Fiber path planning to reduce in-plane curvature

A method of planning fiber paths for a composite ply of a composite layup includes determining a first unit vector field. The first unit vector field represents a first approximation of target directions to be followed by tow centerlines of the composite ply. The first unit vector field is determined based on a specified rosette direction, a surface approximation of a nonplanar contoured surface of an object to be formed, and a fiber angle distribution. The method also includes determining, based on specified angle deviation bounds and the first unit vector field, a second unit vector field. The second unit vector field represents a second approximation of the target directions. The second approximation has reduced in-plane curvature relative to the first approximation. The method further includes planning a fiber placement head path for forming the composite ply of the composite layup based on the second unit vector field.