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On The Algebraic-hyperbolic B-spline Curves

Posted on:2007-02-28Degree:MasterType:Thesis
Country:ChinaCandidate:W ShiFull Text:PDF
GTID:2178360185459654Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Spline curves defined in the space constructed by polynomial and hyperbolic functions are studied in this paper. The main research contents and achievements are as follow:Firstly, we generate the cardinal Extended Complete Chebychevian (ECT) -systems on the space constructed by polynomial and hyperbolic functions, then introduce the Algebraic-hyperbolic B-spline space and identify the dimension law and zero properties. The existence of a basis of splines with minimal compact supports is demonstrated, and functions named Non-uniform Algebraic-hyperbolic B-splines are obtained by solving certain linear equations with a block matrix. As an application, the representation of the low order is given.Secondly, we introduce the recurrence definition of the non-uniform algebraic -hyperbolic B-spline basis using divided differences and the de Boor-Fix recurrence definition on polynomial functions, and based on the new forms, Algebraic-hyperbolic B-spline curves are obtained. They share most of the properties as those of the B-spline curves in the polynomial space. We focus on deducing the calculating and knot inserting formulae for this new kind of curves and then prove that they have the variation diminishing properties. Since the new curves can not only be explored to represent both polynomial curves and hyperbolic curves as special cases without rational form, but also offer evaluation and subdivision. Therefore, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.At last, the spatial definition of periodic spline and natural spline constructed by polynomial and hyperbolic functions is given; the dimension law and zero properties are demonstrated; and therefore the non-uniform algebraic-hyperbolic period and natural spline curves are obtained. The applications of the low order are given in details.
Keywords/Search Tags:Non-uniform algebraic-hyperbolic B-spline, Periodic spline, Natural spline, Curves, Geometric model
PDF Full Text Request
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