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Rail surface scratching occurs with increasing frequency, seriously threatening the safety of vehicles and humans. Online repair of rail-surface scratches on damaged rails with scratch depths >1 mm is of increased importance, because direct rail-replacement has the disadvantages of long operation time, high manpower and high material costs. Advanced online repair of rail-surface scratch using three-dimensional (3D) metal printing technology such as laser cladding has become an increasing trend, desperately demanding a solution for the fast and precise establishment of a complete closed mesh model of rail-surface scratch data. However, there have only been limited studies on the topic so far. In this paper, the complete closed mesh model is well established based on a novel triangulation algorithm relying on the topological features of the point-cloud model (PCM) of scratch-data, which is obtained by implementing a scratch-data-computation process following a rail-geometric-feature-fused algorithm of random sample consensus (RANSAC) performed on the full rail-surface PCM constructed by 3D laser vision. The proposed method is universal for all types of normal-speed rails in China. Experimental results show that the proposed method can accurately acquire the complete closed mesh models of scratch data of one meter of 50 Kg/m-rails within 1 min. [ABSTRACT FROM AUTHOR]