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Deformation of spatial septic Pythagorean hodograph curves using Gauss-Legendre polygon
- Authors
- Kim, Soo Hyun; Moon, Hwan Pyo
- Issue Date
- Aug-2019
- Publisher
- ELSEVIER
- Keywords
- Spatial Pythagorean hodograph curve; Gauss-Legendre quadrature; Rectifying control polygon; Deformation of PH curve; Quatemion representation
- Citation
- COMPUTER AIDED GEOMETRIC DESIGN, v.73, pp 16 - 34
- Pages
- 19
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- COMPUTER AIDED GEOMETRIC DESIGN
- Volume
- 73
- Start Page
- 16
- End Page
- 34
- ISSN
- 0167-8396
1879-2332
- Abstract
- The notion of the rectifying control polygon of planar Pythagorean hodograph (PH) curve is extended to the spatial PH curves. We construct the Gauss-Legendre polygon by applying the Gauss-Legendre quadrature to the Pythagorean hodograph. Since the parametric speed of a PH curve is a polynomial, the Gauss-Legendre polygon with enough edges has the rectifying property, that is, the length of the polygon is the same as the length of the spatial PH curve. We also present the method to compute septic PH curves with the given Gauss-Legendre polygon. This method can be used to develop the deformation algorithm for the spatial septic PH curves. (C) 2019 Elsevier B.V. All rights reserved.
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Related Researcher
- Moon, Hwan Pyo
- College of Natural Science (Department of Mathematics)