Author(s)

PeiPei Ji^*, JunHui Yang

Affiliation(s)

School of Health Management, Xi’an Medical University, Xi’an 710021, Shaanxi, China.

Corresponding Author

PeiPei Ji

ABSTRACT

By using novel recurrence relation, some models with good approximation are constructed, which include three aspects: extension of curve of degree n, extension of surface of degree n over rectangular domain. First, based on a novel recurrence relation, we define a Quasi-Bernstein-basis of degree n with multiple parameters, which includes the classical Bernstein basis of degree n as a special case and has similar properties with the classic Bernstein basis. And the definition, properties, comer cutting algorithm, adjustable effect and quantification of approximation of related curves are discussed in detail. Next, tased on Quasi-Bernstein-basis, we develop a tensor product surface with multiple parameters over rectangular domain, and discuss continuity of Quasi-Bézier-surface at length. Compared with the existing methods, the proposed models keep can beautiful properties of classical method and the multiple parameters introduced in these models can flexibly adjust shape of the generated model and possess good approximation.

KEYWORDS

Recurrence relation; Bernstein basis; Corner cutting algorithm; De Cateljau-type algotithm

CITE THIS PAPER

PeiPei Ji, JunHui Yang. Extension of new model with good approximation based on recurrence relation. Eurasia Journal of Science and Technology. 2025, 7(5): 75-81. DOI: https://doi.org/10.61784/ejst3116.

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