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Construction of intrinsic Delaunay triangulation (iDt for short) on 2-manifolds has attracted considerable attentions recently, due to its theoretical contributions to surface reconstruction. In this paper we analyze a 2-manifold sampling criterion based on iDt in a combinatorial way. The main contribution of this work is to establish the theoretical bounds of iDt mesh quality based on this sampling criterion. In order to construct the iDt mesh from sample points, we propose an approximate iDt mesh reconstruction algorithm using an edge propagation scheme. In real-world point cloud, holes or under sampling regions frequently exist. Based on the sampling criterion, an up sampling scheme and a hole filling algorithm are presented in this paper. Finally examples are presented, illustrating the effectiveness of our proposed algorithms.