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Curve And Surface Fitting On Univariate And Bivariate Cubic Spline Space

Posted on:2020-01-31Degree:MasterType:Thesis
Country:ChinaCandidate:T ZhangFull Text:PDF
GTID:2428330590996834Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
The problem of curve and surface fitting meets commonly in academic research and even engineering practice.It is widely used in computer graphics,in the field of CAD(Computer aided design)and CAGD(Computer aided geometric design)application is also very common.Spline function has the advantages of flexible control,low frequency and local support,which makes it widely used in function approximation,CAGD,finite element and shape design.For curve and surface fitting,popular methods are interpolation,the least square and so on.Spline curve fitting based on least square method is the most important method in curve fitting,especially the DOM that adaptive spline curve fitting based on the selection of dominant points.This method can be said to be a representative of both time saving and labor saving in various curve fitting methods.However,the traditional dominant point selection method still lacks certain efficiency and accuracy for the selection of dominant points.Therefore,this paper proposes an improved dominant point selection method,which improves the efficiency of spline curve fitting algorithm based on the dominant point selection.There is a common problem in least square method and interpolation method,that is,large linear equations are needed to be solved,which makes it difficult to calculate when the number of data points is large.The quasi-interpolation method can directly obtain the advantage of approximation without solving large-scale linear equations,which makes it play a very important role in approximation theory and its application.Therefore,in the aspect of surface fitting,this paper proposes a surface fitting algorithm based on multi-layer spline quasiinterpolation method.This algorithm does not need to solve large linear equations,which greatly simplifies the difficulty of calculation and is very convenient for engineering applications.The specific research work arrangement of this paper is as follows.In chapter 1,the history of curve and surface fitting is reviewed.In chapter 2,some basic methods and theories of curve and surface fitting are described,and the theorical framework of unitary spline space and multivariate spine space is introduced in detail.In chapter 3,this paper makes some changes to the traditional method of the selection of dominant point in the DOM method,and applies the new dominant point election method to the original DOM method,using the unary cubic spline function to carry out the adaptive least square spline fitting of the curve.Several typical examples show that this algorithm is more accurate and efficient than the traditional least square fitting method.Finally,in chapter 4,an adaptive multi-layer surface fitting algorithm based on spline fitting interpolation in cubic spline space is proposed.
Keywords/Search Tags:Curve and Surface fitting, Spline function, Least Squares, 2-type triangulation, Quasi-interpolation
PDF Full Text Request
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