operator*(const SGVec4<T>& v, S s)
{ return SGVec4<T>(s*v(0), s*v(1), s*v(2), s*v(3)); }
+/// multiplication as a multiplicator, that is assume that the first vector
+/// represents a 4x4 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
+SGVec4<T>
+mult(const SGVec4<T>& v1, const SGVec4<T>& v2)
+{ return SGVec4<T>(v1(0)*v2(0), v1(1)*v2(1), v1(2)*v2(2), v1(3)*v2(3)); }
+
/// component wise min
template<typename T>
inline
operator!=(const SGVec4<T>& v1, const SGVec4<T>& v2)
{ return ! (v1 == v2); }
+/// Return true if smaller, good for putting that into a std::map
+template<typename T>
+inline
+bool
+operator<(const SGVec4<T>& v1, const SGVec4<T>& v2)
+{
+ if (v1(0) < v2(0)) return true;
+ else if (v2(0) < v1(0)) return false;
+ else if (v1(1) < v2(1)) return true;
+ else if (v2(1) < v1(1)) return false;
+ else if (v1(2) < v2(2)) return true;
+ else if (v2(2) < v1(2)) return false;
+ else return (v1(3) < v2(3));
+}
+
+template<typename T>
+inline
+bool
+operator<=(const SGVec4<T>& v1, const SGVec4<T>& v2)
+{
+ if (v1(0) < v2(0)) return true;
+ else if (v2(0) < v1(0)) return false;
+ else if (v1(1) < v2(1)) return true;
+ else if (v2(1) < v1(1)) return false;
+ else if (v1(2) < v2(2)) return true;
+ else if (v2(2) < v1(2)) return false;
+ else return (v1(3) <= v2(3));
+}
+
+template<typename T>
+inline
+bool
+operator>(const SGVec4<T>& v1, const SGVec4<T>& v2)
+{ return operator<(v2, v1); }
+
+template<typename T>
+inline
+bool
+operator>=(const SGVec4<T>& v1, const SGVec4<T>& v2)
+{ return operator<=(v2, v1); }
+
/// Return true if equal to the relative tolerance tol
template<typename T>
inline