Geodesic
Planar diagrams of surface-links
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 165-186

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The paper discusses planar diagrams (called charts by S. Kamada) for embedded (in $\Re^{4}$) or mapped in general position (in $\Re^{3}$) surfaces and shows that the diagrams are very suitable for dealing with such surfaces and for easy construction of surface mappings with specific properties. A series of examples is constructed, including an example of a sphere immersion with two triple points and a unique double line. 
@article{ZNSL_2018_476_a12,
     author = {A. V. Tikhonov},
     title = {Planar diagrams of surface-links},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {165--186},
     publisher = {mathdoc},
     volume = {476},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a12/}
}
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A. V. Tikhonov. Planar diagrams of surface-links. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 165-186. http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a12/