An Improved Algorithm of Bi-cubic Triangular Curved Surface-Splicing for Curved Surface Reconstruction Based on Hermite Surface

The technique of curved surface reconstruction is widely applied in different scopes such as computer graphics and has also been a hot spot recently. This article is to introduce an improved algorithm of bi-cubic triangular curved surface-splicing and Hermite surface for computing and remodeling curved surfaces in the topological space. The general expression of Hermite surface Q(u, w) = UM_hBM_h ^TW^T is applied to each triangular surface patch. Through geometric transformation, for the 16 geometric vectors in B matrix, an approximate computation is applied, that is, to approximately regard that the normal line vector of the tangent plane of vertex Q_i(X_i, Y_i, Z_i)over the real object is parallel to the normal lines of the triangle that takes Q_i(X_i, Y_i, Z_i) as a vertex after the unitization. As a result, all geometric and topological information can be obtained. It has been proved by the trial that this algorithm, with a utilization of fewer data points, has a quicker assess to correct topological connection. The computed shape well matches the real ellipsoid, proving its efficiency, reliability and suitability to non-uniform data.