<p>Automated fiber placement (AFP) enables the efficient fabrication of fiber-reinforced composites. However, the complex geometries of aircraft components often require fiber directions with variable angles, complicating the simultaneous satisfaction of three key manufacturing constraints in AFP path planning: path alignment, path parallelism and path curvature. To address it, a field-based partition framework is developed via singularity construction. First, the vector heat method smooths fiber directions to reduce geodesic curvature. Then, benefiting from the singularities that are constructed by eliminating the vector curl, the ply surface is partitioned from the singularities into patches with improved parallelism of each patch’s vector field. The final laying paths are generated on each partition by parallel offsetting the initial path that comprehensively considers fiber directions over the partition. Compared with the exiting path planning strategy, the proposed method finds higher-quality tow paths with enhanced fiber alignment, lower curvature, fewer partitions and full tow coverage, providing a new paradigm for AFP path planning on complex surfaces.</p>