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This paper describes a multi-seeds mesh growing and flat portions first growing algorithm that takes as input an unorganized set of points on an unknown manifold, and produces as output an approximate surface. A priority driven strategy for mesh growing is then used to sweep the advance front ahead in an effective way. The method makes no assumption regarding the points, and the main contributions of the approach are multi-seeds mesh growing and a priority driven based method which forces the mesh growing process to propagate in an efficient way, and a new triangulation method. To demonstrate its efficiency, several 3-D surface reconstruction experiments are presented at the last part.