bool RS_ActionDrawCircleTan3::preparePreview(){
if(getStatus() != SetCenter || valid==false) {
valid=false;
return false;
}
//find the nearest circle
size_t index=candidates.size();
double dist=RS_MAXDOUBLE*RS_MAXDOUBLE;
for(size_t i=0;i<candidates.size();++i){
preview->addEntity(new RS_Point(preview.get(), RS_PointData(candidates.at(i)->center)));
double d;
RS_Circle(nullptr, *candidates.at(i)).getNearestPointOnEntity(coord,false,&d);
double dCenter=coord.distanceTo(candidates.at(i)->center);
d=std::min(d,dCenter);
if(d<dist){
dist=d;
index=i;
}
}
if( index<candidates.size()){
cData=candidates.at(index);
valid=true;
}else{
valid=false;
}
return valid;
}
QList<RS_Circle> RS_Circle::createTan3(const QVector<RS_AtomicEntity*>& circles)
{
QList<RS_Circle> ret;
if(circles.size()!=3) return ret;
QList<RS_Circle> cs;
for(unsigned short i=0;i<3;i++){
cs<<RS_Circle(NULL,RS_CircleData(circles.at(i)->getCenter(),circles.at(i)->getRadius()));
}
unsigned short flags=0;
do{
ret.append(solveAppolloniusSingle(cs));
flags++;
unsigned short j=0;
for(unsigned short i=1u;i<=4u;i<<=1){
if(flags & i) {
cs[j].setRadius( - fabs(cs[j].getRadius()));
}else{
cs[j].setRadius( fabs(cs[j].getRadius()));
}
j++;
}
}while(flags<8u);
// std::cout<<__FILE__<<" : "<<__FUNCTION__<<" : line "<<__LINE__<<std::endl;
// std::cout<<"before testing, ret.size()="<<ret.size()<<std::endl;
for(int i=0;i<ret.size();){
if(ret[i].testTan3(circles) == false) {
ret.erase(ret.begin()+i);
}else{
i++;
}
}
// std::cout<<"after testing, ret.size()="<<ret.size()<<std::endl;
return ret;
}
std::vector<RS_Circle> RS_Circle::createTan3(const std::vector<RS_AtomicEntity*>& circles)
{
std::vector<RS_Circle> ret;
if(circles.size()!=3) return ret;
std::vector<RS_Circle> cs;
for(auto c: circles){
cs.emplace_back(RS_Circle(nullptr, {c->getCenter(),c->getRadius()}));
}
unsigned short flags=0;
do{
for(unsigned short j=0u;j<3u;++j){
if(flags & (1u<<j)) {
cs[j].setRadius( - fabs(cs[j].getRadius()));
}else{
cs[j].setRadius( fabs(cs[j].getRadius()));
}
}
// RS_DEBUG->print(RS_Debug::D_ERROR, "flags=%d\n",flags);
auto list=solveAppolloniusSingle(cs);
if(list.size()>=1){
for(RS_Circle& c0: list){
bool addNew=true;
for(RS_Circle& c: ret){
if((c0.getCenter()-c.getCenter()).squared()<RS_TOLERANCE15 && fabs(c0.getRadius() - c.getRadius())<RS_TOLERANCE){
addNew=false;
break;
}
}
if(addNew) ret.push_back(c0);
}
}
}while(++flags<8u);
// std::cout<<__FILE__<<" : "<<__func__<<" : line "<<__LINE__<<std::endl;
// std::cout<<"before testing, ret.size()="<<ret.size()<<std::endl;
for(size_t i=0;i<ret.size();){
if(ret[i].testTan3(circles) == false) {
ret.erase(ret.begin()+i);
}else{
++i;
}
}
// DEBUG_HEADER
// std::cout<<"after testing, ret.size()="<<ret.size()<<std::endl;
return ret;
}
bool RS_ActionDrawCircleTan3::getData(){
if(getStatus() != SetCircle3) return false;
//find the nearest circle
int i=0;
for(i=0;i<circles.size();i++)
if(circles[i]->rtti() == RS2::EntityLine) break;
candidates.clear();
if(i<circles.size() && circles[i]->rtti() == RS2::EntityLine){
LC_Quadratic lc0(circles[i],circles[(i+1)%3]);
LC_Quadratic lc1(circles[i],circles[(i+2)%3]);
auto&& sol=LC_Quadratic::getIntersection(lc0,lc1);
double d;
//line passes circle center, need a second parabola as the image of the line
for(int j=1;j<=2;j++){
if(circles[(i+j)%3]->rtti() == RS2::EntityCircle){
circles[i]->getNearestPointOnEntity(circles[(i+j)%3]->getCenter(),
false,&d);
if(d<RS_TOLERANCE) {
LC_Quadratic lc2(circles[i],circles[(i+j)%3], true);
sol.appendTo(LC_Quadratic::getIntersection(lc2,lc1));
}
}
}
for(size_t j=0;j<sol.size();j++){
circles[i]->getNearestPointOnEntity(sol[j],false,&d);
RS_CircleData data(sol[j],d);
// DEBUG_HEADER();
// std::cout<<sol[j]<<" r="<<d<<std::endl;
if(circles[(i+1)%3]->isTangent(data)==false) continue;
if(circles[(i+2)%3]->isTangent(data)==false) continue;
candidates<<RS_Circle(NULL,data);
}
}else{
RS_Circle c(NULL,cData);
candidates=c.createTan3(circles);
}
valid = ( candidates.size() >0);
return valid;
}
bool RS_ActionDrawCircleTan3::getData(){
if(getStatus() != SetCircle3) return false;
//find the nearest circle
int i=0;
for(;i<circles.size();++i)
if(circles[i]->rtti() == RS2::EntityLine) break;
candidates.clear();
const int i1=(i+1)%3;
const int i2=(i+2)%3;
if(i<circles.size() && circles[i]->rtti() == RS2::EntityLine){
LC_Quadratic lc0(circles[i],circles[i1],false);
LC_Quadratic lc01(circles[i],circles[i1],true);
LC_Quadratic lc1;
RS_VectorSolutions sol;
//detect degenerate case two circles with the same radius
if(circles[i1]->rtti()== RS2::EntityCircle &&
circles[i2]->rtti()== RS2::EntityCircle
){
RS_Circle* c1=static_cast<RS_Circle*>(circles[i1]);
RS_Circle* c2=static_cast<RS_Circle*>(circles[i2]);
if(fabs(fabs(c1->getRadius())-fabs(c2->getRadius()))<RS_TOLERANCE){
//degenerate
const RS_Vector p0=(c1->getCenter()+c2->getCenter())*0.5;
const RS_Vector p1=p0 + (c1->getCenter() - p0).rotate(0.5*M_PI);
lc1=RS_Line(NULL, RS_LineData(p0,p1 )).getQuadratic();
sol=LC_Quadratic::getIntersection(lc0,lc1);
sol.appendTo(LC_Quadratic::getIntersection(lc01,lc1));
lc1=RS_Line(NULL, RS_LineData(c1->getCenter(),c1->getCenter())).getQuadratic();
sol.appendTo(LC_Quadratic::getIntersection(lc0,lc1));
sol.appendTo(LC_Quadratic::getIntersection(lc01,lc1));
}
}
if(sol.size()==0) {
switch(circles[i2]->rtti()){
case RS2::EntityCircle:
lc1=LC_Quadratic(circles[i],circles[i2], true);
sol.appendTo(LC_Quadratic::getIntersection(lc01,lc1));
if(circles[i1]->rtti()== RS2::EntityCircle )
sol.appendTo(LC_Quadratic::getIntersection(lc01,lc1));
//there's no break, because the default part would be run for circles as well
default:
lc1=LC_Quadratic(circles[i],circles[i2]);
sol.appendTo(LC_Quadratic::getIntersection(lc01,lc1));
if(circles[i1]->rtti()== RS2::EntityCircle )
sol.appendTo(LC_Quadratic::getIntersection(lc01,lc1));
}
}
double d;
//line passes circle center, need a second parabola as the image of the line
for(int j=1;j<=2;j++){
if(circles[(i+j)%3]->rtti() == RS2::EntityCircle){
circles[i]->getNearestPointOnEntity(circles[(i+j)%3]->getCenter(),
false,&d);
if(d<RS_TOLERANCE) {
LC_Quadratic lc2(circles[i],circles[(i+j)%3], true);
sol.appendTo(LC_Quadratic::getIntersection(lc2,lc1));
}
}
}
//clean up duplicate and invalid
RS_VectorSolutions sol1;
for(size_t j=0; j<sol.size(); ++j){
const RS_Vector&& vp=sol.at(j);
if(vp.magnitude()>RS_MAXDOUBLE) continue;
if(sol1.size())
if(sol1.getClosestDistance(vp)<RS_TOLERANCE) continue;
sol1.push_back(vp);
}
for(size_t j=0;j<sol1.size();j++){
circles[i]->getNearestPointOnEntity(sol1[j],false,&d);
RS_CircleData data(sol1[j],d);
if(circles[(i+1)%3]->isTangent(data)==false) continue;
if(circles[(i+2)%3]->isTangent(data)==false) continue;
candidates<<RS_Circle(NULL,data);
}
}else{
RS_Circle c(NULL,cData);
candidates=c.createTan3(circles);
}
valid = ( candidates.size() >0);
return valid;
}
/** solve one of the eight Appollonius Equations
| Cx - Ci|^2=(Rx+Ri)^2
with Cx the center of the common tangent circle, Rx the radius. Ci and Ri are the Center and radius of the i-th existing circle
**/
QList<RS_Circle> RS_Circle::solveAppolloniusSingle(const QList<RS_Circle>& circles)
{
// std::cout<<__FILE__<<" : "<<__FUNCTION__<<" : line "<<__LINE__<<std::endl;
// for(int i=0;i<circles.size();i++){
//std::cout<<"i="<<i<<"\t center="<<circles[i].getCenter()<<"\tr="<<circles[i].getRadius()<<std::endl;
// }
QList<RS_Circle> ret;
QList<RS_Vector> centers;
QList<double> radii;
for(size_t i=0;i<3;i++){
if(circles[i].getCenter().valid==false) return ret;
centers.push_back(circles[i].getCenter());
radii.push_back(fabs(circles[i].getRadius()));
}
/** form the linear equation to solve center in radius **/
QVector<QVector<double> > mat(2,QVector<double>(3,0.));
mat[0][0]=centers[2].x - centers[0].x;
mat[0][1]=centers[2].y - centers[0].y;
mat[1][0]=centers[2].x - centers[1].x;
mat[1][1]=centers[2].y - centers[1].y;
if(fabs(mat[0][0]*mat[1][1] - mat[0][1]*mat[1][0])<RS_TOLERANCE*RS_TOLERANCE){
// DEBUG_HEADER();
// std::cout<<"The provided circles are in a line, not common tangent circle"<<std::endl;
size_t i0=0;
if( centers[0].distanceTo(centers[1]) <= RS_TOLERANCE || centers[0].distanceTo(centers[2]) <= RS_TOLERANCE) i0 = 1;
LC_Quadratic lc0(& (circles[i0]), & (circles[(i0+1)%3]));
LC_Quadratic lc1(& (circles[i0]), & (circles[(i0+2)%3]));
auto&& c0 = LC_Quadratic::getIntersection(lc0, lc1);
// qDebug()<<"c0.size()="<<c0.size();
for(size_t i=0; i<c0.size(); i++){
const double dc = c0[i].distanceTo(centers[i0]);
ret<<RS_Circle(NULL, RS_CircleData(c0[i], fabs(dc - radii[i0])));
if( dc > radii[i0]) {
ret<<RS_Circle(NULL, RS_CircleData(c0[i], dc + radii[i0]));
}
}
return ret;
}
// r^0 term
mat[0][2]=0.5*(centers[2].squared()-centers[0].squared()+radii[0]*radii[0]-radii[2]*radii[2]);
mat[1][2]=0.5*(centers[2].squared()-centers[1].squared()+radii[1]*radii[1]-radii[2]*radii[2]);
std::cout<<__FILE__<<" : "<<__FUNCTION__<<" : line "<<__LINE__<<std::endl;
for(unsigned short i=0;i<=1;i++){
std::cout<<"eqs P:"<<i<<" : "<<mat[i][0]<<"*x + "<<mat[i][1]<<"*y = "<<mat[i][2]<<std::endl;
}
// QVector<QVector<double> > sm(2,QVector<double>(2,0.));
QVector<double> sm(2,0.);
if(RS_Math::linearSolver(mat,sm)==false){
return ret;
}
RS_Vector vp(sm[0],sm[1]);
// std::cout<<__FILE__<<" : "<<__FUNCTION__<<" : line "<<__LINE__<<std::endl;
// std::cout<<"vp="<<vp<<std::endl;
// r term
mat[0][2]= radii[0]-radii[2];
mat[1][2]= radii[1]-radii[2];
// for(unsigned short i=0;i<=1;i++){
// std::cout<<"eqs Q:"<<i<<" : "<<mat[i][0]<<"*x + "<<mat[i][1]<<"*y = "<<mat[i][2]<<std::endl;
// }
if(RS_Math::linearSolver(mat,sm)==false){
return ret;
}
RS_Vector vq(sm[0],sm[1]);
// std::cout<<"vq="<<vq<<std::endl;
//form quadratic equation for r
RS_Vector dcp=vp-centers[0];
double a=vq.squared()-1.;
if(fabs(a)<RS_TOLERANCE*1e-4) {
return ret;
}
std::vector<double> ce(0,0.);
ce.push_back(2.*(dcp.dotP(vq)-radii[0])/a);
ce.push_back((dcp.squared()-radii[0]*radii[0])/a);
std::vector<double>&& vr=RS_Math::quadraticSolver(ce);
for(size_t i=0; i < vr.size();i++){
if(vr.at(i)<RS_TOLERANCE) continue;
ret<<RS_Circle(NULL,RS_CircleData(vp+vq*vr.at(i),vr.at(i)));
}
// std::cout<<__FILE__<<" : "<<__FUNCTION__<<" : line "<<__LINE__<<std::endl;
// std::cout<<"Found "<<ret.size()<<" solutions"<<std::endl;
return ret;
}