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Explict Expression of NUAT B-spline Basis and Its Properties

Author: MaYueWen
Tutor: WangGuoZhao
School: Zhejiang University
Course: Applied Mathematics
Keywords: Truncated function Limited pillars function space Class Vandermonde Determinant Differential defined Quasi-differencing definition Power basis transformation matrix Sequence of nodes function Generalized Vandermonde determinant Explicitly represented
CLC: TP391.41
Type: Master's thesis
Year: 2008
Downloads: 28
Quote: 2
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Abstract


A NUATB spline curves are based on the space span { 1, t , ... , t k -3 , the cost , sint } generated spline curve , it has almost exactly the same as the nature of the B-spline curve , but it can be accurately represented the circular arcs, elliptical arcs , spirals, and the like are widely used in a graph . This article is divided simple node and multi- node two cases discussed explicit representation of the NUAT B -spline basis and its area of ??computational problems . As a special case of a simple node , this paper also discusses the uniform node NUATB spline base to the power - conversion matrix given algorithm obtained the matrix . Sequence Case For simple nodes , we first constructed a truncated functions , trigonometric spline function space limited pillars function space base truncated function determinant to determine NUAT the B - spline basis with the determinant only difference a constant. Determinant of the nature of the research truncated function to its simplified class Vandermonde determinant form , and then eventually identified through the study of the nature of the class Vandermonde determinant coefficient , which will NUAT B - spline basis accurately represented explicitly , the Vandermonde Determinant formula at the same time take advantage of the class got a simple calculation method of the class the Vandermonde Row area . In particular , the results of this paper using a simple node uniform sequence of nodes NUAT B -spline basis explicit expressions and area of , and to come out with this explicit expression to the power basis transformation matrix . Further study of the class Vandermonde determinant , a fast algorithm for solving the power basis transformation matrix . Sequence Case For multiple nodes , the same use of a truncated function to construct a similar truncation function determinant , using a method similar to the simple nodes can be simplified to a broad class of Vandermonde determinant . Nature determined by the generalized class Vandermonde determinant coefficient between class Vandermonde determinant truncated function determinant , has been the area of ??expression for truncated function matrix .

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CLC: > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > Computer applications > Information processing (information processing) > Pattern Recognition and devices > Image recognition device
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