Vertex normal vector estimation methods for manifold triangular mesh

Manifold triangular mesh acts as the most widely used discrete manner to describe the continuous surfaces for its good topologic adaptability and ability of dealing with free form objects. It can meet the requirement in the fields such as scattered point data process, reverse engineering, medical image process scientific computing visualization and so on. The vertex normal vector of the manifold triangular mesh must be estimated ahead of other differential geometry property and is the necessary condition for surface offset and tool position calculation in multi-axis NC machining. There are several methods presented by different researchers on the vertex normal vector estimation for the time being. But no work has been done on the comparison of such methods. So five precedent methods for vertex normal estimation are reviewed and then a new method is proposed to estimate the vertex normal vector for manifold triangular meshes, which uses the sine value of the angle at the vertex as the weight of each triangular facet normal in the first order neighbor field of the vertex. To determine which of these methods is better, the deviation angle between the theoretic normal vector and the estimated one is made the error evaluation standard factor and the ball and elliptical ball manifold triangular mesh models are used to analyze the performance of all these estimation method. Experiments show that the new way can give the more accurate estimation result.