Within the context of in-field path planning, and under the assumption of nonholonomic vehicle models, this paper addresses two tasks: smoothing of headland path edges and smoothing of headland-to-mainfield lane transitions. Both tasks are solved by a two-step hierarchical algorithm. The first step differs for the two tasks generating either a piecewise-affine or a Dubins reference path. The second step leverages a transformation of vehicle dynamics from the time domain into the spatial domain and linear programming. Benefits, such as a hyperparameter-free objective function and spatial constraints useful for area coverage gaps avoidance and precision path planning, are discussed. The method, which is a deterministic optimisation-based method, is evaluated on 5 real-world fields solving 19 instances of the first task and 84 instances of the second task.