Adaptive B-spline Curve And Surface Fitting Based On Progressive Iterative Approximation

The problem of curve or surface fitting meets frequently in engineering research and practical application.It is a basic technique in the computer vision at the model fitting of the graph.Fitting a curve or surface is applied widely not only in computer graphics but also in CAD/CAM.B-spline have been widely used in computer aided configuration design because of its excellent properties like flexible control,lower number of times and local support.The common method of fitting curve or surface is getting parameterization of the data points first,then solving a system of linear equations with the control points as an unknown variable.In recent years,progressive iterative approximation(PIA)method has received widely attention.This method has obvious geometric significance,can add flexible geometric constraints in the iterative process,and can avoid the problem of solving linear equations in curve and surface fitting,so it has a very broad prospect.In the view of PIA's excellent properties,we develop a new adaptive B-spline curve and surface fitting algorithm based on progressive iterative approximation in this paper.This paper reviews the development of curve and surface fitting and introduces the basic form of parametric curve and surface and the basic properties of B spline.Then,give the PIA form of fitting curve.Achieve the adaptive fitting by constructing appropriate knots vector using dominant points.At last,extend the algorithm into tensor product surface,we use a heuristic method for optimizing the position of knots according to the geometric feature distribution of the input data,and then an initial fitting surface is constructed.Finally,the fitting surface is iteratively updated by inserting new knots vector.In each iteration,a least square progressive iterative approximation is presented,which is the method of constructing the fitting surface,and the weights for updating surface are obtained by solving an energy minimization problem with box constraints iteratively.Several examples show that the algorithm is effective compared with the existing methods.