A new approach for the rapid and robust surface reconstruction from a point cloud is presented based on the distance field and the least-squares projection (LSP) algorithm. This novel approach works directly on the point cloud without any explicit or implicit surface reconstruction procedure. First, a coarse base polygonal model was created directly from the distance field for the given point cloud through the iso-surface extraction. After acquiring a rough base polygonal model, we obtain a quality polygonal model through the iterative refinement and least-squares projection which projects current working polygonal model onto the point cloud in a least-squares sense. The main contribution of this work is the robust and fast surface reconstruction from randomly scattered 3D points only without any further information. We demonstrate the validity and efficiency of this new approach through a number of application examples.