Surface Reconstruction With Sharp Feature Using Matrix Weighted Rational Splines Surface

In the area of computer aided design,surface reconstruction is an important research direction.Not only in traditional CAD industry,but also in popular VR and AR industry,it has an extensive application prosperity.Surface reconstruction means using the sampling points of the physical model or the original mesh surface to reconstruct the mathematical model.The new model is not only good for us to analyze the geometric property of the object,but also convenient for us to do some work on it in the computer.The thesis introduces a method to reconstruct the triangular mesh surfaces by using the matrix weighted rational splines surface.Compared with the traditional method,it not only does not need to compute the control points,but also can maintain the object's sharp feature.Moreover,combined with T-splines,it can reduce the numbers of control points and knots.This thesis can be divided into three parts:1.Introduce the matrix weight and matrix weighted rational splines surface.2.Detect the sharp features of triangular mesh and the parameterization of triangular mesh.In this thesis,we compute the discrete curvature of each vertex of triangular mesh.By analyzing the discrete curvature,we can find out the sharp features of the object.In order to obtain the control point of matrix weighted rational splines surface,we need to parametrize the initial triangular mesh.Considering the calculation and parameterization results,we use harmonic parameterization method.3.Surface reconstruction using matrix weighted rational splines surface.In this part,the processes of surface reconstruction using matrix weighted rational B-splines surface and matrix weighted T-splines surface are given.It includes the method of sampling the control point and setting the corresponding deformation coefficient.In order to preserve the sharp features,resampling control points must be on both sides of the sharp features.Firstly,we make a uniform tensor grid.Then,we do an adaptive adjustment.And,it can be used as the control points of matrix weighted rational B-splines surface.Finaly,we sample a subset from it as the final control points.The experimental results show that,compared with the traditional method,our method is more simple and convenient,and it can be very good to retain the sharp features.