Laser-based surface modification methods have attracted considerable interest in the last 20 years due to their flexibility, efficiency, and multiple technical application that are possible. A particular challenge for these methods is the treatment of curved 3D surfaces. The presented study reports on the process optimization in laser texturing of 3D surfaces using Direct Laser Interference Patterning (DLIP). Periodic line-like structures are fabricated using a picosecond-pulsed laser on spherical stainless-steel parts. The aim is to identify the possibility of processing curved geometries using an innovative hexapod positioning system. For this purpose, the effect of two different structuring strategies is investigated and compared by evaluating the obtained structure depths and the structure period of the fabricated structures as function of the position over the samples. All treated surfaces are examined using a confocal microscope. The results demonstrate an improvement in the structure homogeneity in terms of structure depth and period when using the fitted hexapod positioning approach.