(t2, 4) - pow(t1, 4))) * B + ((pow(t2, 3) - pow(t1, 3)) / 3.0) * A;
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
inline double int_a2(const T3DPointD &A, const T3DPointD &B, double t1, double t2)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
	return ellProd(A, A) * (t2 - t1) + ellProd(A, B) * (pow(t2, 2) - pow(t1, 2)) + (ellProd(B, B) * (pow(t2, 3) - pow(t1, 3)) / 3.0);
Toshihiro Shimizu 890ddd
}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
//Penalty is the integral of the square norm of differences between polygonal and quadratics.
Toshihiro Shimizu 890ddd
bool SequenceConverter::penalty(unsigned int a, unsigned int b, Length &len)
Toshihiro Shimizu 890ddd
{
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	unsigned int curr, old;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	const std::vector<t3dpointd> &CPs = len.CPs;</t3dpointd>
Toshihiro Shimizu 890ddd
	T3DPointD A, B, P0, P1, P2;
Toshihiro Shimizu 890ddd
	double p, p_max;
Toshihiro Shimizu 890ddd
	unsigned int k;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	len.n = 2; //A couple of arcs
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Prepare max penalty p_max
Toshihiro Shimizu 890ddd
	p_max = 0;
Toshihiro Shimizu 890ddd
	for (curr = a + 1, old = a, k = 0; curr < b; ++k, old = curr, curr += 2) {
Toshihiro Shimizu 890ddd
		p_max += (middleAddedSequence[curr].z + middleAddedSequence[old].z) * (pars[k + 1] - pars[k]) / 2;
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
	p_max += (middleAddedSequence[b].z + middleAddedSequence[old].z) * (pars[k + 1] - pars[k]) / 2;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Confronting 4th power of error with mean polygonal thickness
Toshihiro Shimizu 890ddd
	// - can be changed
Toshihiro Shimizu 890ddd
	p_max = tmin(sqrt(p_max) * m_penalty, Quad_eps_max);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//CP only integral
Toshihiro Shimizu 890ddd
	p = (ellProd(CPs[0], CPs[0]) + 2 * ellProd(CPs[2], CPs[2]) + ellProd(CPs[4], CPs[4]) +
Toshihiro Shimizu 890ddd
		 ellProd(CPs[0], CPs[1]) + ellProd(CPs[1], CPs[2]) +
Toshihiro Shimizu 890ddd
		 ellProd(CPs[2], CPs[3]) + ellProd(CPs[3], CPs[4])) /
Toshihiro Shimizu 890ddd
			5.0 +
Toshihiro Shimizu 890ddd
		(2 * (ellProd(CPs[1], CPs[1]) + ellProd(CPs[3], CPs[3])) +
Toshihiro Shimizu 890ddd
		 ellProd(CPs[0], CPs[2]) + ellProd(CPs[2], CPs[4])) /
Toshihiro Shimizu 890ddd
			15.0;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Penalty from 0.0 to 1.0
Toshihiro Shimizu 890ddd
	P0 = P1 = P2 = T3DPointD();
Toshihiro Shimizu 890ddd
	for (k = 0, old = a, curr = a + 1; k < middle; ++k, old = curr, curr += 2) {
Toshihiro Shimizu 890ddd
		B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k + 1] - pars[k]));
Toshihiro Shimizu 890ddd
		A = middleAddedSequence[old] - pars[k] * B;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
		//Mixed integral
Toshihiro Shimizu 890ddd
		P0 += int_B0a(A, B, pars[k], pars[k + 1]);
Toshihiro Shimizu 890ddd
		P1 += int_B1a(A, B, pars[k], pars[k + 1]);
Toshihiro Shimizu 890ddd
		P2 += int_B2a(A, B, pars[k], pars[k + 1]);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
		//Sequence integral
Toshihiro Shimizu 890ddd
		p += int_a2(A, B, pars[k], pars[k + 1]);
Toshihiro Shimizu 890ddd
	}
Toshihiro Shimizu 890ddd
	if (curr == b + 1)
Toshihiro Shimizu 890ddd
		curr = b;
Toshihiro Shimizu 890ddd
	B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k + 1] - pars[k]));
Toshihiro Shimizu 890ddd
	A = middleAddedSequence[old] - pars[k] * B;
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Mixed integral
Toshihiro Shimizu 890ddd
	P0 += int_B0a(A, B, pars[k], 1.0);
Toshihiro Shimizu 890ddd
	P1 += int_B1a(A, B, pars[k], 1.0);
Toshihiro Shimizu 890ddd
	P2 += int_B2a(A, B, pars[k], 1.0);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Sequence integral
Toshihiro Shimizu 890ddd
	p += int_a2(A, B, pars[k], 1.0);
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	p -= 2 * (ellProd(P0, CPs[0]) + ellProd(P1, CPs[1]) + ellProd(P2, CPs[2]));
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Penalty from 1.0 to 2.0
Toshihiro Shimizu 890ddd
	P0 = P1 = P2 = T3DPointD();
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	for (k = pars.size() - 1, old = b, curr = b - 1; k > middle + 1; --k, old = curr, curr -= 2) {
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		B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k] - pars[k - 1]));
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		A = middleAddedSequence[curr] - (2 - pars[k - 1]) * B;
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		//Mixed integral
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		P0 += int_B0a(A, B, 2 - pars[k], 2 - pars[k - 1]);
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		P1 += int_B1a(A, B, 2 - pars[k], 2 - pars[k - 1]);
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		P2 += int_B2a(A, B, 2 - pars[k], 2 - pars[k - 1]);
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		//Sequence integral
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		p += int_a2(A, B, 2 - pars[k], 2 - pars[k - 1]);
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	}
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	if (old == a + 1)
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		curr = a;
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	B = (middleAddedSequence[curr] - middleAddedSequence[old]) * (1 / (pars[k] - pars[k - 1]));
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	A = middleAddedSequence[curr] - (2 - pars[k - 1]) * B;
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	//Mixed integral
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	P0 += int_B0a(A, B, 2 - pars[k], 1.0);
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	P1 += int_B1a(A, B, 2 - pars[k], 1.0);
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	P2 += int_B2a(A, B, 2 - pars[k], 1.0);
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	//Sequence integral
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	p += int_a2(A, B, 2 - pars[k], 1.0);
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	p -= 2 * (ellProd(P0, CPs[4]) + ellProd(P1, CPs[3]) + ellProd(P2, CPs[2]));
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	//OCCHIO! Ho visto ancora qualche p<0! Da rivedere - non dovrebbe...
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	if (p > p_max || p < 0)
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		return 0;
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	else
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		len.l = p;
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	return 1;
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}
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//--------------------------------------------------------------------------
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Toshihiro Shimizu 890ddd
//-----------------------------
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//      Convertion Mains
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//-----------------------------
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inline TStroke *convert(const Sequence &s, double penalty)
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{
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	SkeletonGraph *graph = s.m_graphHolder;
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	TStroke *result;
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	//First, we simplify the skeleton sequences found
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	std::vector<unsigned int=""> reducedIndices;</unsigned>
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	//NOTE: If s is circular, we have to protect head==tail 's adjacent nodes.
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	//We then move away s tail and head, and insert them in the reducedIndices
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	//apart from simplification.
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	if (s.m_head == s.m_tail && graph->getNode(s.m_head).degree() == 2) {
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		Sequence t = s;
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		SequenceSimplifier simplifier(&t);
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		reducedIndices.push_back(s.m_head);
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		t.m_head = graph->getNode(s.m_head).getLink(0).getNext();
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		t.m_headLink = !graph->getNode(t.m_head).linkOfNode(s.m_head);
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		t.m_tail = graph->getNode(s.m_tail).getLink(1).getNext();
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		t.m_tailLink = !graph->getNode(t.m_tail).linkOfNode(s.m_tail);
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		simplifier.simplify(reducedIndices);
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		reducedIndices.push_back(s.m_tail);
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	} else {
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		SequenceSimplifier simplifier(&s);
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		simplifier.simplify(reducedIndices);
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	}
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	//For segments, apply this immediate conversion
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	if (reducedIndices.size() == 2) {
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		std::vector<tthickpoint> segment(3);</tthickpoint>
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		segment[0] = *graph->getNode(s.m_head);
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		segment[1] = (*graph->getNode(s.m_head) +
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					  *graph->getNode(s.m_tail)) *
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					 0.5;
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		segment[2] = *graph->getNode(s.m_tail);
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		return new TStroke(segment);
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	}
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	//Then, we convert the sequence in a quadratic stroke
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	SequenceConverter converter(&s, penalty);
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	result = converter(&reducedIndices);
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	//If it is a circular stroke, setSelfLoop
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	//NOTA: Sembra che pero' in questo modo non venga assegnato colore al confine con la cornice!!!
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	//        => Solo nel caso outline...?
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	//NOTA: Considera anche che pure le outline possono essere splittate per la colorazione!!
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	//if(globals->currConfig->m_maxThickness == 0.0 && s.m_head == s.m_tail && s.m_graphHolder->getNode(s.m_head).degree() == 2) //globals->currConfig->m_outline
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	//  result->setSelfLoop(true);
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	//Pass the SkeletonArc::SS_OUTLINE attribute to the output stroke
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	if (graph->getNode(s.m_head).getLink(s.m_headLink)->hasAttribute(SkeletonArc::SS_OUTLINE))
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		result->setFlag(SkeletonArc::SS_OUTLINE, true);
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	else if (graph->getNode(s.m_head).getLink(s.m_headLink)->hasAttribute(SkeletonArc::SS_OUTLINE_REVERSED))
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		result->setFlag(SkeletonArc::SS_OUTLINE_REVERSED, true);
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	return result;
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}
Toshihiro Shimizu 890ddd
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//--------------------------------------------------------------------------
Toshihiro Shimizu 890ddd
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//Converts each forward or single Sequence of the image in its corresponding
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//TStroke. Output is a vector<tstroke*>* whose ownership belongs to the user.</tstroke*>
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//This allow sorts on the TStroke vector *before* adding any stroke to the
Toshihiro Shimizu 890ddd
//output TVectorImage.
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//std::vector<tstroke*>* conversionToStrokes(void)</tstroke*>
Toshihiro Shimizu 890ddd
void conversionToStrokes(std::vector<tstroke *=""> &strokes, VectorizerCoreGlobals &g)</tstroke>
Toshihiro Shimizu 890ddd
{
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	SequenceList &singleSequences = g.singleSequences;
Toshihiro Shimizu 890ddd
	JointSequenceGraphList &organizedGraphs = g.organizedGraphs;
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	double penalty = g.currConfig->m_penalty;
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	unsigned int i, j, k;
Toshihiro Shimizu 890ddd
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	//Convert single sequences
Toshihiro Shimizu 890ddd
	for (i = 0; i < singleSequences.size(); ++i) {
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		if (singleSequences[i].m_head == singleSequences[i].m_tail) {
Toshihiro Shimizu 890ddd
			//If the sequence is circular, move your endpoints to an edge middle, in order
Toshihiro Shimizu 890ddd
			//to allow a soft junction
Toshihiro Shimizu 890ddd
			SkeletonGraph *currGraph = singleSequences[i].m_graphHolder;
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			unsigned int head = singleSequences[i].m_head;
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			unsigned int headLink = singleSequences[i].m_headLink;
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			unsigned int next = currGraph->getNode(head).getLink(headLink).getNext();
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			unsigned int nextLink = currGraph->getNode(next).linkOfNode(head);
Toshihiro Shimizu 890ddd
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			unsigned int addedNode =
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				singleSequences[i].m_graphHolder->newNode((*currGraph->getNode(head) + *currGraph->getNode(next)) * 0.5);
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			singleSequences[i].m_graphHolder->insert(addedNode, head, headLink);
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			*singleSequences[i].m_graphHolder->node(addedNode).link(0) =
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				*singleSequences[i].m_graphHolder->node(head).link(headLink);
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			singleSequences[i].m_graphHolder->insert(addedNode, next, nextLink);
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			*singleSequences[i].m_graphHolder->node(addedNode).link(1) =
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				*singleSequences[i].m_graphHolder->node(next).link(nextLink);
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			singleSequences[i].m_head = addedNode;
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			singleSequences[i].m_headLink = 0;
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			singleSequences[i].m_tail = addedNode;
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			singleSequences[i].m_tailLink = 1;
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		}
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		strokes.push_back(convert(singleSequences[i], penalty));
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	}
Toshihiro Shimizu 890ddd
Toshihiro Shimizu 890ddd
	//Convert graph sequences
Toshihiro Shimizu 890ddd
	for (i = 0; i < organizedGraphs.size(); ++i)
Toshihiro Shimizu 890ddd
		for (j = 0; j < organizedGraphs[i].getNodesCount(); ++j)
Toshihiro Shimizu 890ddd
			if (!organizedGraphs[i].getNode(j).hasAttribute(JointSequenceGraph::ELIMINATED))
Toshihiro Shimizu 890ddd
				//Otherwise eliminated by junction recovery
Toshihiro Shimizu 890ddd
				for (k = 0; k < organizedGraphs[i].getNode(j).getLinksCount(); ++k) {
Toshihiro Shimizu 890ddd
					//A sequence is taken at both extremities in our organized graphs
Toshihiro Shimizu 890ddd
					if (organizedGraphs[i].getNode(j).getLink(k)->isForward())
Toshihiro Shimizu 890ddd
						strokes.push_back(convert(*organizedGraphs[i].getNode(j).getLink(k), penalty));
Toshihiro Shimizu 890ddd
				}
Toshihiro Shimizu 890ddd
}