Fitting And Interpolation For Curve And Surface From Scattered Data Using Moving Least Squares Method

Reverse Engineering (RE) is important research areas in CAD/CAM. Surface reconstruction is the key problem of RE. For several decades of year, research methods on surface reconstruction make a great step. With the development of computer technology and measurement technology, scattered point method has been greatly improved in recent years. Moving Least Square (MLS) method, due to the advantages of meshless, local fitting (or interpolation) and high accuracy characters, is suitable for scattered point data, and has become an increasing hot subject of research.In this paper, Moving Least Square (MLS) method for the cases of linear and quadric basis functions are studied and applied to curve (or surface) fitted (or interpolation) based on scattered points data.In this paper, the "scattered factor" was introduced to describe the scattered point model. For various choice of scattered factor、supported domain size、compactly supported weighted function and basis function, we mainly studied their impact on computational accuracy in curve (or surface) fitting (or interpolation). In addition, orthogonal process on basis functions was used in order to avoid the ill-conditioned matrix problem and save computational time.MLS method not only can be applied for the purpose of curve (or surface) fitting, but also curve (or surface) interpolation when compactly supported singular weighted function was used. The effective measure has been applied to eliminate singularity in MLS interpolation. In addition, the bad fitting or interpolation accuracy near the boundary was improved.Many numerical examples of curve (or surface) fitting (or interpolation) were given in this paper. The numerical results show that MLS is of good adaptability to distribution and shape of scattered points data, and the properties of flexible adjustability on parameters such as weight function and basis function which could be improve high numerical precision and smoothness in the complex curve (or surface) modeling. In addition, Its local fitting or interpolation is very potential compared with the other total method. In a word, MLS method is a potential method in curve (or surface) fitting (or interpolation) in the future.