Dario Sassi
0dd8afedf9
- correzioni nell'intersezione di archi tangenti o quasi - pulizia uso distanze e relative costanti minime.
976 lines
36 KiB
C++
976 lines
36 KiB
C++
//----------------------------------------------------------------------------
|
||
// EgalTech 2014-2014
|
||
//----------------------------------------------------------------------------
|
||
// File : Triangulate.cpp Data : 23.06.14 Versione : 1.5f6
|
||
// Contenuto : Implementazione della classe Triangulate.
|
||
//
|
||
//
|
||
//
|
||
// Modifiche : 08.04.14 DS Creazione modulo.
|
||
// 23.06.14 DS Corretto errore con contorni CW.
|
||
//
|
||
//----------------------------------------------------------------------------
|
||
|
||
//--------------------------- Include ----------------------------------------
|
||
#include "stdafx.h"
|
||
#include "DllMain.h"
|
||
#include "Triangulate.h"
|
||
#include "ProjPlane.h"
|
||
#include "/EgtDev/Include/EGkPolyLine.h"
|
||
#include "/EgtDev/Include/EGkPlane3d.h"
|
||
#include "/EgtDev/Include/EGkStringUtils3d.h"
|
||
#include <algorithm>
|
||
|
||
using namespace std ;
|
||
|
||
//----------------------------------------------------------------------------
|
||
static enum EarStatus{ EAS_NULL = -1, EAS_NO = 0, EAS_OK = 1} ;
|
||
|
||
//----------------------------------------------------------------------------
|
||
static bool ChangeStartPntVector( int nNewStart, PNTVECTOR& vPi) ;
|
||
|
||
//----------------------------------------------------------------------------
|
||
// In : PolyLine
|
||
// Out : PNTVECTOR (Point3d Vector) : points of the polyline
|
||
// INTVECTOR (int Vector) : 3*T indices of above points for T triangles
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::Make( const PolyLine& PL, PNTVECTOR& vPt, INTVECTOR& vTr)
|
||
{
|
||
// verifico che la polilinea sia chiusa e piana e calcolo il piano medio del poligono
|
||
double dArea ;
|
||
Plane3d plPlane ;
|
||
if ( ! PL.IsClosedAndFlat( plPlane, dArea, 50 * EPS_SMALL))
|
||
return false ;
|
||
// determino il piano ottimale di proiezione e il relativo senso di rotazione
|
||
bool bCCW ;
|
||
if ( ! CalcProjPlane( plPlane.vtN, m_nPlane, bCCW))
|
||
return false ;
|
||
// riempio il vettore con i vertici del poligono da triangolare
|
||
vPt.clear() ;
|
||
vPt.reserve( PL.GetPointNbr() - 1) ;
|
||
// salto il primo punto (coincide con l'ultimo)
|
||
Point3d ptP ;
|
||
if ( ! PL.GetFirstPoint( ptP))
|
||
return false ;
|
||
// inserisco i punti
|
||
while ( PL.GetNextPoint( ptP))
|
||
vPt.push_back( ptP) ;
|
||
// se non CCW inverto il vettore dei punti
|
||
if ( ! bCCW)
|
||
reverse( vPt.begin(), vPt.end()) ;
|
||
// creo il vettore degli indici del Poligono
|
||
INTVECTOR vPol ;
|
||
int n = int( vPt.size()) ;
|
||
vPol.reserve( n) ;
|
||
for ( int i = 0 ; i < n ; ++ i)
|
||
vPol.push_back( i) ;
|
||
|
||
// eseguo la triangolazione
|
||
if ( ! MakeByEC2( vPt, vPol, vTr)) {
|
||
LOG_ERROR( GetEGkLogger(), "Error in MakeByEC2(1)")
|
||
return false ;
|
||
}
|
||
|
||
// se era CW, devo invertire il senso dei triangoli
|
||
if ( ! bCCW)
|
||
reverse( vTr.begin(), vTr.end()) ;
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// In : POLYLINEVECTOR : vector of polylines, the first outer, the others inner
|
||
// Out : PNTVECTOR (Point3d Vector) : points of the polyline
|
||
// INTVECTOR (int Vector) : 3*T indices of above points for T triangles
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::Make( const POLYLINEVECTOR& vPL, PNTVECTOR& vPt, INTVECTOR& vTr)
|
||
{
|
||
// pulisco i vettori di ritorno
|
||
vPt.clear() ;
|
||
vTr.clear() ;
|
||
// ci devono essere delle polilinee nel vettore
|
||
if ( &vPL == nullptr || vPL.empty())
|
||
return false ;
|
||
// se una sola polilinea mi riconduco al caso precedente
|
||
if ( vPL.size() == 1)
|
||
return Make( vPL[0], vPt, vTr) ;
|
||
// verifico che la polilinea esterna sia chiusa e piana e calcolo il piano medio del poligono
|
||
double dArea ;
|
||
Plane3d plExtPlane ;
|
||
if ( ! vPL[0].IsClosedAndFlat( plExtPlane, dArea, 50 * EPS_SMALL))
|
||
return false ;
|
||
// determino il piano ottimale di proiezione e il relativo senso di rotazione
|
||
bool bCCW ;
|
||
if ( ! CalcProjPlane( plExtPlane.vtN, m_nPlane, bCCW))
|
||
return false ;
|
||
// verifico le altre polilinee
|
||
for ( int i = 1 ; i < int( vPL.size()) ; ++i) {
|
||
// deve essere chiusa, giacere nello stesso piano ed essere orientata al contrario della esterna
|
||
double dArea ;
|
||
Plane3d plPlane ;
|
||
if ( ! vPL[i].IsClosedAndFlat( plPlane, dArea, 50 * EPS_SMALL) ||
|
||
! AreOppositeVectorApprox( plExtPlane.vtN, plPlane.vtN))
|
||
return false ;
|
||
}
|
||
// se non CCW inverto tutte le polilinee
|
||
if ( ! bCCW) {
|
||
for ( int i = 0 ; i < int( vPL.size()) ; ++i)
|
||
const_cast<PolyLine&>(vPL[i]).Invert( true) ;
|
||
}
|
||
// calcolo ordine decrescente su Xmax o Ymax o Zmax secondo m_nPlane per le curve interne
|
||
INTVECTOR vOrd ;
|
||
if ( ! SortInternalLoops( vPL, vOrd))
|
||
return false ;
|
||
// riempio il vettore con i punti dei poligoni da triangolare
|
||
// calcolo spazio totale e spazio massimo per un percorso interno
|
||
int nTot = vPL[0].GetPointNbr() - 1 ;
|
||
int nMax = 0 ;
|
||
for ( int i = 1 ; i < int( vPL.size()) ; ++i) {
|
||
nTot += vPL[i].GetPointNbr() + 1 ;
|
||
if ( vPL[i].GetPointNbr() > nMax)
|
||
nMax = vPL[i].GetPointNbr() ;
|
||
}
|
||
// riservo spazio pari al totale dei punti (anche quelli ripetuti di chiusura che servono per i link)
|
||
vPt.reserve( nTot) ;
|
||
// inserisco i punti del contorno esterno (tranne il primo che coincide con l'ultimo)
|
||
if ( ! GetPntVectorFromPolyline( vPL[0], false, vPt))
|
||
return false ;
|
||
// ciclo sui percorsi interni ordinati secondo Xmax decrescente
|
||
PNTVECTOR vPi ;
|
||
vPi.reserve( nMax) ;
|
||
for ( int i = 1 ; i < int( vPL.size()) ; ++ i) {
|
||
// riordino il percorso per avere punto iniziale con Xmax
|
||
if ( ! GetPntVectorFromPolyline( vPL[vOrd[i]], true, vPi))
|
||
return false ;
|
||
// cerco un punto del percorso esterno visibile dal punto iniziale del precedente interno
|
||
int nI ;
|
||
if ( ! GetOuterPntToJoin( vPt, vPi[0], nI))
|
||
return false ;
|
||
// riordino percorso esterno per avere questo punto all'inizio
|
||
if ( ! ChangeStartPntVector( nI, vPt))
|
||
return false ;
|
||
// ripeto punto iniziale
|
||
vPt.push_back( vPt[0]) ;
|
||
// accodo percorso interno
|
||
for ( int j = 0 ; j < int( vPi.size()) ; ++j)
|
||
vPt.push_back( vPi[j]) ;
|
||
// ripeto punto iniziale di percorso interno
|
||
vPt.push_back( vPi[0]) ;
|
||
// cancello percorso interno
|
||
vPi.clear() ;
|
||
}
|
||
// ripristino l'orientamento delle polilinee originali per il caso non CCW
|
||
if ( ! bCCW) {
|
||
for ( int i = 0 ; i < int( vPL.size()) ; ++i)
|
||
const_cast<PolyLine&>(vPL[i]).Invert( true) ;
|
||
}
|
||
|
||
// creo il vettore degli indici del Poligono
|
||
INTVECTOR vPol ;
|
||
int n = int( vPt.size()) ;
|
||
vPol.reserve( n) ;
|
||
// non devo gestire separatamente CCW perchè ho già invertito i punti
|
||
for ( int i = 0 ; i < n ; ++ i)
|
||
vPol.push_back( i) ;
|
||
|
||
// eseguo la triangolazione
|
||
if ( ! MakeByEC2( vPt, vPol, vTr)) {
|
||
LOG_ERROR( GetEGkLogger(), "Error in MakeByEC2(N)")
|
||
return false ;
|
||
}
|
||
|
||
// se era CW, devo invertire il senso dei triangoli
|
||
if ( ! bCCW)
|
||
reverse( vTr.begin(), vTr.end()) ;
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::PrepareGrid( const PNTVECTOR& vPt, const INTVECTOR& vPol,
|
||
const INTVECTOR& vPrev, const INTVECTOR& vNext)
|
||
{
|
||
// points number
|
||
int n = int( vPol.size()) ;
|
||
// overall box
|
||
BBox3d b3All ;
|
||
for ( int j = 0 ; j < n ; ++ j)
|
||
b3All.Add( vPt[vPol[j]]) ;
|
||
// grid cell dimension
|
||
double dCellDim ;
|
||
b3All.GetRadius( dCellDim) ;
|
||
dCellDim *= 2 / sqrt( n) ;
|
||
// grid
|
||
if ( ! m_VertGrid.Init( 2 * n, dCellDim))
|
||
return false ;
|
||
for ( int j = 0 ; j < n ; ++ j) {
|
||
// insert only reflex vertex
|
||
if ( ! TriangleIsCCW( vPt[vPol[vPrev[j]]], vPt[vPol[j]], vPt[vPol[vNext[j]]])) {
|
||
if ( ! m_VertGrid.InsertPoint( vPt[vPol[j]], j))
|
||
return false ;
|
||
}
|
||
}
|
||
m_vVert.reserve( n / 5) ;
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Triangulate the CCW n-gon specified by the vertices vPt (Pt[n] != Pt[0])
|
||
// Ear Clipping algorithm
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::MakeByEC( const PNTVECTOR& vPt, const INTVECTOR& vPol, INTVECTOR& vTr)
|
||
{
|
||
// Clear triangle vector
|
||
vTr.clear() ;
|
||
|
||
// At least 3 points
|
||
int n = int( vPol.size()) ;
|
||
if ( n < 3)
|
||
return false ;
|
||
|
||
// Preallocate triangle vector ( #triangles = n - 2)
|
||
vTr.reserve( 3 * ( n - 2)) ;
|
||
|
||
// Set up previous and next links to effectively form a double-linked vertex list
|
||
INTVECTOR vPrev( n) ;
|
||
INTVECTOR vNext( n) ;
|
||
for ( int j = 0 ; j < n ; ++ j) {
|
||
vPrev[j] = j - 1 ;
|
||
vNext[j] = j + 1 ;
|
||
}
|
||
vPrev[0] = n - 1 ;
|
||
vNext[n-1] = 0 ;
|
||
|
||
// Start at vertex 0
|
||
int i = 0 ;
|
||
int nCount = n ;
|
||
// Keep removing vertices until just a triangle left
|
||
while ( n >= 3) {
|
||
// To avoid infinite loop
|
||
if ( nCount <= 0)
|
||
return false ;
|
||
-- nCount ;
|
||
// Test if current vertex, v[i], is an ear
|
||
bool bIsEar = TestTriangle( vPt, vPol, vPrev, vNext, i) ;
|
||
bool bSave = bIsEar ;
|
||
// Verify if triangle is null (accept to discard)
|
||
if ( ! bIsEar) {
|
||
if ( Collinear( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]))
|
||
bIsEar = true ;
|
||
}
|
||
// If current vertex v[i] is an ear, delete it and visit the previous vertex
|
||
if ( bIsEar) {
|
||
// Triangle (v[prev[i]], v[i], v[next[i]]) is an ear
|
||
if ( bSave) {
|
||
vTr.push_back( vPol[vPrev[i]]) ;
|
||
vTr.push_back( vPol[i]) ;
|
||
vTr.push_back( vPol[vNext[i]]) ;
|
||
}
|
||
// ‘Delete’ vertex v[i] by redirecting next and previous links
|
||
// of neighboring verts past it. Decrement vertex count
|
||
vNext[vPrev[i]] = vNext[i] ;
|
||
vPrev[vNext[i]] = vPrev[i] ;
|
||
n--;
|
||
// Visit the previous vertex next
|
||
i = vPrev[i] ;
|
||
// Reset Count
|
||
nCount = n ;
|
||
}
|
||
else {
|
||
// Current vertex is not an ear; visit the next vertex
|
||
i = vNext[i] ;
|
||
}
|
||
}
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Triangulate the CCW n-gon specified by the vertices vPt (Pt[n] != Pt[0])
|
||
// Ear Clipping algorithm enhanced, choose smaller diagonal
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::MakeByEC2( const PNTVECTOR& vPt, const INTVECTOR& vPol, INTVECTOR& vTr)
|
||
{
|
||
// Clear triangle vector
|
||
vTr.clear() ;
|
||
|
||
// At least 3 points
|
||
int n = int( vPol.size()) ;
|
||
if ( n < 3)
|
||
return false ;
|
||
|
||
// Preallocate triangle vector ( #triangles = n - 2)
|
||
vTr.reserve( 3 * ( n - 2)) ;
|
||
|
||
// Set up previous and next links to effectively form a double-linked vertex list
|
||
INTVECTOR vPrev( n) ;
|
||
INTVECTOR vNext( n) ;
|
||
for ( int j = 0 ; j < n ; ++ j) {
|
||
vPrev[j] = j - 1 ;
|
||
vNext[j] = j + 1 ;
|
||
}
|
||
vPrev[0] = n - 1 ;
|
||
vNext[n-1] = 0 ;
|
||
|
||
// Prepare Ear status vector
|
||
INTVECTOR vEar( n, EAS_NULL) ;
|
||
|
||
// Prepare PointGrid
|
||
if ( ! PrepareGrid( vPt, vPol, vPrev, vNext))
|
||
return false ;
|
||
|
||
// Start at vertex 0
|
||
int i = 0 ;
|
||
int nCount = n ;
|
||
// Keep removing vertices until just a triangle left
|
||
while ( n >= 3) {
|
||
// To avoid infinite loop
|
||
if ( nCount <= 0)
|
||
return false ;
|
||
-- nCount ;
|
||
// Test if current vertex, v[i], is an ear
|
||
if ( vEar[i] == EAS_NULL)
|
||
vEar[i] = ( TestTriangle( vPt, vPol, vPrev, vNext, i) ? EAS_OK : EAS_NO) ;
|
||
bool bIsEar = ( vEar[i] == EAS_OK) ;
|
||
bool bSave = bIsEar ;
|
||
if ( bIsEar) {
|
||
// Save square distance of diagonal
|
||
double dSqDist = SqDist(vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]]) ;
|
||
// Try with 3 next
|
||
int j = i ;
|
||
double dSqDist1 = INFINITO ;
|
||
for ( int h = 0 ; h < 3 ; ++ h) {
|
||
j = vNext[j] ;
|
||
if ( vEar[j] == EAS_NULL)
|
||
vEar[j] = ( TestTriangle( vPt, vPol, vPrev, vNext, j) ? EAS_OK : EAS_NO) ;
|
||
if ( vEar[j] == EAS_OK) {
|
||
dSqDist1 = SqDist( vPt[vPol[vPrev[j]]], vPt[vPol[vNext[j]]]) ;
|
||
break ;
|
||
}
|
||
}
|
||
// Try with 3 prev
|
||
int k = i ;
|
||
double dSqDist2 = INFINITO ;
|
||
for ( int h = 0 ; h < 3 ; ++ h) {
|
||
k = vPrev[k] ;
|
||
if ( vEar[k] == EAS_NULL)
|
||
vEar[k] = ( TestTriangle( vPt, vPol, vPrev, vNext, k) ? EAS_OK : EAS_NO) ;
|
||
if ( vEar[k] == EAS_OK) {
|
||
dSqDist2 = SqDist( vPt[vPol[vPrev[k]]], vPt[vPol[vNext[k]]]) ;
|
||
break ;
|
||
}
|
||
}
|
||
// Choose the better (EPS_ZERO to have a difference)
|
||
if ( dSqDist < dSqDist1 + EPS_ZERO && dSqDist < dSqDist2 + EPS_ZERO)
|
||
; // i is the better
|
||
else if ( dSqDist1 < dSqDist2 + EPS_ZERO)
|
||
i = j ;
|
||
else
|
||
i = k ;
|
||
}
|
||
// Verify if triangle is null (accept to discard)
|
||
else {
|
||
if ( Collinear( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]) &&
|
||
! SameDirection( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]))
|
||
bIsEar = true ;
|
||
}
|
||
// If current vertex v[i] is an ear, delete it and visit the previous vertex
|
||
if ( bIsEar) {
|
||
// Triangle (v[prev[i]], v[i], v[next[i]]) is an ear
|
||
if ( bSave) {
|
||
vTr.push_back( vPol[vPrev[i]]) ;
|
||
vTr.push_back( vPol[i]) ;
|
||
vTr.push_back( vPol[vNext[i]]) ;
|
||
}
|
||
// Reset earity of diagonal endpoints
|
||
vEar[vPrev[i]] = EAS_NULL ;
|
||
vEar[vNext[i]] = EAS_NULL ;
|
||
// ‘Delete’ vertex v[i] by redirecting next and previous links
|
||
// of neighboring verts past it. Decrement vertex count
|
||
vNext[vPrev[i]] = vNext[i] ;
|
||
vPrev[vNext[i]] = vPrev[i] ;
|
||
-- n ;
|
||
// Visit the previous vertex next
|
||
i = vPrev[i] ;
|
||
// Reset Count
|
||
nCount = n ;
|
||
}
|
||
else {
|
||
// Current vertex is not an ear; visit the next vertex
|
||
i = vNext[i] ;
|
||
}
|
||
}
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Triangulate the CCW n-gon specified by the vertices vPt (Pt[n] != Pt[0])
|
||
// Ear Clipping algorithm enhanced, choose smaller triangle aspect ratio
|
||
// AR = ( Lmax * Lmax) / ( 2 * Area) = SqLenMax / L1 * L2
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::MakeByEC3( const PNTVECTOR& vPt, const INTVECTOR& vPol, INTVECTOR& vTr)
|
||
{
|
||
// Clear triangle vector
|
||
vTr.clear() ;
|
||
|
||
// At least 3 points
|
||
int n = int( vPol.size()) ;
|
||
if ( n < 3)
|
||
return false ;
|
||
|
||
// Preallocate triangle vector ( #triangles = n - 2)
|
||
vTr.reserve( 3 * ( n - 2)) ;
|
||
|
||
// Set up previous and next links to effectively form a double-linked vertex list
|
||
INTVECTOR vPrev( n) ;
|
||
INTVECTOR vNext( n) ;
|
||
for ( int j = 0 ; j < n ; ++ j) {
|
||
vPrev[j] = j - 1 ;
|
||
vNext[j] = j + 1 ;
|
||
}
|
||
vPrev[0] = n - 1 ;
|
||
vNext[n-1] = 0 ;
|
||
|
||
// Prepare Ear status vector
|
||
INTVECTOR vEar( n, EAS_NULL) ;
|
||
|
||
// Prepare PointGrid
|
||
if ( ! PrepareGrid( vPt, vPol, vPrev, vNext))
|
||
return false ;
|
||
|
||
// Start at vertex 0
|
||
int i = 0 ;
|
||
int nCount = n ;
|
||
// Keep removing vertices until just a triangle left
|
||
while ( n >= 3) {
|
||
// To avoid infinite loop
|
||
if ( nCount <= 0)
|
||
return false ;
|
||
-- nCount ;
|
||
// Test if current vertex, v[i], is an ear
|
||
if ( vEar[i] == EAS_NULL)
|
||
vEar[i] = ( TestTriangle( vPt, vPol, vPrev, vNext, i) ? EAS_OK : EAS_NO) ;
|
||
bool bIsEar = ( vEar[i] == EAS_OK) ;
|
||
bool bSave = bIsEar ;
|
||
if ( bIsEar) {
|
||
// Square Length & Aspect Ratio
|
||
double dSqLen = SqDist(vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]]) ;
|
||
double dAR = CalcTriangleAspectRatio( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]) ;
|
||
// Try with all other verticis
|
||
int ii = i ;
|
||
int j = vNext[i] ;
|
||
while ( j != ii) {
|
||
// New Square Length
|
||
double dNewSqLen = SqDist(vPt[vPol[vPrev[j]]], vPt[vPol[vNext[j]]]) ;
|
||
if ( dNewSqLen < 0.99 * dSqLen) {
|
||
// New Aspect Ratio
|
||
double dNewAR = CalcTriangleAspectRatio( vPt[vPol[vPrev[j]]], vPt[vPol[j]], vPt[vPol[vNext[j]]]) ;
|
||
// if better, test if triangle ok
|
||
if ( dNewAR < 30 || dNewAR < 1.2 * dAR) {
|
||
if ( vEar[j] == EAS_NULL)
|
||
vEar[j] = ( TestTriangle( vPt, vPol, vPrev, vNext, j) ? EAS_OK : EAS_NO) ;
|
||
if ( vEar[j] == EAS_OK) {
|
||
dSqLen = dNewSqLen ;
|
||
dAR = min( dAR, dNewAR) ;
|
||
i = j ;
|
||
}
|
||
}
|
||
}
|
||
j = vNext[j] ;
|
||
}
|
||
}
|
||
// Verify if triangle is null (accept to discard)
|
||
else {
|
||
if ( Collinear( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]) &&
|
||
! SameDirection( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]))
|
||
bIsEar = true ;
|
||
}
|
||
// If current vertex v[i] is an ear, delete it and visit the previous vertex
|
||
if ( bIsEar) {
|
||
// Triangle (v[prev[i]], v[i], v[next[i]]) is an ear to save
|
||
if ( bSave) {
|
||
vTr.push_back( vPol[vPrev[i]]) ;
|
||
vTr.push_back( vPol[i]) ;
|
||
vTr.push_back( vPol[vNext[i]]) ;
|
||
}
|
||
// Reset earity of diagonal endpoints
|
||
vEar[vPrev[i]] = EAS_NULL ;
|
||
vEar[vNext[i]] = EAS_NULL ;
|
||
// ‘Delete’ vertex v[i] by redirecting next and previous links
|
||
// of neighboring verts past it. Decrement vertex count
|
||
vNext[vPrev[i]] = vNext[i] ;
|
||
vPrev[vNext[i]] = vPrev[i] ;
|
||
-- n ;
|
||
// Visit the previous vertex next
|
||
i = vPrev[i] ;
|
||
// Reset Count
|
||
nCount = n ;
|
||
}
|
||
else {
|
||
// Current vertex is not an ear; visit the next vertex
|
||
i = vNext[i] ;
|
||
}
|
||
}
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::TestTriangle( const PNTVECTOR& vPt, const INTVECTOR& vPol,
|
||
const INTVECTOR& vPrev, INTVECTOR& vNext, int i)
|
||
{
|
||
// Test if current vertex, v[i], is an ear
|
||
bool bIsEar = true ;
|
||
// An ear must be convex (here counterclockwise)
|
||
if ( TriangleIsCCW( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]])) {
|
||
// Loop over all vertices not part of the tentative ear
|
||
BBox3d b3Tria ;
|
||
b3Tria.Add( vPt[vPol[vPrev[i]]]) ;
|
||
b3Tria.Add( vPt[vPol[i]]) ;
|
||
b3Tria.Add( vPt[vPol[vNext[i]]]) ;
|
||
// espando in Z per compensare piccole approssimazioni
|
||
b3Tria.Expand( 0, 0, 10 * EPS_SMALL) ;
|
||
m_VertGrid.Find( b3Tria, m_vVert) ;
|
||
for ( int j = 0 ; j < int( m_vVert.size()) ; ++ j) {
|
||
int k = m_vVert[j] ;
|
||
if ( k == i || k == vPrev[i] || k == vNext[i] )
|
||
continue ;
|
||
// If vertex k is on a triangle vertex
|
||
if ( AreSamePoint( vPt[vPol[k]], vPt[vPol[vPrev[i]]]) ||
|
||
AreSamePoint( vPt[vPol[k]], vPt[vPol[i]]) ||
|
||
AreSamePoint( vPt[vPol[k]], vPt[vPol[vNext[i]]])) {
|
||
// Test previous segment with triangle diagonal
|
||
if ( TestIntersection( vPt[vPol[vPrev[k]]], vPt[vPol[k]], vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]])) {
|
||
bIsEar = false ;
|
||
break ;
|
||
}
|
||
// Test next segment with triangle diagonal
|
||
if ( TestIntersection( vPt[vPol[k]], vPt[vPol[vNext[k]]], vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]])) {
|
||
bIsEar = false ;
|
||
break ;
|
||
}
|
||
}
|
||
// If vertex k is inside the ear triangle, then this is not an ear
|
||
else if ( TestPointInTriangle( vPt[vPol[k]], vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]])) {
|
||
bIsEar = false ;
|
||
break ;
|
||
}
|
||
}
|
||
}
|
||
else {
|
||
// The ‘ear’ triangle is clockwise so v[i] is not an ear
|
||
bIsEar = false ;
|
||
}
|
||
|
||
return bIsEar ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Ratio between max side and opposite height
|
||
double
|
||
Triangulate::CalcTriangleAspectRatio( const Point3d& ptPa, const Point3d& ptPb, const Point3d& ptPc)
|
||
{
|
||
double dSqDistA = SquareDist( ptPa, ptPb) ;
|
||
double dSqDistB = SquareDist( ptPb, ptPc) ;
|
||
double dSqDistC = SquareDist( ptPc, ptPa) ;
|
||
double dTwoArea = fabs( TwoArea( ptPa, ptPb, ptPc)) ;
|
||
if ( dTwoArea < SQ_EPS_SMALL)
|
||
return INFINITO ;
|
||
else
|
||
return ( (std::max)( dSqDistA, (std::max)( dSqDistB, dSqDistC)) / dTwoArea) ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
double
|
||
Triangulate::SquareDist( const Point3d& ptA, const Point3d& ptB)
|
||
{
|
||
switch ( m_nPlane) {
|
||
default : // PL_XY
|
||
return (( ptB.x - ptA.x) * ( ptB.x - ptA.x) + ( ptB.y - ptA.y) * ( ptB.y - ptA.y)) ;
|
||
case PL_YZ :
|
||
return (( ptB.y - ptA.y) * ( ptB.y - ptA.y) + ( ptB.z - ptA.z) * ( ptB.z - ptA.z)) ;
|
||
case PL_ZX :
|
||
return (( ptB.z - ptA.z) * ( ptB.z - ptA.z) + ( ptB.x - ptA.x) * ( ptB.x - ptA.x)) ;
|
||
}
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Vector product is double of the area (positive if CCW)
|
||
double
|
||
Triangulate::TwoArea( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC)
|
||
{
|
||
switch ( m_nPlane) {
|
||
default : // PL_XY
|
||
return ( ptB.x - ptA.x) * ( ptC.y - ptB.y) - ( ptB.y - ptA.y) * ( ptC.x - ptB.x) ;
|
||
case PL_YZ :
|
||
return ( ptB.y - ptA.y) * ( ptC.z - ptB.z) - ( ptB.z - ptA.z) * ( ptC.y - ptB.y) ;
|
||
case PL_ZX :
|
||
return ( ptB.z - ptA.z) * ( ptC.x - ptB.x) - ( ptB.x - ptA.x) * ( ptC.z - ptB.z) ;
|
||
}
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Distance less than tolerance
|
||
bool
|
||
Triangulate::AreSamePoint( const Point3d& ptA, const Point3d& ptB, double dToler)
|
||
{
|
||
return ( SquareDist( ptA, ptB) < dToler * dToler) ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Same Direction <--> Scalar Product Positive
|
||
bool
|
||
Triangulate::SameDirection( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC)
|
||
{
|
||
switch ( m_nPlane) {
|
||
default : // PL_XY
|
||
return (( ptB.x - ptA.x) * ( ptC.x - ptB.x) + ( ptB.y - ptA.y) * ( ptC.y - ptB.y)) > 0 ;
|
||
case PL_YZ :
|
||
return (( ptB.y - ptA.y) * ( ptC.y - ptB.y) + ( ptB.z - ptA.z) * ( ptC.z - ptB.z)) > 0 ;
|
||
case PL_ZX :
|
||
return (( ptB.z - ptA.z) * ( ptC.z - ptB.z) + ( ptB.x - ptA.x) * ( ptC.x - ptB.x)) > 0 ;
|
||
}
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Collinear <--> Null Area
|
||
bool
|
||
Triangulate::Collinear( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC, double dToler)
|
||
{
|
||
return ( fabs( TwoArea( ptA, ptB, ptC)) < dToler * dToler) ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Positive Area means A -> B -> C counterclockwise
|
||
bool
|
||
Triangulate::TriangleIsCCW( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC, double dToler)
|
||
{
|
||
return ( TwoArea( ptA, ptB, ptC) > dToler * dToler) ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Proper intersection between line segments
|
||
bool
|
||
Triangulate::TestIntersection( const Point3d& ptA1, const Point3d& ptA2,
|
||
const Point3d& ptB1, const Point3d& ptB2)
|
||
{
|
||
// Collinearity is not considered intersection
|
||
if ( Collinear( ptA1, ptA2, ptB1) ||
|
||
Collinear( ptA1, ptA2, ptB2) ||
|
||
Collinear( ptB1, ptB2, ptA1) ||
|
||
Collinear( ptB1, ptB2, ptA2))
|
||
return false ;
|
||
// To intersect, the endpoints of a line segment must be on opposite side of the other line segment
|
||
return ( TriangleIsCCW( ptA1, ptA2, ptB1) != TriangleIsCCW( ptA1, ptA2, ptB2) &&
|
||
TriangleIsCCW( ptB1, ptB2, ptA1) != TriangleIsCCW( ptB1, ptB2, ptA2)) ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
// Test if point p is contained in triangle (a, b, c)
|
||
bool
|
||
Triangulate::TestPointInTriangle( const Point3d& ptP, const Point3d& ptA, const Point3d& ptB, const Point3d& ptC)
|
||
{
|
||
// If P is on a vertex is considered outside
|
||
if ( AreSamePoint( ptP, ptA))
|
||
return false ;
|
||
if ( AreSamePoint( ptP, ptB))
|
||
return false ;
|
||
if ( AreSamePoint( ptP, ptC))
|
||
return false ;
|
||
// If P is on the right of at least one edge is outside
|
||
if ( TriangleIsCCW( ptA, ptP, ptB))
|
||
return false ;
|
||
if ( TriangleIsCCW( ptB, ptP, ptC))
|
||
return false ;
|
||
if ( TriangleIsCCW( ptC, ptP, ptA))
|
||
return false ;
|
||
// P is in triangle
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::SortInternalLoops( const POLYLINEVECTOR& vPL, INTVECTOR& vOrd)
|
||
{
|
||
// riempio vettore con indice e massimo specifico per ogni loop interno
|
||
typedef std::pair<int,double> INDMAX ; // coppia indice, massimo
|
||
typedef std::vector<INDMAX> INDMAXVECTOR ; // vettore di coppie indice, massimo
|
||
INDMAXVECTOR vMax ;
|
||
vMax.reserve( vPL.size()) ;
|
||
vMax.emplace_back( 0, 0.0) ;
|
||
for ( int i = 1 ; i < int( vPL.size()) ; ++ i) {
|
||
BBox3d b3Loc ;
|
||
vPL[i].GetLocalBBox( b3Loc) ;
|
||
switch ( m_nPlane) {
|
||
default : // PL_XY
|
||
vMax.emplace_back( i, b3Loc.GetMax().x) ;
|
||
break ;
|
||
case PL_YZ :
|
||
vMax.emplace_back( i, b3Loc.GetMax().y) ;
|
||
break ;
|
||
case PL_ZX :
|
||
vMax.emplace_back( i, b3Loc.GetMax().z) ;
|
||
break ;
|
||
}
|
||
}
|
||
// ordino vettore in senso decrescente rispetto al massimo
|
||
sort( vMax.begin() + 1, vMax.end(),
|
||
[]( const INDMAX& a, const INDMAX& b) { return ( a.second > b.second) ; }) ;
|
||
// copio indice nel vettore di ordine
|
||
vOrd.reserve( vPL.size()) ;
|
||
for ( int i = 0 ; i < int( vPL.size()) ; ++ i)
|
||
vOrd.push_back( vMax[i].first) ;
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::GetPntVectorFromPolyline( const PolyLine& PL, bool bXmaxStart, PNTVECTOR& vPi)
|
||
{
|
||
// copio i punti nel vettore (tranne il primo che coincide con l'ultimo)
|
||
Point3d ptP ;
|
||
if ( ! PL.GetFirstPoint( ptP))
|
||
return false ;
|
||
while ( PL.GetNextPoint( ptP)) {
|
||
vPi.push_back( ptP) ;
|
||
}
|
||
// se non richiesto riordino per Xmax o Ymax o Zmax, ho finito
|
||
if ( ! bXmaxStart)
|
||
return true ;
|
||
// determino l'indice del punto con Xmax
|
||
int nI = - 1 ;
|
||
double dXmax = - INFINITO ;
|
||
for ( int i = 0 ; i < int( vPi.size()) ; ++ i) {
|
||
switch ( m_nPlane) {
|
||
default : // PL_XY
|
||
if ( vPi[i].x > dXmax) {
|
||
dXmax = vPi[i].x ;
|
||
nI = i ;
|
||
}
|
||
break ;
|
||
case PL_YZ :
|
||
if ( vPi[i].y > dXmax) {
|
||
dXmax = vPi[i].y ;
|
||
nI = i ;
|
||
}
|
||
break ;
|
||
case PL_ZX :
|
||
if ( vPi[i].z > dXmax) {
|
||
dXmax = vPi[i].z ;
|
||
nI = i ;
|
||
}
|
||
break ;
|
||
}
|
||
}
|
||
if ( nI == - 1)
|
||
return false ;
|
||
// riordino il vettore, per avere il punto con Xmax in prima posizione
|
||
return ChangeStartPntVector( nI, vPi) ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::GetOuterPntToJoin( const PNTVECTOR& vPt, const Point3d& ptP, int& nI)
|
||
{
|
||
// cerco prima intersezione del raggio dal punto con direzione X+ al contorno esterno
|
||
nI = - 1 ;
|
||
double dMinDist = INFINITO ;
|
||
Point3d ptInt ;
|
||
int nNumPt = int( vPt.size()) ;
|
||
for ( int i = 0 ; i < nNumPt ; ++ i) {
|
||
// indice punto precedente
|
||
int h = ( i - 1 >= 0 ) ? i - 1 : nNumPt - 1 ;
|
||
// indice punto successivo
|
||
int j = ( i + 1 < nNumPt) ? i + 1 : 0 ;
|
||
// mi metto nel piano principale
|
||
switch (m_nPlane) {
|
||
default : // PL_XY
|
||
// se i punti coincidono
|
||
if ( fabs( vPt[i].x - ptP.x) < EPS_SMALL && fabs( vPt[i].y - ptP.y) < EPS_SMALL) {
|
||
dMinDist = 0 ;
|
||
nI = i ;
|
||
ptInt = vPt[i] ;
|
||
}
|
||
// se punto esattamente sul raggio e raggio interno al settore
|
||
else if ( vPt[i].x > ptP.x && fabs( vPt[i].y - ptP.y) < EPS_SMALL &&
|
||
PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
|
||
// se distanza minore della minima, nuovo minimo
|
||
if ( ( vPt[i].x - ptP.x) < dMinDist) {
|
||
dMinDist = vPt[i].x - ptP.x ;
|
||
nI = i ;
|
||
ptInt = vPt[i] ;
|
||
}
|
||
}
|
||
// se segmento al punto successivo che attraversa il raggio e raggio interno ovvero a sinistra ( segmento crescente in Y)
|
||
else if ( vPt[i].y < ptP.y && vPt[j].y > ptP.y) {
|
||
// calcolo l'ascissa di intersezione
|
||
double dCoeff = ( ptP.y - vPt[i].y) / ( vPt[j].y - vPt[i].y) ;
|
||
double dX = vPt[i].x + ( vPt[j].x - vPt[i].x) * dCoeff ;
|
||
// se sta sul raggio e distanza minore della minima
|
||
if ( dX > ptP.x - EPS_SMALL && ( dX - ptP.x) < dMinDist) {
|
||
dMinDist = dX - ptP.x ;
|
||
nI = ( vPt[i].x >= vPt[j].x) ? i : j ;
|
||
double dZ = vPt[i].z + ( vPt[j].z - vPt[i].z) * dCoeff ;
|
||
ptInt.Set( dX, ptP.y, dZ) ;
|
||
}
|
||
}
|
||
break ;
|
||
case PL_YZ :
|
||
// se i punti coincidono
|
||
if ( fabs( vPt[i].y - ptP.y) < EPS_SMALL && fabs( vPt[i].z - ptP.z) < EPS_SMALL) {
|
||
dMinDist = 0 ;
|
||
nI = i ;
|
||
ptInt = vPt[i] ;
|
||
}
|
||
// se punto esattamente sul raggio e raggio interno al settore
|
||
else if ( vPt[i].y > ptP.y && fabs( vPt[i].z - ptP.z) < EPS_SMALL &&
|
||
PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
|
||
// se distanza minore della minima, nuovo minimo
|
||
if ( ( vPt[i].y - ptP.y) < dMinDist) {
|
||
dMinDist = vPt[i].y - ptP.y ;
|
||
nI = i ;
|
||
ptInt = vPt[i] ;
|
||
}
|
||
}
|
||
// se segmento al punto successivo che attraversa il raggio e raggio interno ovvero a sinistra ( segmento crescente in Y)
|
||
else if ( vPt[i].z < ptP.z && vPt[j].z > ptP.z) {
|
||
// calcolo l'ascissa di intersezione
|
||
double dCoeff = ( ptP.z - vPt[i].z) / ( vPt[j].z - vPt[i].z) ;
|
||
double dY = vPt[i].y + ( vPt[j].y - vPt[i].y) * dCoeff ;
|
||
// se sta sul raggio e distanza minore della minima
|
||
if ( dY > ptP.y - EPS_SMALL && ( dY - ptP.y) < dMinDist) {
|
||
dMinDist = dY - ptP.y ;
|
||
nI = ( vPt[i].y >= vPt[j].y) ? i : j ;
|
||
double dX = vPt[i].x + ( vPt[j].x - vPt[i].x) * dCoeff ;
|
||
ptInt.Set( dX, dY, ptP.z) ;
|
||
}
|
||
}
|
||
break ;
|
||
case PL_ZX :
|
||
// se i punti coincidono
|
||
if ( fabs( vPt[i].z - ptP.z) < EPS_SMALL && fabs( vPt[i].x - ptP.x) < EPS_SMALL) {
|
||
dMinDist = 0 ;
|
||
nI = i ;
|
||
ptInt = vPt[i] ;
|
||
}
|
||
// se punto esattamente sul raggio e raggio interno al settore
|
||
else if ( vPt[i].z > ptP.z && fabs( vPt[i].x - ptP.x) < EPS_SMALL &&
|
||
PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
|
||
// se distanza minore della minima, nuovo minimo
|
||
if ( ( vPt[i].z - ptP.z) < dMinDist) {
|
||
dMinDist = vPt[i].z - ptP.z ;
|
||
nI = i ;
|
||
ptInt = vPt[i] ;
|
||
}
|
||
}
|
||
// se segmento al punto successivo che attraversa il raggio e raggio interno ovvero a sinistra ( segmento crescente in Y)
|
||
else if ( vPt[i].x < ptP.x && vPt[j].x > ptP.x) {
|
||
// calcolo l'ascissa di intersezione
|
||
double dCoeff = ( ptP.x - vPt[i].x) / ( vPt[j].x - vPt[i].x) ;
|
||
double dZ = vPt[i].z + ( vPt[j].z - vPt[i].z) * dCoeff ;
|
||
// se sta sul raggio e distanza minore della minima
|
||
if ( dZ > ptP.z - EPS_SMALL && ( dZ - ptP.z) < dMinDist) {
|
||
dMinDist = dZ - ptP.z ;
|
||
nI = ( vPt[i].z >= vPt[j].z) ? i : j ;
|
||
double dY = vPt[i].y + ( vPt[j].y - vPt[i].y) * dCoeff ;
|
||
ptInt.Set( ptP.y, dY, dZ) ;
|
||
}
|
||
}
|
||
break ;
|
||
}
|
||
}
|
||
// non ho trovato alcunché, errore
|
||
if ( nI == - 1)
|
||
return false ;
|
||
// se ho trovato un punto esatto del contorno, non devo fare altri controlli
|
||
if ( AreSamePointApprox( ptInt, vPt[nI]))
|
||
return true ;
|
||
// devo ora verificare che il segmento che unisce i punti non intersechi altri lati del contorno esterno
|
||
// altrimenti tengo il punto con raggio più vicino a X_AX o Y_AX o Z_AX secondo m_nPlane
|
||
int nJ = nI ;
|
||
Point3d ptPa = ptP ;
|
||
Point3d ptPb = vPt[nI] ;
|
||
Point3d ptPc = ptInt ;
|
||
bool bSwap = false ;
|
||
switch ( m_nPlane) {
|
||
default : /* PL_XY */ bSwap = ( ptPb.y > ptPc.y) ; break ;
|
||
case PL_YZ : bSwap = ( ptPb.z > ptPc.z) ; break ;
|
||
case PL_ZX : bSwap = ( ptPb.x > ptPc.x) ; break ;
|
||
}
|
||
if ( bSwap)
|
||
swap( ptPb, ptPc) ;
|
||
double dMinTan = INFINITO ;
|
||
double dMinSqDist = INFINITO * INFINITO ;
|
||
for ( int i = 0 ; i < nNumPt ; ++ i) {
|
||
// salto il punto già trovato
|
||
if ( i == nJ)
|
||
continue ;
|
||
// verifico se sta nel triangolo
|
||
if ( TestPointInTriangle( vPt[i], ptPa, ptPb, ptPc)) {
|
||
double dTan = INFINITO ;
|
||
switch ( m_nPlane) {
|
||
default : /* PL_XY */ dTan = fabs(vPt[i].y - ptP.y) / (vPt[i].x - ptP.x) ; break ;
|
||
case PL_YZ : dTan = fabs(vPt[i].z - ptP.z) / (vPt[i].y - ptP.y) ; break ;
|
||
case PL_ZX : dTan = fabs(vPt[i].x - ptP.x) / (vPt[i].z - ptP.z) ; break ;
|
||
}
|
||
if ( dTan < dMinTan + EPS_ZERO) {
|
||
// indice punto precedente
|
||
int h = ( i - 1 >= 0) ? i - 1 : nNumPt - 1 ;
|
||
// indice punto successivo
|
||
int j = ( i + 1 < nNumPt) ? i + 1 : 0 ;
|
||
// verifico che il raggio che unisce i punti stia nel settore
|
||
if ( PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
|
||
double dSqDist = SqDist( vPt[i], ptP) ;
|
||
if ( dTan < dMinTan - EPS_ZERO || dSqDist < dMinSqDist) {
|
||
dMinTan = dTan ;
|
||
dMinSqDist = dSqDist ;
|
||
nI = i ;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
return true ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
Triangulate::PointInSector( const Point3d& ptTest, const Point3d& ptPrev, const Point3d& ptCorn, const Point3d& ptNext)
|
||
{
|
||
// la parte valida del settore è a sinistra dei segmenti ptPrev --> ptCorn --> ptNext
|
||
// se corner convesso
|
||
if ( TriangleIsCCW( ptPrev, ptCorn, ptNext, 0))
|
||
return ( TriangleIsCCW( ptPrev, ptCorn, ptTest) &&
|
||
TriangleIsCCW( ptTest, ptCorn, ptNext)) ;
|
||
// altrimenti corner concavo ( reflex)
|
||
else
|
||
return ! ( TriangleIsCCW( ptTest, ptCorn, ptPrev, 0) &&
|
||
TriangleIsCCW( ptNext, ptCorn, ptTest, 0)) ;
|
||
}
|
||
|
||
//----------------------------------------------------------------------------
|
||
bool
|
||
ChangeStartPntVector( int nNewStart, PNTVECTOR& vPi)
|
||
{
|
||
// se il nuovo inizio coincide col vecchio, non devo fare alcunché
|
||
if ( nNewStart == 0)
|
||
return true ;
|
||
// se il nuovo indice è oltre la dimensione del vettore, errore
|
||
if ( nNewStart >= int( vPi.size()))
|
||
return false ;
|
||
// ciclo di aggiustamento
|
||
rotate( vPi.begin(), vPi.begin() + nNewStart, vPi.end()) ;
|
||
return true ;
|
||
}
|