Space curve of the 3rd order. 
Onebranch space curve of the 4th order. 
Twobranch space curve of the 4th order. 
Let \(k\) be the intersection curve of the surfaces \(\Phi\) and \(\Psi\) and let the point \(T\in k\) be a regular point on \(\Phi\) and \(\Psi\). if and only if the surfaces \(\Phi\) and \(\Psi\) have a common tangent plane in that point. 


Tangent line of an intersection curveThe tangent plane of a surface contains the tangent lines of all curves that lie on that surface, so we conclude the following:intersection line of the tangent planes of the surfaces in that point. 
Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja  3DGeomTeh  Developing project of the University of Zagreb