+// Copyright (C) 2007-2016 CEA/DEN, EDF R&D
+//
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+//
+// See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
+//
+
+// Author : Lioka RAZAFINDRAZAKA (CEA)
+
+#include "SMESH_ControlPnt.hxx"
+
+#include <BRepBndLib.hxx>
+#include <BRepMesh_IncrementalMesh.hxx>
+#include <BRep_Tool.hxx>
+#include <Bnd_Box.hxx>
+#include <GCPnts_UniformAbscissa.hxx>
+#include <GeomAdaptor_Curve.hxx>
+#include <Geom_Curve.hxx>
+#include <IntCurvesFace_Intersector.hxx>
+#include <Poly_Array1OfTriangle.hxx>
+#include <Poly_Triangle.hxx>
+#include <Poly_Triangulation.hxx>
+#include <Precision.hxx>
+#include <TColgp_Array1OfPnt.hxx>
+#include <TopExp_Explorer.hxx>
+#include <TopLoc_Location.hxx>
+#include <TopoDS.hxx>
+#include <TopoDS_Edge.hxx>
+#include <TopoDS_Face.hxx>
+#include <TopoDS_Iterator.hxx>
+#include <TopoDS_Solid.hxx>
+#include <gp_Ax3.hxx>
+#include <gp_Dir.hxx>
+#include <gp_Lin.hxx>
+#include <gp_Trsf.hxx>
+#include <gp_Vec.hxx>
+
+#include <set>
+
+namespace SMESHUtils
+{
+ // Some functions for surface sampling
+ void subdivideTriangle( const gp_Pnt& p1,
+ const gp_Pnt& p2,
+ const gp_Pnt& p3,
+ const double& theSize,
+ std::vector<ControlPnt>& thePoints );
+
+ std::vector<gp_Pnt> computePointsForSplitting( const gp_Pnt& p1,
+ const gp_Pnt& p2,
+ const gp_Pnt& p3 );
+ gp_Pnt tangencyPoint(const gp_Pnt& p1,
+ const gp_Pnt& p2,
+ const gp_Pnt& Center);
+
+}
+
+//================================================================================
+/*!
+ * \brief Fills a vector of points from which a size map input file can be written
+ */
+//================================================================================
+
+void SMESHUtils::createControlPoints( const TopoDS_Shape& theShape,
+ const double& theSize,
+ std::vector<ControlPnt>& thePoints )
+{
+ if ( theShape.ShapeType() == TopAbs_VERTEX )
+ {
+ gp_Pnt aPnt = BRep_Tool::Pnt( TopoDS::Vertex(theShape) );
+ ControlPnt aControlPnt( aPnt, theSize );
+ thePoints.push_back( aControlPnt );
+ }
+ if ( theShape.ShapeType() == TopAbs_EDGE )
+ {
+ createPointsSampleFromEdge( TopoDS::Edge( theShape ), theSize, thePoints );
+ }
+ else if ( theShape.ShapeType() == TopAbs_WIRE )
+ {
+ TopExp_Explorer Ex;
+ for (Ex.Init(theShape,TopAbs_EDGE); Ex.More(); Ex.Next())
+ {
+ createPointsSampleFromEdge( TopoDS::Edge( Ex.Current() ), theSize, thePoints );
+ }
+ }
+ else if ( theShape.ShapeType() == TopAbs_FACE )
+ {
+ createPointsSampleFromFace( TopoDS::Face( theShape ), theSize, thePoints );
+ }
+ else if ( theShape.ShapeType() == TopAbs_SOLID )
+ {
+ createPointsSampleFromSolid( TopoDS::Solid( theShape ), theSize, thePoints );
+ }
+ else if ( theShape.ShapeType() == TopAbs_COMPOUND )
+ {
+ TopoDS_Iterator it( theShape );
+ for(; it.More(); it.Next())
+ {
+ createControlPoints( it.Value(), theSize, thePoints );
+ }
+ }
+}
+
+//================================================================================
+/*!
+ * \brief Fills a vector of points with point samples approximately
+ * \brief spaced with a given size
+ */
+//================================================================================
+
+void SMESHUtils::createPointsSampleFromEdge( const TopoDS_Edge& theEdge,
+ const double& theSize,
+ std::vector<ControlPnt>& thePoints )
+{
+ double step = theSize;
+ double first, last;
+ Handle( Geom_Curve ) aCurve = BRep_Tool::Curve( theEdge, first, last );
+ GeomAdaptor_Curve C ( aCurve );
+ GCPnts_UniformAbscissa DiscretisationAlgo(C, step , first, last, Precision::Confusion());
+ int nbPoints = DiscretisationAlgo.NbPoints();
+
+ ControlPnt aPnt;
+ aPnt.SetSize(theSize);
+
+ for ( int i = 1; i <= nbPoints; i++ )
+ {
+ double param = DiscretisationAlgo.Parameter( i );
+ aCurve->D0( param, aPnt );
+ thePoints.push_back( aPnt );
+ }
+}
+
+//================================================================================
+/*!
+ * \brief Fills a vector of points with point samples approximately
+ * \brief spaced with a given size
+ */
+//================================================================================
+
+void SMESHUtils::createPointsSampleFromFace( const TopoDS_Face& theFace,
+ const double& theSize,
+ std::vector<ControlPnt>& thePoints )
+{
+ BRepMesh_IncrementalMesh M(theFace, 0.01, Standard_True);
+ TopLoc_Location aLocation;
+
+ // Triangulate the face
+ Handle(Poly_Triangulation) aTri = BRep_Tool::Triangulation (theFace, aLocation);
+
+ // Get the transformation associated to the face location
+ gp_Trsf aTrsf = aLocation.Transformation();
+
+ // Get triangles
+ int nbTriangles = aTri->NbTriangles();
+ Poly_Array1OfTriangle triangles(1,nbTriangles);
+ triangles=aTri->Triangles();
+
+ // GetNodes
+ int nbNodes = aTri->NbNodes();
+ TColgp_Array1OfPnt nodes(1,nbNodes);
+ nodes = aTri->Nodes();
+
+ // Iterate on triangles and subdivide them
+ for(int i=1; i<=nbTriangles; i++)
+ {
+ Poly_Triangle aTriangle = triangles.Value(i);
+ gp_Pnt p1 = nodes.Value(aTriangle.Value(1));
+ gp_Pnt p2 = nodes.Value(aTriangle.Value(2));
+ gp_Pnt p3 = nodes.Value(aTriangle.Value(3));
+
+ p1.Transform(aTrsf);
+ p2.Transform(aTrsf);
+ p3.Transform(aTrsf);
+
+ subdivideTriangle(p1, p2, p3, theSize, thePoints);
+ }
+}
+
+//================================================================================
+/*!
+ * \brief Fills a vector of points with point samples approximately
+ * \brief spaced with a given size
+ */
+//================================================================================
+
+void SMESHUtils::createPointsSampleFromSolid( const TopoDS_Solid& theSolid,
+ const double& theSize,
+ std::vector<ControlPnt>& thePoints )
+{
+ // Compute the bounding box
+ double Xmin, Ymin, Zmin, Xmax, Ymax, Zmax;
+ Bnd_Box B;
+ BRepBndLib::Add(theSolid, B);
+ B.Get(Xmin, Ymin, Zmin, Xmax, Ymax, Zmax);
+
+ // Create the points
+ double step = theSize;
+
+ for ( double x=Xmin; x-Xmax<Precision::Confusion(); x=x+step )
+ {
+ for ( double y=Ymin; y-Ymax<Precision::Confusion(); y=y+step )
+ {
+ // Step1 : generate the Zmin -> Zmax line
+ gp_Pnt startPnt(x, y, Zmin);
+ gp_Pnt endPnt(x, y, Zmax);
+ gp_Vec aVec(startPnt, endPnt);
+ gp_Lin aLine(startPnt, aVec);
+ double endParam = Zmax - Zmin;
+
+ // Step2 : for each face of theSolid:
+ std::set<double> intersections;
+ std::set<double>::iterator it = intersections.begin();
+
+ TopExp_Explorer Ex;
+ for (Ex.Init(theSolid,TopAbs_FACE); Ex.More(); Ex.Next())
+ {
+ // check if there is an intersection
+ IntCurvesFace_Intersector anIntersector(TopoDS::Face(Ex.Current()), Precision::Confusion());
+ anIntersector.Perform(aLine, 0, endParam);
+
+ // get the intersection's parameter and store it
+ int nbPoints = anIntersector.NbPnt();
+ for(int i = 0 ; i < nbPoints ; i++ )
+ {
+ it = intersections.insert( it, anIntersector.WParameter(i+1) );
+ }
+ }
+ // Step3 : go through the line chunk by chunk
+ if ( intersections.begin() != intersections.end() )
+ {
+ std::set<double>::iterator intersectionsIterator=intersections.begin();
+ double first = *intersectionsIterator;
+ intersectionsIterator++;
+ bool innerPoints = true;
+ for ( ; intersectionsIterator!=intersections.end() ; intersectionsIterator++ )
+ {
+ double second = *intersectionsIterator;
+ if ( innerPoints )
+ {
+ // If the last chunk was outside of the shape or this is the first chunk
+ // add the points in the range [first, second] to the points vector
+ double localStep = (second -first) / ceil( (second - first) / step );
+ for ( double z = Zmin + first; z < Zmin + second; z = z + localStep )
+ {
+ thePoints.push_back(ControlPnt( x, y, z, theSize ));
+ }
+ thePoints.push_back(ControlPnt( x, y, Zmin + second, theSize ));
+ }
+ first = second;
+ innerPoints = !innerPoints;
+ }
+ }
+ }
+ }
+}
+
+//================================================================================
+/*!
+ * \brief Subdivides a triangle until it reaches a certain size (recursive function)
+ */
+//================================================================================
+
+void SMESHUtils::subdivideTriangle( const gp_Pnt& p1,
+ const gp_Pnt& p2,
+ const gp_Pnt& p3,
+ const double& theSize,
+ std::vector<ControlPnt>& thePoints)
+{
+ // Size threshold to stop subdividing
+ // This value ensures that two control points are distant no more than 2*theSize
+ // as shown below
+ //
+ // The greater distance D of the mass center M to each Edge is 1/3 * Median
+ // and Median < sqrt(3/4) * a where a is the greater side (by using Apollonius' thorem).
+ // So D < 1/3 * sqrt(3/4) * a and if a < sqrt(3) * S then D < S/2
+ // and the distance between two mass centers of two neighbouring triangles
+ // sharing an edge is < 2 * 1/2 * S = S
+ // If the traingles share a Vertex and no Edge the distance of the mass centers
+ // to the Vertices is 2*D < S so the mass centers are distant of less than 2*S
+
+ double threshold = sqrt( 3. ) * theSize;
+
+ if ( (p1.Distance(p2) > threshold ||
+ p2.Distance(p3) > threshold ||
+ p3.Distance(p1) > threshold))
+ {
+ std::vector<gp_Pnt> midPoints = computePointsForSplitting(p1, p2, p3);
+
+ subdivideTriangle( midPoints[0], midPoints[1], midPoints[2], theSize, thePoints );
+ subdivideTriangle( midPoints[0], p2, midPoints[1], theSize, thePoints );
+ subdivideTriangle( midPoints[2], midPoints[1], p3, theSize, thePoints );
+ subdivideTriangle( p1, midPoints[0], midPoints[2], theSize, thePoints );
+ }
+ else
+ {
+ double x = (p1.X() + p2.X() + p3.X()) / 3 ;
+ double y = (p1.Y() + p2.Y() + p3.Y()) / 3 ;
+ double z = (p1.Z() + p2.Z() + p3.Z()) / 3 ;
+
+ ControlPnt massCenter( x ,y ,z, theSize );
+ thePoints.push_back( massCenter );
+ }
+}
+
+//================================================================================
+/*!
+ * \brief Returns the appropriate points for splitting a triangle
+ * \brief the tangency points of the incircle are used in order to have mostly
+ * \brief well-shaped sub-triangles
+ */
+//================================================================================
+
+std::vector<gp_Pnt> SMESHUtils::computePointsForSplitting( const gp_Pnt& p1,
+ const gp_Pnt& p2,
+ const gp_Pnt& p3 )
+{
+ std::vector<gp_Pnt> midPoints;
+ //Change coordinates
+ gp_Trsf Trsf_1; // Identity transformation
+ gp_Ax3 reference_system(gp::Origin(), gp::DZ(), gp::DX()); // OXY
+
+ gp_Vec Vx(p1, p3);
+ gp_Vec Vaux(p1, p2);
+ gp_Dir Dx(Vx);
+ gp_Dir Daux(Vaux);
+ gp_Dir Dz = Dx.Crossed(Daux);
+ gp_Ax3 current_system(p1, Dz, Dx);
+
+ Trsf_1.SetTransformation( reference_system, current_system );
+
+ gp_Pnt A = p1.Transformed(Trsf_1);
+ gp_Pnt B = p2.Transformed(Trsf_1);
+ gp_Pnt C = p3.Transformed(Trsf_1);
+
+ double a = B.Distance(C) ;
+ double b = A.Distance(C) ;
+ double c = B.Distance(A) ;
+
+ // Incenter coordinates
+ // see http://mathworld.wolfram.com/Incenter.html
+ double Xi = ( b*B.X() + c*C.X() ) / ( a + b + c );
+ double Yi = ( b*B.Y() ) / ( a + b + c );
+ gp_Pnt Center(Xi, Yi, 0);
+
+ // Calculate the tangency points of the incircle
+ gp_Pnt T1 = tangencyPoint( A, B, Center);
+ gp_Pnt T2 = tangencyPoint( B, C, Center);
+ gp_Pnt T3 = tangencyPoint( C, A, Center);
+
+ gp_Pnt p1_2 = T1.Transformed(Trsf_1.Inverted());
+ gp_Pnt p2_3 = T2.Transformed(Trsf_1.Inverted());
+ gp_Pnt p3_1 = T3.Transformed(Trsf_1.Inverted());
+
+ midPoints.push_back(p1_2);
+ midPoints.push_back(p2_3);
+ midPoints.push_back(p3_1);
+
+ return midPoints;
+}
+
+//================================================================================
+/*!
+ * \brief Computes the tangency points of the circle of center Center with
+ * \brief the straight line (p1 p2)
+ */
+//================================================================================
+
+gp_Pnt SMESHUtils::tangencyPoint(const gp_Pnt& p1,
+ const gp_Pnt& p2,
+ const gp_Pnt& Center)
+{
+ double Xt = 0;
+ double Yt = 0;
+
+ // The tangency point is the intersection of the straight line (p1 p2)
+ // and the straight line (Center T) which is orthogonal to (p1 p2)
+ if ( fabs(p1.X() - p2.X()) <= Precision::Confusion() )
+ {
+ Xt=p1.X(); // T is on (p1 p2)
+ Yt=Center.Y(); // (Center T) is orthogonal to (p1 p2)
+ }
+ else if ( fabs(p1.Y() - p2.Y()) <= Precision::Confusion() )
+ {
+ Yt=p1.Y(); // T is on (p1 p2)
+ Xt=Center.X(); // (Center T) is orthogonal to (p1 p2)
+ }
+ else
+ {
+ // First straight line coefficients (equation y=a*x+b)
+ double a = (p2.Y() - p1.Y()) / (p2.X() - p1.X()) ;
+ double b = p1.Y() - a*p1.X(); // p1 is on this straight line
+
+ // Second straight line coefficients (equation y=c*x+d)
+ double c = -1 / a; // The 2 lines are orthogonal
+ double d = Center.Y() - c*Center.X(); // Center is on this straight line
+
+ Xt = (d - b) / (a - c);
+ Yt = a*Xt + b;
+ }
+
+ return gp_Pnt( Xt, Yt, 0 );
+}
