期刊
COMPUTER AIDED GEOMETRIC DESIGN
卷 25, 期 4-5, 页码 305-319出版社
ELSEVIER
DOI: 10.1016/j.cagd.2007.11.004
关键词
Weierstrass approximation; Pythagorean hodograph; Minkowski Pythagorean hodograph; Bernstein approximation; Chebyshev approximation
We prove the Weierstrass-type approximation theorem that states every C-1 curve in the 2-dimensional or 3-dimensional Euclidean space or in the 3-dimensional Minkowski space can be uniformly approximated by Pythagorean hodograph curves in the corresponding space. This abundance of PH curves is another theoretical confirmation of the usefulness and the versatility of the PH curves. We also address some algorithmic aspects of proposed PH approximation schemes and their convergence rates. (C) 2007 Elsevier B.V. All rights reserved.
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