Question

Given the following class

template <typename T>
class Plane
{
public:
    Plane<T>(T A, T B, T C, const Vector3<T>& vec):
        A(A),
        B(B),
        C(C),
        D(-1*A*vec.x-B*vec.y-C*vec.z)
    {

    }

    Plane<T>():
        A(0),
        B(0),
        C(0),
        D(0)
    {

    }


    bool CalculateTime(const Vector3<T>& r0,  const Vector3<T>& rd, T& result )
    {
        Vector3<T> vec(A,B,C);

        if ( vec.dot(rd))
        {
            result = -1;
            return false;
        }
        else
        {
            result = (vec.dot(r0) + D)/vec.dot(rd);
            return true;
        }
    }

    T A;
    T B;
    T C;
    T D;
};

For some strange reason when I do the following

    std::set<Plane<float> > s;
    s.insert(Plane<float>(10,20,30,Vector3f(10,30,40)));

this produced a massive error

1>          with
1>          [
1>              T=float
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\xtree(2245) : see declaration of 'std::operator <'
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\xstddef(179) : while compiling class template member function 'bool std::less<_Ty>::operator ()(const _Ty &,const _Ty &) const'
1>          with
1>          [
1>              _Ty=Plane<float>
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\xutility(559) : see reference to function template instantiation 'bool std::less<_Ty>::operator ()(const _Ty &,const _Ty &) const' being compiled
1>          with
1>          [
1>              _Ty=Plane<float>
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\type_traits(743) : see reference to class template instantiation 'std::less<_Ty>' being compiled
1>          with
1>          [
1>              _Ty=Plane<float>
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\xtree(1028) : see reference to class template instantiation 'std::is_empty<_Ty>' being compiled
1>          with
1>          [
1>              _Ty=std::less<Plane<float>>
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\set(44) : see reference to class template instantiation 'std::_Tree<_Traits>' being compiled
1>          with
1>          [
1>              _Traits=std::_Tset_traits<Plane<float>,std::less<Plane<float>>,std::allocator<Plane<float>>,false>
1>          ]
1>          c:\users\awesome2\google drive\university\eng 3gc3\assignment 3\voxelmodeler\voxelmodeler\voxelcube.h(44) : see reference to class template instantiation 'std::set<_Kty>' being compiled
1>          with
1>          [
1>              _Kty=Plane<float>
1>          ]
1>c:\program files (x86)\microsoft visual studio 11.0\vc\include\xstddef(180): error C2784: 'bool std::operator <(const std::move_iterator<_RanIt> &,const std::move_iterator<_RanIt2> &)' : could not deduce template argument for 'const std::move_iterator<_RanIt> &' from 'const Plane<T>'
1>          with
1>          [
1>              T=float
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\xutility(1983) : see declaration of 'std::operator <'
1>c:\program files (x86)\microsoft visual studio 11.0\vc\include\xstddef(180): error C2784: 'bool std::operator <(const std::reverse_iterator<_RanIt> &,const std::reverse_iterator<_RanIt2> &)' : could not deduce template argument for 'const std::reverse_iterator<_RanIt> &' from 'const Plane<T>'
1>          with
1>          [
1>              T=float
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\xutility(1259) : see declaration of 'std::operator <'
1>c:\program files (x86)\microsoft visual studio 11.0\vc\include\xstddef(180): error C2784: 'bool std::operator <(const std::_Revranit<_RanIt,_Base> &,const std::_Revranit<_RanIt2,_Base2> &)' : could not deduce template argument for 'const std::_Revranit<_RanIt,_Base> &' from 'const Plane<T>'
1>          with
1>          [
1>              T=float
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\xutility(1075) : see declaration of 'std::operator <'
1>c:\program files (x86)\microsoft visual studio 11.0\vc\include\xstddef(180): error C2784: 'bool std::operator <(const std::pair<_Ty1,_Ty2> &,const std::pair<_Ty1,_Ty2> &)' : could not deduce template argument for 'const std::pair<_Ty1,_Ty2> &' from 'const Plane<T>'
1>          with
1>          [
1>              T=float
1>          ]
1>          c:\program files (x86)\microsoft visual studio 11.0\vc\include\utility(232) : see declaration of 'std::operator <'
1>c:\program files (x86)\microsoft visual studio 11.0\vc\include\xstddef(180): error C2676: binary '<' : 'const Plane<T>' does not define this operator or a conversion to a type acceptable to the predefined operator
1>          with
1>          [
1>              T=float
1>          ]

Answer 1

The set (as multiset, map and multimap) need a comparision function, or operator. When not specified set, multiset, map and multimap use the std::less functior object to ordinate elements in the set.
So you have to write something like this

template <typename T>
class Plane {
public:
    friend bool operator < (const Plane<T>& p1, const Plane<T>& p2)
    {
         return ???
    }
};

As you can see is not a good a class like Plane in a set, maybe is better an unordered_set or simply a std::vector