To address the challenge of rapidly generating the multi-constrained reentry landing footprint for multi-dimensional trans-atmospheric morphing vehicles, a rapid generation method is proposed by integrating virtual point approximation with an hp-adaptive Gauss pseudospectral method. The method first decomposes the complex problem of footprint boundary determination into a series of optimal trajectory generation subproblems targeting virtual points, which effectively reduces the solution's dimensionality and computational complexity. Subsequently, a segmented Gauss pseudospectral method is employed to transcribe each multi-constrained optimal control problem into a nonlinear programming problem, efficiently solving for reentry trajectories of vehicles with simultaneous span-extension and sweep-angle morphing capabilities. Furthermore, high-quality initial guesses are generated by leveraging the distribution of these virtual points, which significantly enhances the algorithm's convergence speed. Simulation results demonstrate that the proposed method significantly improves both the generation efficiency and convergence for the reachable footprint, providing an efficient analysis tool for the mission planning and performance evaluation of morphing vehicles.