//Time that will take the point with a given speed to hit a circle
arrow::Vct::Mod tth (const Pnt &p, const arrow::Vct &pv, const Crl &c)
{
//If they are alredy at contact, the tth is 0
if (p.contact(c))
return 0;
else
if(!(pv))//If they are not at contact and the speed is null, they will never meet
return -1;
//Get the distance and the componets of the speed
arrow::Vct d(p.get_center()-c.get_center());
arrow::Vct::Mod dx(d.mod_tan_part(pv));
//Get the a, b and c coefficientes of the second degree ecuation
double
ac=pv.sq_mod(),
bc=2*dx*pv.mod(),
cc=d.sq_mod()-c.get_size()*c.get_size();
//Get the value of the discriminant
double disc=bc*bc-4*ac*cc;
//Check that the 2nd degree equation has solution
if (disc<0)//No solution
return -1;//No contact
else//Has solution
{
//Find the two solutions
double
sol1=(-bc-std::sqrt(disc))/(2*ac),
sol2=(-bc+std::sqrt(disc))/(2*ac);
double sol=std::min(sol1,sol2);//Find the final solution
if (sol<0) return -1;//No contact return value
return sol;
}
}
//Contact between a point and a circle
bool collide (const Crl &c, const Pnt &p)
{
return (c.get_center()-p.get_center()).sq_mod()<=c.get_size()*c.get_size();
}