Constrained multi-degree reduction with respect to Jacobi norms

Rachid Ait-Haddou; Michael Barton

doi:10.1016/j.cagd.2015.12.003

Constrained multi-degree reduction with respect to Jacobi norms

Rachid Ait-Haddou, Michael Barton

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

17 Scopus citations

Abstract

We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2L2-norm is presented.

Original language	English (US)
Pages (from-to)	23-30
Number of pages	8
Journal	Computer Aided Geometric Design
Volume	42
DOIs	https://doi.org/10.1016/j.cagd.2015.12.003
State	Published - Dec 31 2015

ASJC Scopus subject areas

Modeling and Simulation
Computer Graphics and Computer-Aided Design
Automotive Engineering
Aerospace Engineering

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10.1016/j.cagd.2015.12.003

https://repository.kaust.edu.sa/bitstream/10754/592755/1/1-s2.0-S0167839615001429-main.pdf

Cite this

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title = "Constrained multi-degree reduction with respect to Jacobi norms",

abstract = "We show that a weighted least squares approximation of B{\'e}zier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2L2-norm is presented.",

author = "Rachid Ait-Haddou and Michael Barton",

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AU - Barton, Michael

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Y1 - 2015/12/31

N2 - We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2L2-norm is presented.

AB - We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2L2-norm is presented.

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JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

ER -

Constrained multi-degree reduction with respect to Jacobi norms

Abstract

ASJC Scopus subject areas

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