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// File: ShapeFix.cxx
// Created: Fri Jan 21 12:00:39 2000
// Author: data exchange team
// <det@nnov.matra-dtv.fr>
#include <ShapeFix.hxx>
//:k2 abv 16.12.98: eliminating code duplication
//pdn 18.12.98: checking deviation for SP edges
//: abv 22.02.99: method FillFace() removed since PRO13123 is fixed
//szv#4 S4163
//szv#9:S4244:19Aug99: Added method FixWireGaps
//szv#10:S4244:23Aug99: Added method FixFaceGaps
#include <BRep_Builder.hxx>
#include <BRep_Tool.hxx>
#include <Geom2d_Curve.hxx>
#include <Geom_Curve.hxx>
#include <Precision.hxx>
#include <Standard_ErrorHandler.hxx>
#include <Standard_Failure.hxx>
#include <TopExp_Explorer.hxx>
#include <TopLoc_Location.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Edge.hxx>
#include <TopoDS_Face.hxx>
#include <Geom_Surface.hxx>
//:i2
#include <gp_Pnt.hxx>
#include <Geom_Plane.hxx>
#include <ShapeFix_Edge.hxx>
#include <Geom2dAdaptor_HCurve.hxx>
#include <Adaptor3d_CurveOnSurface.hxx>
#include <Geom_RectangularTrimmedSurface.hxx>
#include <ShapeAnalysis_Surface.hxx>
#include <ShapeFix_Edge.hxx>
#include <ShapeFix_Shape.hxx>
#include <ShapeFix_Wire.hxx>
#include <ShapeFix_Face.hxx>
#include <TopoDS_Iterator.hxx>
#include <GeomAdaptor_HSurface.hxx>
#include <TopTools_MapOfShape.hxx>
#include <BRepLib.hxx>
#include <ShapeAnalysis_Edge.hxx>
#include <ShapeBuild_Edge.hxx>
#include <TopoDS_Vertex.hxx>
#include <ShapeBuild_ReShape.hxx>
#include <TColgp_SequenceOfPnt.hxx>
#include <TopTools_ListOfShape.hxx>
#include <TopTools_ListIteratorOfListOfShape.hxx>
#include <TopTools_SequenceOfShape.hxx>
#include <TopTools_IndexedDataMapOfShapeListOfShape.hxx>
#include <TopExp.hxx>
//=======================================================================
//function : SameParameter
//purpose :
//=======================================================================
Standard_Boolean ShapeFix::SameParameter(const TopoDS_Shape& shape,
const Standard_Boolean enforce,
const Standard_Real preci)
{
BRep_Builder B;
//Standard_Integer nbexcp = 0;
Standard_Integer nbfail = 0, numedge = 0;
Standard_Boolean status = Standard_True;
Standard_Real tol = preci;
Standard_Boolean iatol = (tol > 0);
Handle(ShapeFix_Edge) sfe = new ShapeFix_Edge;
TopExp_Explorer ex(shape,TopAbs_EDGE);
while (ex.More()) {
TopoDS_Edge E;
while (ex.More()) {
numedge ++;
int ierr = 0;
TopLoc_Location loc; //Standard_Real u0,u1; //szv#4:S4163:12Mar99 moved down unused
E = TopoDS::Edge (ex.Current());
ex.Next();
//pdn degenerated edges shuld be samerange and sameparameter.
//if (BRep_Tool::Degenerated(E)) continue; // ne vaut pas
if (!iatol) tol = BRep_Tool::Tolerance (E);
if (enforce) {
B.SameRange (E,Standard_False);
B.SameParameter (E,Standard_False);
}
//:pdn if (BRep_Tool::SameParameter(E)) continue;
// Handle(Geom_Curve) crv = BRep_Tool::Curve (E,loc,u0,u1);
// if (crv.IsNull()) BRepLib::BuildCurve3d (E,tol);
sfe->FixSameParameter (E); // et non BRepLib:: jusqu a K2-SEP97
if (!BRep_Tool::SameParameter (E)) { ierr = 1; nbfail ++; }
if (ierr) {
status = Standard_False;
B.SameRange (E,Standard_False);
B.SameParameter (E,Standard_False);
}
} // -- end while
}
//:i2 abv 21 Aug 98: ProSTEP TR8 Motor.rle face 710:
// Update tolerance of edges on planes (no pcurves are stored)
for ( TopExp_Explorer exp ( shape, TopAbs_FACE ); exp.More(); exp.Next() ) {
TopoDS_Face face = TopoDS::Face ( exp.Current() );
Handle(Geom_Surface) Surf = BRep_Tool::Surface ( face );
Handle(Geom_Plane) plane = Handle(Geom_Plane)::DownCast ( Surf );
if ( plane.IsNull() ) {
Handle(Geom_RectangularTrimmedSurface) GRTS =
Handle(Geom_RectangularTrimmedSurface)::DownCast ( Surf );
if ( ! GRTS.IsNull() )
plane = Handle(Geom_Plane)::DownCast ( GRTS->BasisSurface() );
if ( plane.IsNull() ) continue;
}
// Handle(ShapeConstruct_ProjectCurveOnSurface) Proj = new ShapeConstruct_ProjectCurveOnSurface; //:k2 abv 16 Dec 98: use existing tool //smh#14
// Handle(ShapeAnalysis_Surface) sas = new ShapeAnalysis_Surface ( plane );
// Proj->Init ( sas, Precision::Confusion() ); // projection will be analitic
Handle(GeomAdaptor_HSurface) AS = new GeomAdaptor_HSurface ( plane );
for ( TopExp_Explorer ed ( face, TopAbs_EDGE ); ed.More(); ed.Next() ) {
TopoDS_Edge edge = TopoDS::Edge ( ed.Current() );
Standard_Real f, l;
Handle(Geom_Curve) crv = BRep_Tool::Curve ( edge, f, l );
if ( crv.IsNull() ) continue;
// Handle(Geom2d_Curve) c2d;
// Proj->Perform ( crv, f, l, c2d );
Handle(Geom2d_Curve) c2d = BRep_Tool::CurveOnSurface ( edge, face, f, l );;
if ( c2d.IsNull() ) continue;
Handle(Geom2dAdaptor_HCurve) GHPC = new Geom2dAdaptor_HCurve ( c2d, f, l );
Adaptor3d_CurveOnSurface ACS(GHPC,AS);//sas->Adaptor3d());
Standard_Real tol0 = BRep_Tool::Tolerance ( edge );
tol = tol0;
Standard_Real tol2 = tol*tol;
const Standard_Integer NCONTROL = 23;
for ( Standard_Integer i=0; i < NCONTROL; i++ ) {
Standard_Real par = ( f * ( NCONTROL - 1 - i ) + l * i ) / ( NCONTROL - 1 );
gp_Pnt pnt = crv->Value ( par );
gp_Pnt prj = ACS.Value( par );
Standard_Real dist = pnt.SquareDistance(prj);
if ( tol2 < dist ) tol2 = dist;
}
tol = 1.00005 * sqrt(tol2); // coeff: see trj3_pm1-ct-203.stp #19681, edge 10
if ( tol >= tol0 ) {
B.UpdateEdge ( edge, tol );
for ( TopoDS_Iterator itV(edge); itV.More(); itV.Next() ) {
TopoDS_Shape S = itV.Value();
B.UpdateVertex ( TopoDS::Vertex ( S ), tol );
}
}
}
}
if (!status) {
#ifdef DEB
cout<<"** SameParameter not complete. On "<<numedge<<" Edges:";
if (nbfail > 0) cout<<" "<<nbfail<<" Failed";
//if (nbexcp > 0) cout<<" "<<nbexcp<<" Raised"; //SK original
cout<<endl;
#endif
}
return status;
}
//=======================================================================
//function : EncodeRegularity
//purpose :
//=======================================================================
static void EncodeRegularity (const TopoDS_Shape& shape,
const Standard_Real tolang,
TopTools_MapOfShape &aMap)
{
TopoDS_Shape S = shape;
TopLoc_Location L;
S.Location ( L );
if ( ! aMap.Add ( S ) ) return;
if ( S.ShapeType() == TopAbs_COMPOUND ||
S.ShapeType() == TopAbs_COMPSOLID ) {
for ( TopoDS_Iterator it(S); it.More(); it.Next() ) {
EncodeRegularity ( it.Value(), tolang, aMap );
}
return;
}
try {
OCC_CATCH_SIGNALS
BRepLib::EncodeRegularity ( S, tolang );
}
catch(Standard_Failure) {
#ifdef DEB
cout << "Warning: Exception in ShapeFix::EncodeRegularity(): ";
Standard_Failure::Caught()->Print ( cout );
cout << endl;
#endif
}
}
void ShapeFix::EncodeRegularity (const TopoDS_Shape& shape,
const Standard_Real tolang)
{
TopTools_MapOfShape aMap;
::EncodeRegularity ( shape, tolang, aMap );
}
//=======================================================================
//function : RemoveSmallEdges
//purpose :
//=======================================================================
TopoDS_Shape ShapeFix::RemoveSmallEdges (TopoDS_Shape& Shape,
const Standard_Real Tolerance,
Handle(ShapeBuild_ReShape)& context)
{
Handle(ShapeFix_Shape) sfs = new ShapeFix_Shape;
sfs->Init(Shape);
sfs->SetPrecision(Tolerance);
Handle(ShapeFix_Face)::DownCast(sfs->FixFaceTool())->FixMissingSeamMode() = Standard_False;
Handle(ShapeFix_Face)::DownCast(sfs->FixFaceTool())->FixOrientationMode() = Standard_False;
Handle(ShapeFix_Face)::DownCast(sfs->FixFaceTool())->FixSmallAreaWireMode() = Standard_False;
sfs->FixWireTool()->ModifyTopologyMode() = Standard_True;
//sfs.FixWireTool().FixReorderMode() = Standard_False;
sfs->FixWireTool()->FixConnectedMode() = Standard_False;
sfs->FixWireTool()->FixEdgeCurvesMode() = Standard_False;
sfs->FixWireTool()->FixDegeneratedMode() = Standard_False;
Handle(ShapeFix_Wire)::DownCast(sfs->FixWireTool())->FixSelfIntersectionMode() = Standard_False;
Handle(ShapeFix_Wire)::DownCast(sfs->FixWireTool())->FixLackingMode() = Standard_False;
Handle(ShapeFix_Wire)::DownCast(sfs->FixWireTool())->FixSmallMode() = Standard_True;
sfs->Perform();
TopoDS_Shape result = sfs->Shape();
context = sfs->Context();
return result;
}
//=======================================================================
//function : ReplaceVertex
//purpose : auxilary for FixVertexPosition
//=======================================================================
static TopoDS_Edge ReplaceVertex(const TopoDS_Edge& theEdge,
const gp_Pnt theP,
const Standard_Boolean theFwd)
{
TopoDS_Vertex aNewVertex;
BRep_Builder aB;
aB.MakeVertex(aNewVertex,theP,Precision::Confusion());
TopoDS_Vertex aV1,aV2;
if(theFwd) {
aV1 = aNewVertex;
aV1.Orientation( TopAbs_FORWARD);
}
else {
aV2 = aNewVertex;
aV2.Orientation( TopAbs_REVERSED);
}
ShapeBuild_Edge aSbe;
TopoDS_Edge e1 = theEdge;
TopAbs_Orientation Ori = e1.Orientation();
e1.Orientation(TopAbs_FORWARD);
TopoDS_Edge aNewEdge = aSbe.CopyReplaceVertices(e1,aV1,aV2);
aNewEdge.Orientation(Ori);
return aNewEdge;
}
//=======================================================================
//function : getNearPoint
//purpose : auxilary for FixVertexPosition
//=======================================================================
static Standard_Real getNearPoint(const TColgp_SequenceOfPnt& aSeq1,
const TColgp_SequenceOfPnt& aSeq2,
gp_XYZ& acent)
{
Standard_Integer i =1;
Standard_Integer ind1 =0,ind2 =0;
Standard_Real mindist =RealLast();
for( ; i <= aSeq1.Length(); i++) {
gp_Pnt p1 = aSeq1.Value(i);
Standard_Integer j=1;
for( ; j <= aSeq2.Length(); j++) {
gp_Pnt p2 = aSeq2.Value(j);
Standard_Real d = p1.Distance(p2);
if(fabs(d -mindist ) <= Precision::Confusion())
continue;
if(d < mindist) {
mindist = d;
ind1 =i;
ind2 = j;
}
}
}
if(ind1 && ind2)
acent = (aSeq1.Value(ind1).XYZ() + aSeq2.Value(ind2).XYZ())/2.0;
return mindist;
}
//=======================================================================
//function : getNearestEdges
//purpose : auxilary for FixVertexPosition
//=======================================================================
static Standard_Boolean getNearestEdges(TopTools_ListOfShape& theLEdges,
const TopoDS_Vertex theVert,
TopTools_SequenceOfShape& theSuitEdges,
TopTools_SequenceOfShape& theRejectEdges,
const Standard_Real theTolerance,
gp_XYZ& thecentersuit,
gp_XYZ& thecenterreject)
{
if(theLEdges.IsEmpty())
return Standard_False;
TopTools_MapOfShape aMapEdges;
TopTools_ListOfShape atempList;
atempList= theLEdges;
TopTools_ListIteratorOfListOfShape alIter(atempList);
TopoDS_Edge aEdge1 = TopoDS::Edge(alIter.Value());
TopoDS_Vertex aVert11,aVert12;
TopExp::Vertices(aEdge1, aVert11,aVert12 );
aMapEdges.Add(aEdge1);
Standard_Real aFirst1,aLast1;
Handle(Geom_Curve) aCurve1 = BRep_Tool::Curve(aEdge1,aFirst1,aLast1);
gp_Pnt p11;
gp_Pnt p12;
Standard_Boolean isFirst1 = theVert.IsSame(aVert11);
Standard_Boolean isSame1 = aVert11.IsSame(aVert12);
if( !aCurve1.IsNull()) {
if(isFirst1)
p11 = aCurve1->Value(aFirst1);
else if(!isSame1)
p11 = aCurve1->Value(aLast1);
if(isSame1)
p12 = aCurve1->Value(aLast1);
}
else return Standard_False;
alIter.Next();
TopTools_SequenceOfShape aseqreject;
TopTools_SequenceOfShape aseqsuit;
Standard_Integer anumLoop =0;
for( ; alIter.More(); ) {
TopoDS_Edge aEdge = TopoDS::Edge(alIter.Value());
if( aMapEdges.Contains(aEdge)) {
atempList.Remove(alIter);
continue;
}
TopoDS_Vertex aVert1,aVert2;
TopExp::Vertices(aEdge, aVert1,aVert2 );
Standard_Real isFirst = theVert.IsSame(aVert1);
Standard_Boolean isSame = aVert1.IsSame(aVert2);
Standard_Boolean isLoop = ((aVert1.IsSame(aVert11) && aVert2.IsSame(aVert12)) ||
(aVert1.IsSame(aVert12) && aVert2.IsSame(aVert11)));
if(isLoop /*&& !aseqsuit.Length()*/ && (atempList.Extent() >anumLoop)) {
atempList.Append(aEdge);
atempList.Remove(alIter);
anumLoop++;
continue;
}
aMapEdges.Add(aEdge);
Standard_Real aFirst,aLast;
Handle(Geom_Curve) aCurve = BRep_Tool::Curve(aEdge,aFirst,aLast);
if( !aCurve.IsNull()) {
gp_Pnt p1;
gp_Pnt p2;
if(isFirst)
p1 = aCurve->Value(aFirst);
else
p1 = aCurve->Value(aLast);
if(isSame)
p2 = aCurve->Value(aLast);
Standard_Real aMinDist = RealLast();
gp_XYZ acent;
if(!isSame && ! isSame1) {
aMinDist = p1.Distance(p11);
acent = (p1.XYZ() + p11.XYZ())/2.0;
}
else {
TColgp_SequenceOfPnt aSeq1;
TColgp_SequenceOfPnt aSeq2;
aSeq1.Append(p11);
if(isSame1)
aSeq1.Append(p12);
aSeq2.Append(p1);
if(isSame)
aSeq2.Append(p2);
aMinDist = getNearPoint(aSeq1,aSeq2,acent);
}
if(aMinDist > theTolerance) {
if(!aseqreject.Length())
thecenterreject = acent;
aseqreject.Append(aEdge);
}
else {
if(!aseqsuit.Length()) {
thecentersuit = acent;
aseqsuit.Append(aEdge);
}
else if(!isSame1)
aseqsuit.Append(aEdge);
else if((thecentersuit - acent).Modulus() < theTolerance)
aseqsuit.Append(aEdge);
else
aseqreject.Append(aEdge);
}
}
atempList.Remove(alIter);
}
Standard_Boolean isDone = (!aseqsuit.IsEmpty() || !aseqreject.IsEmpty());
if(isDone) {
if(aseqsuit.IsEmpty()) {
theRejectEdges.Append(aEdge1);
theLEdges.RemoveFirst();
getNearestEdges(theLEdges,theVert,theSuitEdges,theRejectEdges,
theTolerance,thecentersuit,thecenterreject);
}
else {
theSuitEdges.Append(aEdge1);
theSuitEdges.Append(aseqsuit);
theRejectEdges.Append(aseqreject);
}
}
else
theRejectEdges.Append(aEdge1);
return isDone;
}
//=======================================================================
//function : FixVertexPosition
//purpose :
//=======================================================================
Standard_Boolean ShapeFix::FixVertexPosition(TopoDS_Shape& theshape,
const Standard_Real theTolerance,
const Handle(ShapeBuild_ReShape)& thecontext)
{
TopTools_IndexedDataMapOfShapeListOfShape aMapVertEdges;
TopExp_Explorer aExp1(theshape,TopAbs_EDGE);
for( ; aExp1.More(); aExp1.Next()) {
TopoDS_Shape aVert1;
Standard_Integer nV =1;
TopoDS_Iterator aExp3(aExp1.Current());
for( ; aExp3.More(); aExp3.Next(),nV++) {
TopoDS_Shape aVert = aExp3.Value();
if(nV ==1)
aVert1 = aVert;
else if(aVert1.IsSame(aVert))
continue;
if(aMapVertEdges.Contains(aVert))
aMapVertEdges.ChangeFromKey(aVert).Append(aExp1.Current());
else {
TopTools_ListOfShape alEdges;
alEdges.Append(aExp1.Current());
aMapVertEdges.Add(aVert,alEdges);
}
}
}
Standard_Boolean isDone = Standard_False;
Standard_Integer i=1;
for( ; i <= aMapVertEdges.Extent(); i++) {
TopoDS_Vertex aVert = TopoDS::Vertex(aMapVertEdges.FindKey(i));
Standard_Real aTolVert = BRep_Tool::Tolerance(aVert);
if(aTolVert <= theTolerance)
continue;
BRep_Builder aB1;
aB1.UpdateVertex(aVert,theTolerance);
gp_Pnt aPvert = BRep_Tool::Pnt(aVert);
gp_XYZ acenter(aPvert.XYZ()), acenterreject(aPvert.XYZ());
TopTools_SequenceOfShape aSuitEdges;
TopTools_SequenceOfShape aRejectEdges;
TopTools_ListOfShape aledges;
aledges= aMapVertEdges.FindFromIndex(i);
if(aledges.Extent() ==1)
continue;
//if tolerance of vertex is more than specified tolerance
// check distance between curves and vertex
if(!getNearestEdges(aledges,aVert,aSuitEdges,aRejectEdges,theTolerance,acenter,acenterreject))
continue;
//update vertex by nearest point
Standard_Boolean isAdd = Standard_False;
Standard_Integer k =1;
for( ; k <= aSuitEdges.Length(); k++) {
TopoDS_Edge aEdgeOld = TopoDS::Edge(aSuitEdges.Value(k));
TopoDS_Vertex aVert1,aVert2;
TopExp::Vertices(aEdgeOld, aVert1,aVert2 );
Standard_Boolean isFirst = (aVert1.IsSame(aVert));
Standard_Boolean isLast = (aVert2.IsSame(aVert));
if(!isFirst && !isLast)
continue;
Standard_Real aFirst,aLast;
Handle(Geom_Curve) aCurve;
TopoDS_Edge aEdge = TopoDS::Edge(thecontext->Apply(aEdgeOld));
TopoDS_Vertex aVert1n,aVert2n;
TopExp::Vertices(aEdge, aVert1n,aVert2n );
aCurve = BRep_Tool::Curve(aEdge,aFirst,aLast);
if( !aCurve.IsNull()) {
gp_Pnt p1 = aCurve->Value(aFirst);
gp_Pnt p2 = aCurve->Value(aLast);
//if distance between ends of curve more than specified tolerance
//but vertices are the same that one of the vertex will be replaced.
Standard_Boolean isReplace = (aVert1n.IsSame(aVert2n) && p1.Distance(p2) >theTolerance);
//Standard_Real dd1 = (acenter - p1.XYZ()).Modulus();
//Standard_Real dd2 = (acenter - p2.XYZ()).Modulus();
if(isFirst) {
if( k>2) {
acenter += p1.XYZ();
acenter /= 2.0;
}
if(isReplace) {
TopoDS_Edge enew;
if(p1.Distance(acenter) < p2.Distance(acenter))
enew = ReplaceVertex(aEdge,p2,Standard_False);
else
enew = ReplaceVertex(aEdge,p1,Standard_True);
thecontext->Replace(aEdge,enew);
isDone = Standard_True;
}
}
else {
if( k>2) {
acenter += p2.XYZ();
acenter /= 2.0;
}
if(isReplace) {
TopoDS_Edge enew;
if(p1.Distance(acenter) < p2.Distance(acenter))
enew = ReplaceVertex(aEdge,p2,Standard_False);
else
enew = ReplaceVertex(aEdge,p1,Standard_True);
thecontext->Replace(aEdge,enew);
isDone = Standard_True;
}
}
isAdd = Standard_True;
}
}
if(isAdd && aPvert.Distance(acenter) > theTolerance)
{
BRep_Builder aB;
// aB.UpdateVertex(aVert,Precision::Confusion());
//else {
isDone = Standard_True;
TopoDS_Vertex aNewVertex;
aB.MakeVertex(aNewVertex,acenter,Precision::Confusion());
aNewVertex.Orientation(aVert.Orientation());
thecontext->Replace(aVert,aNewVertex);
}
for( k =1; k <= aRejectEdges.Length(); k++) {
TopoDS_Edge aEdgeOld = TopoDS::Edge( aRejectEdges.Value(k));
TopoDS_Vertex aVert1,aVert2;
TopExp::Vertices(aEdgeOld, aVert1,aVert2 );
Standard_Boolean isFirst = (aVert1.IsSame(aVert));
Standard_Boolean isLast = (aVert2.IsSame(aVert));
if(!isFirst && !isLast)
continue;
Standard_Boolean isSame = aVert1.IsSame(aVert2);
Handle(Geom_Curve) aCurve;
TopoDS_Edge aEdge = TopoDS::Edge(thecontext->Apply(aEdgeOld));
TopoDS_Vertex aVert1n,aVert2n;
TopExp::Vertices(aEdge, aVert1n,aVert2n );
Standard_Real aFirst,aLast;
aCurve = BRep_Tool::Curve(aEdge,aFirst,aLast);
if( !aCurve.IsNull()) {
gp_Pnt p1 = aCurve->Value(aFirst);
gp_Pnt p2 = aCurve->Value(aLast);
TopoDS_Edge enew;
if(isFirst) {
enew = ReplaceVertex(aEdge,p1,Standard_True);
if(isSame)
enew = ReplaceVertex(enew,p2,Standard_False);
}
else {
enew = ReplaceVertex(aEdge,p2,Standard_False);
if(isSame)
enew = ReplaceVertex(enew ,p1,Standard_True);
}
thecontext->Replace(aEdge,enew);
isDone = Standard_True;
}
}
}
if(isDone)
theshape = thecontext->Apply(theshape);
return isDone;
}
//=======================================================================
//function : LeastEdgeSize
//purpose :
//=======================================================================
Standard_Real ShapeFix::LeastEdgeSize(TopoDS_Shape& theShape)
{
Standard_Real aRes = RealLast();
for(TopExp_Explorer exp(theShape,TopAbs_EDGE); exp.More(); exp.Next()) {
TopoDS_Edge edge = TopoDS::Edge ( exp.Current() );
Standard_Real first,last;
Handle(Geom_Curve) c3d = BRep_Tool::Curve(edge, first, last);
if(!c3d.IsNull()) {
Bnd_Box bb;
bb.Add(c3d->Value(first));
bb.Add(c3d->Value(last));
bb.Add(c3d->Value((last+first)/2.));
Standard_Real x1,x2,y1,y2,z1,z2,size;
bb.Get(x1,y1,z1,x2,y2,z2);
size = (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1) + (z2-z1)*(z2-z1);
if(size<aRes) aRes = size;
}
}
aRes = sqrt(aRes);
return aRes;
}
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