Distances with rational triangular Bézier surfaces

Abedallah Rababah

doi:10.1016/j.amc.2003.11.005

Distances with rational triangular Bézier surfaces

Abedallah Rababah

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

12 Citations (Scopus)

Abstract

In this paper, we give the matrix form for the degree elevation of rational triangular Bézier surfaces. We use the L₂ measure to find a formula for the distance between two rational triangular Bézier surfaces. A polynomial triangular Bézier surface approximation of a rational triangular Bézier surface based on the least-squares method is given. The final formulas contain only Bézier points and matrix of degree elevation.

Original language	English
Pages (from-to)	379-386
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	160
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2003.11.005
Publication status	Published - Jan 14 2005
Externally published	Yes

Keywords

Computer aided geometric design
Degree raising
Generalized Bernstein polynomials
Rational triangular Bézier surfaces

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2003.11.005

Cite this

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abstract = "In this paper, we give the matrix form for the degree elevation of rational triangular B{\'e}zier surfaces. We use the L2 measure to find a formula for the distance between two rational triangular B{\'e}zier surfaces. A polynomial triangular B{\'e}zier surface approximation of a rational triangular B{\'e}zier surface based on the least-squares method is given. The final formulas contain only B{\'e}zier points and matrix of degree elevation.",

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AU - Rababah, Abedallah

PY - 2005/1/14

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N2 - In this paper, we give the matrix form for the degree elevation of rational triangular Bézier surfaces. We use the L2 measure to find a formula for the distance between two rational triangular Bézier surfaces. A polynomial triangular Bézier surface approximation of a rational triangular Bézier surface based on the least-squares method is given. The final formulas contain only Bézier points and matrix of degree elevation.

AB - In this paper, we give the matrix form for the degree elevation of rational triangular Bézier surfaces. We use the L2 measure to find a formula for the distance between two rational triangular Bézier surfaces. A polynomial triangular Bézier surface approximation of a rational triangular Bézier surface based on the least-squares method is given. The final formulas contain only Bézier points and matrix of degree elevation.

KW - Computer aided geometric design

KW - Degree raising

KW - Generalized Bernstein polynomials

KW - Rational triangular Bézier surfaces

UR - https://www.scopus.com/pages/publications/9644265485

UR - https://www.scopus.com/pages/publications/9644265485#tab=citedBy

U2 - 10.1016/j.amc.2003.11.005

DO - 10.1016/j.amc.2003.11.005

M3 - Article

AN - SCOPUS:9644265485

SN - 0096-3003

VL - 160

SP - 379

EP - 386

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Distances with rational triangular Bézier surfaces

Abstract

Keywords

ASJC Scopus subject areas

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