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In this article we obtain a rigid isotopy classification of generic pointed quartic curves ( A ,  p ) in    $${\mathbb {R}}{\mathbb {P}}^{2}$$  R P 2 by studying the combinatorial properties of dessins. The dessins are real versions, proposed by Orevkov (Ann Fac Sci Toulouse 12(4):517–531, 2003), of Grothendieck’s  dessins d’enfants . This classification contains 20 classes determined by the number of ovals of  A , the parity of the oval containing the marked point  p , the number of ovals that the tangent line    $$T_p A$$  T p A intersects, the nature of connected components of    $$A\setminus T_p A$$  A \ T p A adjacent to  p , and in the maximal case, on the convexity of the position of the connected components of    $$A\setminus T_p A$$  A \ T p A . We study the combinatorial properties and decompositions of dessins corresponding to real uninodal trigonal curves in real ruled surfaces. Uninodal dessins in any surface with non-empty boundary can be decomposed in blocks corresponding to cubic dessins in the disk    $${\mathbf {D}}^2$$  D 2 , which produces a classification of these dessins. The classification of dessins under consideration leads to a rigid isotopy classification of generic pointed quartic curves in    $${\mathbb {R}}{\mathbb {P}}^{2}$$  R P 2 . This classification was first obtained in Rieken (Geometr Ded 185(1):171–203, 2016) based on the relation between quartic curves and del Pezzo surfaces.

Generic pointed quartic curves in $${\mathbb {R}}{\mathbb {P}}^{2}$$ and uninodal dessins