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C-1 HERMITE INTERPOLATION WITH MPH CURVES USING PH-MPH TRANSITIVE MAPPINGS
- Authors
- Kim, Gwangil; Kong, Jae Noon; Lee, Hyun Chol
- Issue Date
- May-2019
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- Minkowski Pythagorean-hodograph curve; PH-MPH transitive mapping; MPH-preserving mapping; C-1 Hermite data-set; C-1 Hermite interpolation
- Citation
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.56, no.3, pp.805 - 823
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 56
- Number
- 3
- Start Page
- 805
- End Page
- 823
- ISSN
- 0304-9914
- Abstract
- We introduce polynomial PH-MPH transitive mappings which transform planar PH curves to MPH curves in R-2,R-1, and prove that parameterizations of Enneper surfaces of the 1st and the 2nd kind and conjugates of Enneper surfaces of the 2nd kind are PH-MPH transitive. We show how to solve C-1 Hermite interpolation problems in R-2,R-1, for an admissible C-1 Hermite data-set, by using the parametrization of Enneper surfaces of the 1st kind. We also show that we can obtain interpolants for at least some inadmissible data-sets by using MPH biarcs on Enneper surfaces of the 1st kind.
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