/** construct a ellipse or hyperbola as the path of center of common tangent circles
of this two given entities*/
LC_Quadratic::LC_Quadratic(const RS_AtomicEntity* circle0,
const RS_AtomicEntity* circle1,
bool mirror):
m_mQuad(2,2)
,m_vLinear(2)
,m_bValid(false)
{
// DEBUG_HEADER
if(!( circle0->isArcCircleLine() && circle1->isArcCircleLine())) {
return;
}
if(circle1->rtti() != RS2::EntityLine)
std::swap(circle0, circle1);
if(circle0->rtti() == RS2::EntityLine) {
//two lines
RS_Line* line0=(RS_Line*) circle0;
RS_Line* line1=(RS_Line*) circle1;
auto centers=RS_Information::getIntersection(line0,line1);
// DEBUG_HEADER
if(centers.size()!=1) return;
double angle=0.5*(line0->getAngle1()+line1->getAngle1());
m_bValid=true;
m_bIsQuadratic=true;
m_mQuad(0,0)=0.;
m_mQuad(0,1)=0.5;
m_mQuad(1,0)=0.5;
m_mQuad(1,1)=0.;
m_vLinear(0)=0.;
m_vLinear(1)=0.;
m_dConst=0.;
rotate(angle);
move(centers.get(0));
// DEBUG_HEADER
// std::cout<<*this<<std::endl;
return;
}
if(circle1->rtti() == RS2::EntityLine) {
// DEBUG_HEADER
//one line, one circle
const RS_Line* line1=static_cast<const RS_Line*>(circle1);
RS_Vector normal=line1->getNormalVector()*circle0->getRadius();
RS_Vector disp=line1->getNearestPointOnEntity(circle0->getCenter(),
false)-circle0->getCenter();
if(normal.dotP(disp)>0.) normal *= -1.;
if(mirror) normal *= -1.;
RS_Line directrix{line1->getStartpoint()+normal,
line1->getEndpoint()+normal};
LC_Quadratic lc0(&directrix,circle0->getCenter());
*this = lc0;
return;
m_mQuad=lc0.getQuad();
m_vLinear=lc0.getLinear();
m_bIsQuadratic=true;
m_bValid=true;
m_dConst=lc0.m_dConst;
return;
}
//two circles
double const f=(circle0->getCenter()-circle1->getCenter()).magnitude()*0.5;
double const a=fabs(circle0->getRadius()+circle1->getRadius())*0.5;
double const c=fabs(circle0->getRadius()-circle1->getRadius())*0.5;
// DEBUG_HEADER
// qDebug()<<"circle center to center distance="<<2.*f<<"\ttotal radius="<<2.*a;
if(a<RS_TOLERANCE) return;
RS_Vector center=(circle0->getCenter()+circle1->getCenter())*0.5;
double angle=center.angleTo(circle0->getCenter());
if( f<a){
//ellipse
double const ratio=sqrt(a*a - f*f)/a;
RS_Vector const& majorP=RS_Vector{angle}*a;
RS_Ellipse const ellipse{center,majorP,ratio,0.,0.,false};
auto const& lc0=ellipse.getQuadratic();
m_mQuad=lc0.getQuad();
m_vLinear=lc0.getLinear();
m_bIsQuadratic=lc0.isQuadratic();
m_bValid=lc0.isValid();
m_dConst=lc0.m_dConst;
// DEBUG_HEADER
// std::cout<<"ellipse: "<<*this;
return;
}
// DEBUG_HEADER
if(c<RS_TOLERANCE){
//two circles are the same radius
//degenerate hypberbola: straight lines
//equation xy = 0
m_bValid=true;
m_bIsQuadratic=true;
m_mQuad(0,0)=0.;
m_mQuad(0,1)=0.5;
m_mQuad(1,0)=0.5;
m_mQuad(1,1)=0.;
m_vLinear(0)=0.;
m_vLinear(1)=0.;
m_dConst=0.;
rotate(angle);
move(center);
return;
}
//hyperbola
// equation: x^2/c^2 - y^2/(f^2 -c ^2) = 1
// f: from hyperbola center to one circle center
// c: half of difference of two circles
double b2= f*f - c*c;
m_bValid=true;
m_bIsQuadratic=true;
m_mQuad(0,0)=1./(c*c);
m_mQuad(0,1)=0.;
m_mQuad(1,0)=0.;
m_mQuad(1,1)=-1./b2;
m_vLinear(0)=0.;
m_vLinear(1)=0.;
m_dConst=-1.;
rotate(angle);
move(center);
return;
}
