NDLI: A novel algorithm for explicit optimal multi-degree reduction of triangular surfaces

Content Provider	Springer Nature Link
Author	Hu, QianQian Wang, GuoJin
Copyright Year	2008
Abstract	This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials and Jacobi polynomials, we naturally deduce a novel algorithm for multi-degree reduction of triangular Bézier surfaces. This algorithm possesses four characteristics: ability of error forecast, explicit expression, less time consumption, and best precision. That is, firstly, whether there exists a multi-degree reduced surface within a prescribed tolerance is judged beforehand; secondly, all the operations of multi-degree reduction are just to multiply the column vector generated by sorting the series of the control points of the original surface in lexicographic order by a matrix; thirdly, this matrix can be computed at one time and stored in an array before processing degree reduction; fourthly, the multi-degree reduced surface achieves an optimal approximation in the norm L $_{2}$. Some numerical experiments are presented to validate the effectiveness of this algorithm, and to show that the algorithm is applicable to information processing of products in CAD system.
Starting Page	13
Ending Page	24
Page Count	12
File Format	PDF
ISSN	10092757
Journal	Science in China Series : Information Sciences
Volume Number	51
Issue Number	1
e-ISSN	18622836
Language	English
Publisher	Science in China Press
Publisher Date	2008-01-01
Publisher Place	Beijing
Access Restriction	Subscribed
Subject Keyword	computer aided design data compression triangular Bézier surface multi-degree reduction Bernstein polynomial Jacobi polynomial L $_{2}$ norm Information Systems and Communication Service
Content Type	Text
Resource Type	Article
Subject	Computer Science

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