On the normal vector estimation for point cloud data from smooth surfaces

Reliable estimation of the normal vector at a discrete data point in a scanned cloud data set is essential to the correct implementation of modern CAD/CAM technologies when the continuous CAD model representation is not available. A new method based on fitted directional tangent vectors at the data point has been developed to determine its normal vector. A local Voronoi mesh, based on the 3D Voronoi diagram and the proposed mesh growing heuristic rules, is first created to identify the neighboring points that characterize the local geometry. These local Voronoi mesh neighbors are used to fit a group of quadric curves through which the directional tangent vectors are obtained. The normal vector is then determined by minimizing the variance of the dot products between a normal vector candidate and the associated directional tangent vectors. Implementation results from extensive simulated and practical point cloud data sets have demonstrated that the present method is robust and estimates normal vectors with reliable consistency in comparison with the existing plane fitting, quadric surface fitting, triangle-based area weighted average, and triangle-based angle weighted average methods.