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This paper presents a solution for globally optimized trajectory planning with respect to the shortest distance for multicopters, particularly in two dimensional space to avoid restricted airspaces. The presented approach relies on a sparse visibility-graph, a classic roadmap of combinatorial planning in computer geometry which is able to retain the complete-feature of the algorithm. The set of restricted airspaces is seen as a set of obstacles and to build a sparse visibility-graph based on tangents between obstacles, the proposed method takes O(n + h2logn), in which h is the number of obstacles with n vertices in total. The developed technique here outperforms the original method, which is demonstrated by without the data structure of balanced tree and without trigonometric functions, whereas still keeping the computation and storage complexity unchanged as previous studies. Through extensive experimental results, with a real multicopter system, the approach indicates to be efficient, feasible and straightforward to apply into practice.