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2013•Unpublished venueRequires access

Accurate, Validated and Fast Evaluation of Bézier Tensor Product Surfaces.

Hao Jiang, Housen Li, Lizhi Cheng, Roberto Barrio, Canbin Hu, Xiangke Liao

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Abstract

This paper proposes a compensated algorithm to evaluate Bézier tensor product surfaces with floating-point coefficients and coordinates. This algorithm is based on the application of error-free transformations to improve the traditional de Casteljau tensor product algorithm. This compensated algorithm extends the compensated de Casteljau algorithm for the evaluation of a Bézier curve to the case of tensor product surfaces. Forward error analysis and numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.

About this research paper

What this paper is about

This paper proposes a compensated algorithm to evaluate Bézier tensor product surfaces with floating-point coefficients and coordinates. This algorithm is based on the application of error-free transformations to improve the traditional de Casteljau tensor product algorithm. This compensated algorithm extends the compensated de Casteljau algorithm for the evaluation of a Bézier curve to the case of tensor product surfaces. Forward error analysis and numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper proposes a compensated algorithm to evaluate Bézier tensor product surfaces with floating-point coefficients and coordinates. This algorithm is based on the application of error-free transformations to improve the traditional de Casteljau tensor product algorithm. This compensated algorithm extends the compensated de Casteljau algorithm for the evaluation of a Bézier curve to the case of tensor product surfaces. Forward error analysis and numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.

Key concepts: Tensor product, Bézier curve, Product (mathematics), Tensor (intrinsic definition), Mathematics, Algorithm, Point (geometry), Bézier surface

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