A method of determining fibers paths for a composite ply includes generating a triangulated surface of the composite ply, and defining a first unit vector field establishing a 0-degree direction for the triangulated surface. A second unit vector field is defined by rotating, through specified fiber angles measured relative to the 0-degree direction, the first unit vector field about surface normals of the triangulated surface. A third unit vector field representing a gradient direction of a potential function is defined by rotating the second unit vector field over 90° about the respective surface normals. The third unit vector field is scaled to create a non-unit vector field, and a first potential function is determined by performing a least-squares fit such that the direction and magnitude of the gradient best approximate the direction and the magnitude of the non-unit vector field. A normalization of the potential function uniformly distributes contour lines of the potential function across the triangulated surface. The contour lines are used as fiber paths for laying up courses of composite material to fabricate the composite ply. |