Geodesic
Interpolation with closed parametric quadratic spline curves of class~$C^2$ on the plain
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 251-266.

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In the article the global interpolation by planar closed piecewise parabolic curves with continuous tangent direction and curvature is considered. The problems of existence and uniqueness of such curves are solved for some sets of nodes on the plane. The examples of nonexistence and nonuniqueness are given. 
@article{FPM_1996_2_1_a12,
     author = {A. V. Tomilin},
     title = {Interpolation with closed parametric quadratic spline curves of class~$C^2$ on the plain},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {251--266},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a12/}
}
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A. V. Tomilin. Interpolation with closed parametric quadratic spline curves of class~$C^2$ on the plain. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 251-266. http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a12/