mirror of https://github.com/CGAL/cgal
105 lines
2.2 KiB
C++
105 lines
2.2 KiB
C++
#ifndef ELLIPSE_H
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#define ELLIPSE_H
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template <class R>
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class Ellipse_2 {
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typedef typename R::Point_2 Point_2;
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typedef typename R::Vector_2 Vector_2;
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typedef typename R::Conic_2 Conic_2;
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Point_2 ce;
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Vector_2 va_, vb_;
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double a_,b_;
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public:
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template <class T>
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Ellipse_2(const CGAL::Min_ellipse_2<T>& me)
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{
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CGAL::Simple_cartesian<double>::Conic_2 co;
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me.ellipse().double_conic(co);
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double a11 = co.r();
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double a12 = co.t()/2.0;
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double a22 = co.s();
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double b1 = co.u();
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double b2 = co.v();
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double c = co.w();
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assert(a11*a22-a12*a12 >= 0);
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double delta = (a11>a22)? a11-a22 : a22-a11;
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if( (delta < 0.00000000001) && (a12 == 0)){
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ce = Point_2(-b1/(2*a11), -b2/(2*a11));
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a_ = b_ = std::sqrt(b1*b1+b2*b2-4*a11*c)/(2*a11);
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va_ = Vector_2(a_, 0);
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vb_ = Vector_2(0, b_);
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return;
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}
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double kden = 2.0*(a12*a12 - a11*a22);
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double k1 = (a22*b1 - a12*b2)/kden;
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double k2 = (a11*b2 - a12*b1)/kden;
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ce = Point_2(k1,k2);
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double mu = 1/(a11*k1*k1 + 2.0*a12*k1*k2 + a22*k2*k2 - c);
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double m11 = mu*a11;
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double m12 = mu*a12;
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double m22 = mu*a22;
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double r = std::sqrt((m11-m22)*(m11-m22) + 4.0*m12*m12);
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double lambda1 = ((m11+m22) + r)/2.0;
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double lambda2 = ((m11+m22) - r)/2.0;
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b_ = 1.0/sqrt(lambda1);
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a_ = 1.0/sqrt(lambda2);
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double omega = 1.0/
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std::sqrt((lambda1-m22)*(lambda1-m22) + m12*m12);
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double u1x = - a_ * omega*m12;
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double u1y = a_ * omega * (lambda1-m22);
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double u2x = b_* omega * (lambda1-m22);
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double u2y = b_* omega*m12;
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va_ = Vector_2(u1x,u1y);
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vb_ = Vector_2(u2x,u2y);
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}
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Point_2 center() const
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{
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return ce;
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}
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double a() const
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{
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return a_;
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}
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double b() const
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{
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return b_;
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}
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double eccentricity() const
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{
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if(a_ == b_){
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return 0;
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}
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return std::sqrt(1.0 - (b_*b_)/(a_*a_));
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}
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const Vector_2& va() const
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{
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return va_;
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}
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const Vector_2& vb() const
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{
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return vb_;
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}
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};
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#endif // ELLIPSE_H
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