great_circle::arc great_circle::arc::shortest_path( const coordinates &c ) const
{
Eigen::Vector3d cc(c.to_cartesian());
if (angle() == 0) { return arc(cc, begin()); }
if (has_inside(c)) { return arc(cc, cc); }
Eigen::Vector3d n = end() - begin();
Eigen::Vector3d p((n*(n.dot(cc - begin())))/n.dot(n) + begin());
boost::optional< coordinates > t = intersection_with(arc(p, cc));
if (! t)
{
arc a1(cc, begin());
arc a2(cc, end());
return a1.angle() < a2.angle() ? a1 : a2;
}
return arc(cc, *t);
}
bool intersects(range<U> const& b) const {
return static_cast<bool>(intersection_with(b));
}
