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A new algorithm is proposed for triangular mesh reconstruction from 3D scattered points based on the existing intrinsic property driven (IPD) method. The improvements include a new approach to determine the seed triangle, a new approach to define the influence region for active edge, and a new approach to select the best active point. The new triangle is also tested with the constraint of geometric integrity. Our algorithm has been tested on some unorganized 3D point clouds. From the experimental results it can be found that our approach has the ability to generate more accurate details in the recovered surfaces.