L-2 Degree reduction of triangular Bézier surfaces with common tangent planes at vertices

Abedallah Rababah

doi:10.1142/S0218195905001798

L-2 Degree reduction of triangular Bézier surfaces with common tangent planes at vertices

Abedallah Rababah

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

12 Citations (Scopus)

Abstract

In this paper, we present a method of degree reduction for triangular Bézier surfaces. The approximate and the original triangular Bézier surfaces have common tangent planes at the vertices. We use the least squares method with the L2 and l2 norms to get a closed form for the reduction of the degree and show that both solutions are the same. This scheme uses the matrix representations of the degree raising and the Bézier control vertices. The computational cost of the method is evaluated. The error term is derived and a numerical example is given.

Original language	English
Pages (from-to)	477-490
Number of pages	14
Journal	International Journal of Computational Geometry and Applications
Volume	15
Issue number	5
DOIs	https://doi.org/10.1142/S0218195905001798
Publication status	Published - Oct 2005
Externally published	Yes

Keywords

Computer aided geometric design
Degree raising
Degree reduction
Generalized Bernstein polynomials
Tangent plane continuity
Triangular Bézier surfaces

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1142/S0218195905001798

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title = "L-2 Degree reduction of triangular B{\'e}zier surfaces with common tangent planes at vertices",

abstract = "In this paper, we present a method of degree reduction for triangular B{\'e}zier surfaces. The approximate and the original triangular B{\'e}zier surfaces have common tangent planes at the vertices. We use the least squares method with the L2 and l2 norms to get a closed form for the reduction of the degree and show that both solutions are the same. This scheme uses the matrix representations of the degree raising and the B{\'e}zier control vertices. The computational cost of the method is evaluated. The error term is derived and a numerical example is given.",

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language = "English",

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AU - Rababah, Abedallah

PY - 2005/10

Y1 - 2005/10

N2 - In this paper, we present a method of degree reduction for triangular Bézier surfaces. The approximate and the original triangular Bézier surfaces have common tangent planes at the vertices. We use the least squares method with the L2 and l2 norms to get a closed form for the reduction of the degree and show that both solutions are the same. This scheme uses the matrix representations of the degree raising and the Bézier control vertices. The computational cost of the method is evaluated. The error term is derived and a numerical example is given.

AB - In this paper, we present a method of degree reduction for triangular Bézier surfaces. The approximate and the original triangular Bézier surfaces have common tangent planes at the vertices. We use the least squares method with the L2 and l2 norms to get a closed form for the reduction of the degree and show that both solutions are the same. This scheme uses the matrix representations of the degree raising and the Bézier control vertices. The computational cost of the method is evaluated. The error term is derived and a numerical example is given.

KW - Computer aided geometric design

KW - Degree raising

KW - Degree reduction

KW - Generalized Bernstein polynomials

KW - Tangent plane continuity

KW - Triangular Bézier surfaces

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JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

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ER -

L-2 Degree reduction of triangular Bézier surfaces with common tangent planes at vertices

Abstract

Keywords

ASJC Scopus subject areas

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