Degree reduction of triangular Bézier surfaces with Cα-vertices

Abedallah Rababah

Degree reduction of triangular Bézier surfaces with C^α-vertices

Research output: Contribution to journal › Article › peer-review

Abstract

The issue of Cα-degree reduction of triangular Bézier surfaces is exposed. It is anticipated that both triangular Bézier surfaces are Cα-continuous at the vertices. The Euclidean norm as well as the L₂-norm is used. The final solutions are given in terms of the matrix of degree raising, the Gram matrix, and the Bézier points. Moreover, it is shown that the solutions using both norms are equivalent.

Original language	English
Pages (from-to)	1055-1066
Number of pages	12
Journal	International Journal of Mathematical Analysis
Volume	4
Issue number	21-24
Publication status	Published - 2010
Externally published	Yes

Keywords

Bivariate Bernstein polynomials
Cα-continuity
Cα-degree reduction
Triangular Bézier surfaces

ASJC Scopus subject areas

Mathematics(all)

Cite this

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abstract = "The issue of Cα-degree reduction of triangular B{\'e}zier surfaces is exposed. It is anticipated that both triangular B{\'e}zier surfaces are Cα-continuous at the vertices. The Euclidean norm as well as the L2-norm is used. The final solutions are given in terms of the matrix of degree raising, the Gram matrix, and the B{\'e}zier points. Moreover, it is shown that the solutions using both norms are equivalent.",

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AB - The issue of Cα-degree reduction of triangular Bézier surfaces is exposed. It is anticipated that both triangular Bézier surfaces are Cα-continuous at the vertices. The Euclidean norm as well as the L2-norm is used. The final solutions are given in terms of the matrix of degree raising, the Gram matrix, and the Bézier points. Moreover, it is shown that the solutions using both norms are equivalent.

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KW - Cα-continuity

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KW - Triangular Bézier surfaces

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Degree reduction of triangular Bézier surfaces with C^α-vertices

Abstract

Keywords

ASJC Scopus subject areas

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