<p>Optimization-based planner of parking path has been widely studied due to the ability to provide the optimal path for different parking scenarios. However, environmental changes during the parking process impose higher demands on the real-time performance. To address this, the geometric characteristics of the shortest path are analyzed through numerical simulations, which are subsequently used to formulate the parking path planning task as a nonlinear programming problem with sparse discretization points. In addition, to further reduce the number of nonlinear inequality constraints, a new collision avoidance function is established based on the theoretical analysis of the geometric relationship between the circular curves and obstacle boundary lines. It can ensure that the planned path is completely collision-free by evaluating the constraint function for collision avoidance only at the endpoints of the circular curves. Several comparative simulations are conducted to verify the comprehensive performance of the proposed planner of parking path, including length, computation time, and terminal pose. Moreover, the improvement in computation efficiency is statistically analyzed across different parking spaces and dynamic environments.</p>