Curve Reconstruction Algorithm Based On Discrete Data Points And Normal Vectors

In many practical problems,curves need be constructed satisfying certain flow field of dynamic constraints.One key problem can be transformed into the curve reconstruction based on discrete data points and normal vectors.The main difficulty of this kind of problem is that the fitting error of discrete data points and the error of normal vector constraints should be taken into account at the same time.Moreover,the problem is an ill-posed problem,which results in that the result of curve reconstruction is greatly affected by data noise.This thesis presents a curve reconstruction algorithm based on discrete data points and normal vectors using the B-splines.By adding normal constraints,this method can still keep good fitting results when the data noise is large.This method consists of four steps: parameterization of discrete points,selection of B-spline dominant pints,determination of knot vector,and curve fitting based on discrete data point errors and normal vector errors.The proposed approach is different from the previous approaches except for the determination of knot vector.Therefore,we transform the B-spline fitting problem into three sub-problems.Using normal vectors to obtain more precise parameterization,arranging more knots appropriately in the complex regions,and using de Boor's method to select the weight which balances the data point fitting error and normal vector constraint error,we are able to simplify the calculation of the algorithm and obtain B-spline curve adaptively.Compared with other approaches,the B-spline curve reconstructed by our approach can maintain better geometric features of the original curve when the given data set contains high strength noise.