Point cloud reconstruction is a critical process in 3D representation and reverse engineering. When it comes to CAD models, edges are significant features that play a crucial role in characterizing the geometry of 3D shapes. However, few points are exactly sampled on edges during acquisition, resulting in apparent artifacts for the reconstruction task. Upsampling point cloud is a direct technical route, but there is a main challenge that the upsampled points may not align with the model edge accurately. To overcome this, we develop an integrated framework to estimate edges by joint regression of three geometry features—point-to-edge direction, point-to-edge distance and point normal. Benefiting these features, we implement a novel refinement process to move and produce more points which lie accurately on edges of the model, allowing for high-quality edge-preserving reconstruction. Experiments and comparisons against previous methods demonstrate our method's effectiveness and superiority.