Surface Reconstruction Via Interpolation Constrained By Shapes And Positions Of Triangular B(?)zier Patches

The surface geometric reconstruction is the hot issue in the fields of reverse engineering and computer vision etc.In order to achieve a trade-off between the efficiency and geometric continuity of surface reconstruction,quadratic triangular Bézier surface patches as piecewise parameter models is proposed to construct an approximate G~1 continuous surface interpolated into surface samples and its normal,which can simplify the reconstruction process and improve the efficiency while maintaining approximate G~1 continuity highly.The main research contents and achievements are as follows:(1)In order to robustly estimate the normal of the sample points needed to construct a triangular Bézier surface,we present a weighting normal estimation algorithm for sample points based on bounded Poisson surface as constraint of surface local sample.The Poisson surface is used to approximate this local sample in the Frenet frame of the sample point,and the discrete meshes of the Poisson surface are transformed into bounded form based on the boundary protection area of gain-optimized locale sample,then the surface constraint of the neighborhood of the sample point is builded.In the discrete meshes of bounded Poisson surface,the nearest triangular facet of the sample point is used as the reference facet of the sample point.The vertex normal of the reference facet is estimated based on the vertex neighbor facet regularity and the geodesic distance from the neighbor facet to the vertex,and the weighted summation of the vertices’normals of the reference facet is used to be the estimation results of sample point’s normal.The proposed algorithm is suitable for the sample of complex surface and can robustly deal with the problem of normal estimation of surface samples with noise and non-uniformly sampling,and can provide normal constraints of smooth transition for constructing smooth Bézier surfaces;(2)In order to reduce the number of sample points and improve the efficiency of surface geometry reconstruction,a shape-preserving reduction algorithm for surface samples with local isotropic constraints is proposed.Local samples are constructed which adaptive to sampling density based on the neighborhood relationship between sample points.The distribution of local sample points is analyzed by the normal Gaussian mapping results of sample points.Local samples are isotropized by isotropic segmentation and directional gain.Surface samples are simplified based on isotropic local samples.In order to preserve features,feature points are extracted based on local surface variations.The feature points and non-feature points are simplified by different reduction ratios.The proposed algorithm can reduce the number of sample points,at the same time maintain the shape of the surface with high precision,and improve the efficiency of subsequent surface reconstruction;(3)A shape-position interpolation reconstruction algorithm based on the piecewise quadratic triangular Bézier surface is proposed.The G~1 continuity condition of adjacent quadratic triangular Bézier surface patches is analyzed and deduced,and the geometric constraint conflict in constructing integral G~1 continuity surface with quadratic triangular Bézier surface patches is analyzed.Based on the deduced G~1 continuity condition,the geometric constraint conflict is quantified.Heuristic adjustment of control points was carried out to mitigate geometric constraint conflicts..For the patches that still have large geometric constraint conflict after adjustment,the conflict patches are subdivided by inserting new points,the local degree of freedom is increased,and the continuity of approximate G~1of the surface is improved.The proposed algorithm can simplifies the geometric reconstruction process and improves the reconstruction efficiency while maintaining the high approximation G~1 continuity.