Abstract
In this article, it is shown that a space curve in Rd can be approximated by a piecewise polynomial curve of degree m with order (m + 1) + ⌊ (m + 1) / (2 d - 1) ⌋ rather than m + 1. Moreover, we show that the optimal order (m + 1) + ⌊ (m - 1) / (d - 1) ⌋ is possible for a particular set of curves of nonzero measure. Analogous results were shown to be true for Taylor polynomial interpolation in [A. Rababah, High order approximation method for curves, Comput. Aided Geom. Design 12 (1995) 89-102].
Original language | English |
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Pages (from-to) | 920-931 |
Number of pages | 12 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 325 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jan 15 2007 |
Externally published | Yes |
Keywords
- Approximation order
- Computer aided geometric design
- Hermite approximation
- High accuracy
- Space curves
ASJC Scopus subject areas
- Analysis
- Applied Mathematics