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**Chebyshev economization for parametric surfaces.**
*(English)*
Zbl 0709.65012

Summary: The communication of polynomial curve and surface data between various CAD systems frequently requires that a degree reduction is performed. The most common way of accomplishing this reduction at present is via ‘black box’ methods. In this note we extend the notion of Chebyshev economization from real polynomials to parametric polynomials in three dimensions, thus providing an analytical approach to degree reduction. More importantly, we propose a generalization for parametric surfaces which enjoys many of the properties associated with Chebyshev economization.

### MSC:

65D17 | Computer-aided design (modeling of curves and surfaces) |

### Keywords:

parametric polynomial curves and surfaces; constrained Chebyshev polynomials; constrained Chebyshev economization; Remez algorithm
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\textit{M. A. Lachance}, Comput. Aided Geom. Des. 5, No. 3, 195--208 (1988; Zbl 0709.65012)

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### References:

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