In this paper, a new methodology is proposed to enhance the conformal mapping applications in the process of optimum trajectory planning in Terrain Following (TF) and Terrain Avoidance (TA) Flights. The new approach uses the conformal mapping concept as a attener tool to transform the constrained trajectory-planning problem with ight altitude restrictions due to the presence of obstacles into a regenerated problem with no obstacle and minimal height constraints. In this regard, the Schwarz-Christo el theorem was utilized to incorporate the height constraints into the aircraft dynamic equations of motion. The regenerated optimal control problem was then solved by a numerical method, namely the direct Legendre-Gauss-Radau pseudospectral algorithm. A composite performance index of ight time, terrain masking, and aerodynamic control e ort was optimized. Furthermore, to obtain realistic trajectories, the aircraft maximum climb and descent rates were imposed as inequality constraints in the solution algorithm. Several case studies for two-dimensional ight scenarios show the applicability of this approach in TF/TA trajectory planning. Extensive simulations con rm the e ciency of the proposed approach and verify the feasibility of solutions, satisfying all of the constraints underlying the problem.