-// Copyright (C) 2007-2016 CEA/DEN, EDF R&D
+// Copyright (C) 2007-2019 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
#include <sstream>
#include <algorithm>
+#include <limits>
using namespace INTERP_KERNEL;
a2.getCenter(centerL); radiusL=a2.getRadius();
a1.getCenter(centerB); radiusB=a1.getRadius();
}
- // dividing from the begining by radiusB^2 to keep precision
+ // dividing from the beginning by radiusB^2 to keep precision
distBetweenCenters=Node::distanceBtw2PtSq(centerL,centerB);
cst=distBetweenCenters/(radiusB*radiusB);
cst+=radiusL*radiusL/(radiusB*radiusB);
- return Node::areDoubleEqualsWP(cst,1.,2.);
+ return Node::areDoubleEqualsWPRight(cst,1.,2.);
}
bool ArcCArcCIntersector::areArcsOverlapped(const EdgeArcCircle& a1, const EdgeArcCircle& a2)
delete merge;
//
tmp=sqrt(tmp);
- if(Node::areDoubleEqualsWP(tmp,0.,1/(10*std::max(radiusL,radiusB))))
+ if(Node::areDoubleEqualsWPLeft(tmp,0.,10*std::max(radiusL,radiusB)))
return Node::areDoubleEquals(radiusL,radiusB);
double phi=EdgeArcCircle::GetAbsoluteAngleOfNormalizedVect((centerL[0]-centerB[0])/tmp,(centerL[1]-centerB[1])/tmp);
double cst2=2*radiusL*tmp/(radiusB*radiusB);
if(EdgeArcCircle::IsIn2Pi(angle0L,angleL,a))
cmpContainer[sizeOfCmpContainer++]=cst-cst2;
a=*std::max_element(cmpContainer,cmpContainer+sizeOfCmpContainer);
- return Node::areDoubleEqualsWP(a,1.,2.);
+ return Node::areDoubleEqualsWPRight(a,1.,2.);
}
-void ArcCArcCIntersector::areOverlappedOrOnlyColinears(const Bounds *whereToFind, bool& obviousNoIntersection, bool& areOverlapped)
+void ArcCArcCIntersector::areOverlappedOrOnlyColinears(bool& obviousNoIntersection, bool& areOverlapped)
{
_dist=Node::distanceBtw2Pt(getE1().getCenter(),getE2().getCenter());
double radius1=getE1().getRadius(); double radius2=getE2().getRadius();
}
}
+/**
+ Heart of the algorithm for arc/arc intersection.
+ See http://mathworld.wolfram.com/Circle-CircleIntersection.html
+ The computation is done in the coordinate system where Ox is the line between the 2 circle centers.
+*/
std::list< IntersectElement > ArcCArcCIntersector::getIntersectionsCharacteristicVal() const
{
std::list< IntersectElement > ret;
const double *center1=getE1().getCenter();
const double *center2=getE2().getCenter();
double radius1=getE1().getRadius(); double radius2=getE2().getRadius();
- double d1_1=(_dist*_dist-radius2*radius2+radius1*radius1)/(2.*_dist);
+ double d1_1=(_dist*_dist-radius2*radius2+radius1*radius1)/(2.*_dist); // computation of 'x' on wolfram
double u[2];//u is normalized vector from center1 to center2.
u[0]=(center2[0]-center1[0])/_dist; u[1]=(center2[1]-center1[1])/_dist;
- double d1_1y=EdgeArcCircle::SafeSqrt(radius1*radius1-d1_1*d1_1);
+ double d1_1y=EdgeArcCircle::SafeSqrt(radius1*radius1-d1_1*d1_1); // computation of 'y' on wolfram
double angleE1=EdgeArcCircle::NormalizeAngle(getE1().getAngle0()+getE1().getAngle());
double angleE2=EdgeArcCircle::NormalizeAngle(getE2().getAngle0()+getE2().getAngle());
if(!Node::areDoubleEquals(d1_1y,0))
{
//2 intersections
double v1[2],v2[2];
+ // coming back to our coordinate system:
v1[0]=u[0]*d1_1-u[1]*d1_1y; v1[1]=u[1]*d1_1+u[0]*d1_1y;
v2[0]=u[0]*d1_1+u[1]*d1_1y; v2[1]=u[1]*d1_1-u[0]*d1_1y;
Node *node1=new Node(center1[0]+v1[0],center1[1]+v1[1]); node1->declareOn();
v4[0]=center1[0]-center2[0]+v2[0]; v4[1]=center1[1]-center2[1]+v2[1];
double angle1_2=EdgeArcCircle::GetAbsoluteAngleOfNormalizedVect(v3[0]/radius2,v3[1]/radius2);
double angle2_2=EdgeArcCircle::GetAbsoluteAngleOfNormalizedVect(v4[0]/radius2,v4[1]/radius2);
+ // Check whether intersection points are exactly ON the other arc or not
+ // -> the curvilinear distance (=radius*angle) must below eps
+ bool e1_1S=Node::areDoubleEqualsWPLeft(angle1_1,getE1().getAngle0(),radius1);
+ bool e1_1E=Node::areDoubleEqualsWPLeft(angle1_1,angleE1,radius1);
+ bool e1_2S=Node::areDoubleEqualsWPLeft(angle1_2,getE2().getAngle0(),radius1);
+ bool e1_2E=Node::areDoubleEqualsWPLeft(angle1_2,angleE2,radius1);
//
- bool e1_1S=Node::areDoubleEqualsWP(angle1_1,getE1().getAngle0(),radius1);
- bool e1_1E=Node::areDoubleEqualsWP(angle1_1,angleE1,radius1);
- bool e1_2S=Node::areDoubleEqualsWP(angle1_2,getE2().getAngle0(),radius1);
- bool e1_2E=Node::areDoubleEqualsWP(angle1_2,angleE2,radius1);
- //
- bool e2_1S=Node::areDoubleEqualsWP(angle2_1,getE1().getAngle0(),radius2);
- bool e2_1E=Node::areDoubleEqualsWP(angle2_1,angleE1,radius2);
- bool e2_2S=Node::areDoubleEqualsWP(angle2_2,getE2().getAngle0(),radius2);
- bool e2_2E=Node::areDoubleEqualsWP(angle2_2,angleE2,radius2);
+ bool e2_1S=Node::areDoubleEqualsWPLeft(angle2_1,getE1().getAngle0(),radius2);
+ bool e2_1E=Node::areDoubleEqualsWPLeft(angle2_1,angleE1,radius2);
+ bool e2_2S=Node::areDoubleEqualsWPLeft(angle2_2,getE2().getAngle0(),radius2);
+ bool e2_2E=Node::areDoubleEqualsWPLeft(angle2_2,angleE2,radius2);
ret.push_back(IntersectElement(angle1_1,angle1_2,e1_1S,e1_1E,e1_2S,e1_2E,node1,_e1,_e2,keepOrder()));
ret.push_back(IntersectElement(angle2_1,angle2_2,e2_1S,e2_1E,e2_2S,e2_2E,node2,_e1,_e2,keepOrder()));
}
v2[0]=center1[0]-center2[0]+v1[0]; v2[1]=center1[1]-center2[1]+v1[1];
double angle0_1=EdgeArcCircle::GetAbsoluteAngleOfNormalizedVect(v1[0]/radius1,v1[1]/radius1);
double angle0_2=EdgeArcCircle::GetAbsoluteAngleOfNormalizedVect(v2[0]/radius2,v2[1]/radius2);
- bool e0_1S=Node::areDoubleEqualsWP(angle0_1,getE1().getAngle0(),radius1);
- bool e0_1E=Node::areDoubleEqualsWP(angle0_1,angleE1,radius1);
- bool e0_2S=Node::areDoubleEqualsWP(angle0_2,getE2().getAngle0(),radius2);
- bool e0_2E=Node::areDoubleEqualsWP(angle0_2,angleE2,radius2);
+ bool e0_1S=Node::areDoubleEqualsWPLeft(angle0_1,getE1().getAngle0(),radius1);
+ bool e0_1E=Node::areDoubleEqualsWPLeft(angle0_1,angleE1,radius1);
+ bool e0_2S=Node::areDoubleEqualsWPLeft(angle0_2,getE2().getAngle0(),radius2);
+ bool e0_2E=Node::areDoubleEqualsWPLeft(angle0_2,angleE2,radius2);
Node *node=new Node(center1[0]+d1_1*u[0],center1[1]+d1_1*u[1]); node->declareOnTangent();
ret.push_back(IntersectElement(angle0_1,angle0_2,e0_1S,e0_1E,e0_2S,e0_2E,node,_e1,_e2,keepOrder()));
}
}
return ret;*/
-ArcCSegIntersector::ArcCSegIntersector(const EdgeArcCircle& e1, const EdgeLin& e2, bool reverse):CrossTypeEdgeIntersector(e1,e2,reverse)
-{
-}
-
-void ArcCSegIntersector::areOverlappedOrOnlyColinears(const Bounds *whereToFind, bool& obviousNoIntersection, bool& areOverlapped)
+ArcCSegIntersector::ArcCSegIntersector(const EdgeArcCircle& e1, const EdgeLin& e2, bool reverse):
+ CrossTypeEdgeIntersector(e1,e2,reverse),
+ _deltaRoot_div_dr(0.),
+ _i1S2E(false),_i1E2E(false)
{
- areOverlapped=false;//No overlapping by construction
const double *center=getE1().getCenter();
_dx=(*(_e2.getEndNode()))[0]-(*(_e2.getStartNode()))[0];
_dy=(*(_e2.getEndNode()))[1]-(*(_e2.getStartNode()))[1];
_cross=
((*(_e2.getStartNode()))[0]-center[0])*((*(_e2.getEndNode()))[1]-center[1])-
((*(_e2.getStartNode()))[1]-center[1])*((*(_e2.getEndNode()))[0]-center[0]);
- _determinant=getE1().getRadius()*getE1().getRadius()/_drSq-_cross*_cross/(_drSq*_drSq);
- if(_determinant>-2*QuadraticPlanarPrecision::getPrecision())//QuadraticPlanarPrecision::getPrecision()*QuadraticPlanarPrecision::getPrecision()*_drSq*_drSq/(2.*_dx*_dx))
+}
+
+/**
+ See http://mathworld.wolfram.com/Circle-LineIntersection.html
+ _cross is 'D', the computation is done with the translation to put back the circle at the origin
+*/
+void ArcCSegIntersector::areOverlappedOrOnlyColinears(bool& obviousNoIntersection, bool& areOverlapped)
+{
+ areOverlapped=false;//No overlapping by construction
+
+ // Similar optimisation than SegSegIntersector::areOverlappedOrOnlyColinears()
+ bool dnu1, dnu2;
+ identifyEarlyIntersection(dnu1, dnu2, _i1S2E, _i1E2E);
+
+ const double R = getE1().getRadius();
+
+ // We need to compute d = R*R-_cross*_cross/_drSq
+ // In terms of numerical precision, this can trigger 'catastrophic cancellation' and is hence better expressed as:
+ double _dr = sqrt(_drSq);
+ double diff = (R-_cross/_dr), add=(R+_cross/_dr);
+ // Ah ah: we will be taking a square root later. If we want the user to be able to use an epsilon finer than 1.0e-8, then we need
+ // to prevent ourselves going below machine precision (typ. 1.0e-16 for double).
+ const double eps_machine = std::numeric_limits<double>::epsilon();
+ diff = fabs(diff/R) < eps_machine ? 0.0 : diff;
+ add = fabs(add/R) < eps_machine ? 0.0 : add;
+ double d = add*diff;
+ // Compute deltaRoot_div_dr := sqrt(delta)/dr, where delta has the meaning of Wolfram.
+ // Then 2*deltaRoot_div_dr is the distance between the two intersection points of the line with the circle. This is what we compare to eps.
+ // We compute it in such a way that it can be used in boolean tests too (a very negative value means we're far apart from intersection)
+ _deltaRoot_div_dr = Node::sign(d)*sqrt(fabs(d));
+
+ if( 2*_deltaRoot_div_dr > -QuadraticPlanarPrecision::getPrecision())
obviousNoIntersection=false;
else
- obviousNoIntersection=true;
+ obviousNoIntersection=true;
}
/*!
{
std::list< IntersectElement > ret;
const double *center=getE1().getCenter();
- if(!(fabs(_determinant)<(2.*QuadraticPlanarPrecision::getPrecision())))//QuadraticPlanarPrecision::getPrecision()*QuadraticPlanarPrecision::getPrecision()*_drSq*_drSq/(2.*_dx*_dx))
- {
- double determinant=EdgeArcCircle::SafeSqrt(_determinant);
+ if(!(2*fabs(_deltaRoot_div_dr) < QuadraticPlanarPrecision::getPrecision())) // see comments in areOverlappedOrOnlyColinears()
+ { // Two intersection nodes
+ // -> if a common node found, there is a chance that this is the only one (i.e. second intersection point is outside e1 and e2)
+ if(_earlyInter)
+ {
+ // Check tangent vector of the arc circle at the common node with the linear segment.
+ // There we can tell if the arc of circle is 'moving away' from the seg, or if it might intersect it twice
+ const Node &n(*_earlyInter->getNodeOnly());
+ const double * center(getE1().getCenter());
+
+ double tang[2] = {-(n[1]-center[1]), n[0]-center[0]}; // (-y, x) is the tangent vector in the trigo direction with (x,y) = (center->node)
+ bool invSeg = _i1S2E || _i1E2E;
+ double linEdge[2] = {invSeg ? (-_dx) : _dx, invSeg ? (-_dy) : _dy};
+ if(tang[1]*linEdge[0]-tang[0]*linEdge[1] < 0)
+ {
+ ret.push_back(*_earlyInter);
+ return ret;
+ }
+ }
+
+ double determinant=fabs(_deltaRoot_div_dr)/sqrt(_drSq);
double x1=(_cross*_dy/_drSq+Node::sign(_dy)*_dx*determinant)+center[0];
double y1=(-_cross*_dx/_drSq+fabs(_dy)*determinant)+center[1];
Node *intersect1=new Node(x1,y1); intersect1->declareOn();
- bool i1_1S=_e1.getStartNode()->isEqual(*intersect1);
- bool i1_1E=_e1.getEndNode()->isEqual(*intersect1);
- bool i1_2S=_e2.getStartNode()->isEqual(*intersect1);
- bool i1_2E=_e2.getEndNode()->isEqual(*intersect1);
- ret.push_back(IntersectElement(getE1().getCharactValue(*intersect1),getE2().getCharactValue(*intersect1),i1_1S,i1_1E,i1_2S,i1_2E,intersect1,_e1,_e2,keepOrder()));
- //
double x2=(_cross*_dy/_drSq-Node::sign(_dy)*_dx*determinant)+center[0];
double y2=(-_cross*_dx/_drSq-fabs(_dy)*determinant)+center[1];
Node *intersect2=new Node(x2,y2); intersect2->declareOn();
- bool i2_1S=_e1.getStartNode()->isEqual(*intersect2);
- bool i2_1E=_e1.getEndNode()->isEqual(*intersect2);
- bool i2_2S=_e2.getStartNode()->isEqual(*intersect2);
- bool i2_2E=_e2.getEndNode()->isEqual(*intersect2);
- ret.push_back(IntersectElement(getE1().getCharactValue(*intersect2),getE2().getCharactValue(*intersect2),i2_1S,i2_1E,i2_2S,i2_2E,intersect2,_e1,_e2,keepOrder()));
+
+ bool isN1(false), isN2(false);
+ if (_earlyInter)
+ {
+ // Which node do we actually already found? Assume this is the closest ...
+ const Node &iN = *(_earlyInter->getNodeOnly());
+ const Node &n1(*intersect1), &n2(*intersect2);
+ double d1 = std::max(fabs(iN[0]-n1[0]), fabs(iN[1]-n1[1]));
+ double d2 = std::max(fabs(iN[0]-n2[0]), fabs(iN[1]-n2[1]));
+ isN1 = d1 < d2; isN2 = !isN1;
+ if (isN1) intersect1->decrRef();
+ if (isN2) intersect2->decrRef();
+ ret.push_back(*_earlyInter);
+ }
+ if (!isN1)
+ {
+ bool i1_1S=_e1.getStartNode()->isEqual(*intersect1);
+ bool i1_1E=_e1.getEndNode()->isEqual(*intersect1);
+ bool i1_2S=_e2.getStartNode()->isEqual(*intersect1);
+ bool i1_2E=_e2.getEndNode()->isEqual(*intersect1);
+ ret.push_back(IntersectElement(getE1().getCharactValue(*intersect1),getE2().getCharactValue(*intersect1),i1_1S,i1_1E,i1_2S,i1_2E,intersect1,_e1,_e2,keepOrder()));
+ }
+ if(!isN2)
+ {
+ bool i2_1S=_e1.getStartNode()->isEqual(*intersect2);
+ bool i2_1E=_e1.getEndNode()->isEqual(*intersect2);
+ bool i2_2S=_e2.getStartNode()->isEqual(*intersect2);
+ bool i2_2E=_e2.getEndNode()->isEqual(*intersect2);
+ ret.push_back(IntersectElement(getE1().getCharactValue(*intersect2),getE2().getCharactValue(*intersect2),i2_1S,i2_1E,i2_2S,i2_2E,intersect2,_e1,_e2,keepOrder()));
+ }
}
else//tangent intersection
{
+ if (_earlyInter)
+ {
+ ret.push_back(*_earlyInter);
+ return ret;
+ }
double x=(_cross*_dy)/_drSq+center[0];
double y=(-_cross*_dx)/_drSq+center[1];
Node *intersect3=new Node(x,y); intersect3->declareOnTangent();
/*!
* 'eps' is expected to be > 0.
* 'conn' is of size 3. conn[0] is start id, conn[1] is end id and conn[2] is middle id.
- * 'offset' is typically the number of nodes already existing in global 2D curve mesh. Additionnal coords 'addCoo' ids will be put after the already existing.
+ * 'offset' is typically the number of nodes already existing in global 2D curve mesh. Additional coords 'addCoo' ids will be put after the already existing.
*/
void EdgeArcCircle::tesselate(const int *conn, int offset, double eps, std::vector<int>& newConn, std::vector<double>& addCoo) const
{
/*!
* Given a \b normalized vector defined by (ux,uy) returns its angle in ]-Pi;Pi].
- * So before using this method ux*ux+uy*uy should as much as possible close to 1.
- * This methods is quite time consuming in order to keep as much as possible precision.
- * It is NOT ALWAYS possible to do that only in one call of acos. Sometimes call to asin is necessary
- * due to imperfection of acos near 0. and Pi (cos x ~ 1-x*x/2.)
+ * Actually in the current implementation, the vector does not even need to be normalized ...
*/
double EdgeArcCircle::GetAbsoluteAngleOfNormalizedVect(double ux, double uy)
{
if(IsIn2Pi(_angle0,_angle,M_PI))
_bounds[0]=_center[0]-_radius;
}
-
-void EdgeArcCircle::fillGlobalInfoAbs(bool direction, const std::map<INTERP_KERNEL::Node *,int>& mapThis, const std::map<INTERP_KERNEL::Node *,int>& mapOther, int offset1, int offset2, double fact, double baryX, double baryY,
- std::vector<int>& edgesThis, std::vector<double>& addCoo, std::map<INTERP_KERNEL::Node *,int> mapAddCoo) const
-{
- int tmp[2];
- _start->fillGlobalInfoAbs(mapThis,mapOther,offset1,offset2,fact,baryX,baryY,addCoo,mapAddCoo,tmp);
- _end->fillGlobalInfoAbs(mapThis,mapOther,offset1,offset2,fact,baryX,baryY,addCoo,mapAddCoo,tmp+1);
- if(direction)
- {
- edgesThis.push_back(tmp[0]);
- edgesThis.push_back(tmp[1]);
- }
- else
- {
- edgesThis.push_back(tmp[1]);
- edgesThis.push_back(tmp[0]);
- }
-}
-
-void EdgeArcCircle::fillGlobalInfoAbs2(const std::map<INTERP_KERNEL::Node *,int>& mapThis, const std::map<INTERP_KERNEL::Node *,int>& mapOther, int offset1, int offset2, double fact, double baryX, double baryY,
- std::vector<int>& edgesOther, std::vector<double>& addCoo, std::map<INTERP_KERNEL::Node *,int>& mapAddCoo) const
-{
- _start->fillGlobalInfoAbs2(mapThis,mapOther,offset1,offset2,fact,baryX,baryY,addCoo,mapAddCoo,edgesOther);
- _end->fillGlobalInfoAbs2(mapThis,mapOther,offset1,offset2,fact,baryX,baryY,addCoo,mapAddCoo,edgesOther);
-}
