operator*(const SGVec2<T>& v, S s)
{ return SGVec2<T>(s*v(0), s*v(1)); }
+/// multiplication as a multiplicator, that is assume that the first vector
+/// represents a 2x2 diagonal matrix with the diagonal elements in the vector.
+/// Then the result is the product of that matrix times the second vector.
+template<typename T>
+inline
+SGVec2<T>
+mult(const SGVec2<T>& v1, const SGVec2<T>& v2)
+{ return SGVec2<T>(v1(0)*v2(0), v1(1)*v2(1)); }
+
+/// component wise min
+template<typename T>
+inline
+SGVec2<T>
+min(const SGVec2<T>& v1, const SGVec2<T>& v2)
+{return SGVec2<T>(SGMisc<T>::min(v1(0), v2(0)), SGMisc<T>::min(v1(1), v2(1)));}
+template<typename S, typename T>
+inline
+SGVec2<T>
+min(const SGVec2<T>& v, S s)
+{ return SGVec2<T>(SGMisc<T>::min(s, v(0)), SGMisc<T>::min(s, v(1))); }
+template<typename S, typename T>
+inline
+SGVec2<T>
+min(S s, const SGVec2<T>& v)
+{ return SGVec2<T>(SGMisc<T>::min(s, v(0)), SGMisc<T>::min(s, v(1))); }
+
+/// component wise max
+template<typename T>
+inline
+SGVec2<T>
+max(const SGVec2<T>& v1, const SGVec2<T>& v2)
+{return SGVec2<T>(SGMisc<T>::max(v1(0), v2(0)), SGMisc<T>::max(v1(1), v2(1)));}
+template<typename S, typename T>
+inline
+SGVec2<T>
+max(const SGVec2<T>& v, S s)
+{ return SGVec2<T>(SGMisc<T>::max(s, v(0)), SGMisc<T>::max(s, v(1))); }
+template<typename S, typename T>
+inline
+SGVec2<T>
+max(S s, const SGVec2<T>& v)
+{ return SGVec2<T>(SGMisc<T>::max(s, v(0)), SGMisc<T>::max(s, v(1))); }
+
/// Scalar dot product
template<typename T>
inline
norm1(const SGVec2<T>& v)
{ return fabs(v(0)) + fabs(v(1)); }
+/// The inf-norm of the vector
+template<typename T>
+inline
+T
+normI(const SGVec2<T>& v)
+{ return SGMisc<T>::max(fabs(v(0)), fabs(v(1))); }
+
/// The euclidean norm of the vector, that is what most people call length
template<typename T>
inline
operator!=(const SGVec2<T>& v1, const SGVec2<T>& v2)
{ return ! (v1 == v2); }
+/// Return true if smaller, good for putting that into a std::map
+template<typename T>
+inline
+bool
+operator<(const SGVec2<T>& v1, const SGVec2<T>& v2)
+{
+ if (v1(0) < v2(0)) return true;
+ else if (v2(0) < v1(0)) return false;
+ else return (v1(1) < v2(1));
+}
+
+template<typename T>
+inline
+bool
+operator<=(const SGVec2<T>& v1, const SGVec2<T>& v2)
+{
+ if (v1(0) < v2(0)) return true;
+ else if (v2(0) < v1(0)) return false;
+ else return (v1(1) <= v2(1));
+}
+
+template<typename T>
+inline
+bool
+operator>(const SGVec2<T>& v1, const SGVec2<T>& v2)
+{ return operator<(v2, v1); }
+
+template<typename T>
+inline
+bool
+operator>=(const SGVec2<T>& v1, const SGVec2<T>& v2)
+{ return operator<=(v2, v1); }
+
/// Return true if equal to the relative tolerance tol
template<typename T>
inline