Integral Surface Reconstruction Method Based On Manifolds

Surface reconstruction is the key technology in reverse engineering.It is a random distribution of three-dimensional space acquired by equipment.The irregular point cloud data reconstructs continuous surface,which is widely used in industrial,commercial,entertainment,medical and other fields.At present,the method of reconstructing surface is very diverse,and the NURBS method has been widely applied,because it can accurately represent all kinds of surfaces from rules to free.In practical applications,complex models with arbitrary topologies are generally constructed by splicing the whole surface,and then splicing them to form the final surface.However,the smooth splicing between NURBS patches is complicated to achieve second or third order smoothness,and the reconstruction of complex surface models with arbitrary topologies is time consuming and has some limitations.In order to avoid the complex surface splicing operation of the NURBS method,the differential manifolds in the topology are introduced into the complex process of surface reconstruction.The differential manifold is used to describe the geometric form in mathematics,which is a space with Euclidean space property.It transforms the unstructured point cloud into the point cloud data with certain topological structure,and uses the local structural features to reflect the original point cloud data characteristics of the information,and through the mapping to reflect the corresponding relationship between local data.In this paper,based on the differential manifold theory and surface reconstruction method,the surface reconstruction method of complex physical surface model with scattered point cloud is studied.The main work is as follows:Firstly,the HandySCAN 700 three-dimensional hand-held laser scanner is used to obtain the 3D point cloud information of the object.And then combined with the curvature and normal vector to simply,and the feature points are preserved at the same time.Secondly,in order to avoid the complex splicing operation of the NURBS method,the rectangle domain of the NURBS is extended to the differential manifold.Through the localized parameterization the potential functions construct the basis function on the domain.Finally,the basis function is normalized to obtain the unit decomposition on the differential manifold,the composite control vertex and the unit decomposition on the differential manifold to achieve the surface reconstruction.This method has a significant improvement in the precision and efficiency of the physical model of any topology.