Actually, they do give a comprehensive analysis of infection points and singularities for the cubic polynomial segment with given endpoints, tangents and magnit

Actually, they do give a comprehensive analysis of infection points and singularities for the cubic polynomial segment with given endpoints, tangents and magnitudes. There's a diagram of square with some (maybe superficial) similarity to the one in "High Accuracy Geometric Hermite Interpolation". Chapter III Parametric Cubic Spline Curves 4 A Theorem Concerning Segments of Parametric Cubic Curves Also, it's based on earlier papers by Su Buqing from around 1977.