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Random direction mobility model is commonly used in the simulation-based performance analysis for ad hoc networks. Recent works have shown that the distribution of nodes moving according to random direction is non-uniform. Apparently, the node distribution of the model will influence the accuracy of related researches and simulations. So in this paper, we give some in-depth investigation of random direction, and present a new method using the geometric probability to get the node distribution of random direction mobility. At last several simulations are provided to validate our results.