Anisotropic spreading of liquids and elongated droplet shapes are often encountered on surfaces decorated with a periodic micropattern of linear surface topographies. Numerical calculations and wetting experiments show that the shape evolution of droplets that are slowly growing on a surface with parallel grooves can be grouped into two distinct morphological regimes. In the first regime, the liquid of the growing droplet spreads only into the direction parallel to the grooves. In the second regime, the three-phase contact line advances also perpendicular to the grooves, whereas the growing droplets approach a scale-invariant shape. Here, we demonstrate that shapes of droplets in contact with a large number of linear grooves are identical to the shapes of droplets confined to a plane chemical stripe, where this mapping of shapes is solely based on the knowledge of the cross section of the linear grooves and the material contact angle. The spectrum of interfacial shapes on the chemical stripe can be exploited to predict the particular growth mode and the asymptotic value of the base eccentricity in the limit of droplets covering a large number of grooves. The proposed model shows an excellent agreement with experimentally observed base eccentricities for droplets on grooves of various cross sections. The universality of the model is underlined by the accurate match with available literature data for droplet eccentricities on parallel chemical stripes.