논문KCI 등재
RATIONAL CURVES ARE NOT UNIT SPEED IN THE GENERAL EUCLIDEAN SPACE
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참고문헌
키워드
주제분류수학
초록
We invoke the characterization of Pythagorean-hodograph polynomial curves and prove that it is impossible to parameterize any real curves, other than a straight line, by rational functions of its arc length.
Abstract
We invoke the characterization of Pythagorean-hodograph polynomial curves and prove that it is impossible to parameterize any real curves, other than a straight line, by rational functions of its arc length.
참고문헌 (8)
- L. V. Ahlfors, "Complex Analysis, Third Edition" (1979), McGraw-Hill Book Co.
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- R. T. Farouki, "Real rational curves are not `unit speed'", Comput. Aided Geom. Design, 8, pp.151~157 (1991)
- R. T. Farouki, "Rational space curves are not \unit speed", Comput. Aided Geom. Design, 24, pp.238~240 (2007)
- G.-I. Kim, "Higher dimensional PH curves", Proc. Japan Acad., 통권 : 78, pp.185~187 (2002)
- K. K. Kubota, "Pythagorean triples in unique factorization domains", Amer. Math. Monthly, 79, pp.503~505 (1972)
- S. Lee, "Characterization of Minkowski Pythagorean-hodograph curves", J. Appl. Math. & Computing, 24, pp.521~528 (2007)
- T. Sakkalis, "Non-existence of rational arc length pa-rameterizations for curves in Rn", J. Comput. Appl. Math., 228, pp.494~497 (2009)
관련 논문AI추천
GEOMETRIC HERMITE INTERPOLATION FOR PLANAR PYTHAGOREAN-HODOGRAPH CUBICS이선홍, 이현철영남수학회 · East Asian Mathematical Journal2013 · 제29권 제1호PYTHAGOREAN-HODOGRAPH CUBICS AND GEOMETRIC HERMITE INTERPOLATION이선홍, Hyun Chol Lee영남수학회 · East Asian Mathematical Journal2012 · 제28권 제1호HERMITE INTERPOLATION USING PH CURVES WITH UNDETERMINED JUNCTION POINTS공재훈, 김광일, 정승필대한수학회 · 대한수학회보2012 · 제49권 제1호$C^1$ Hermite interpolation with MPH curves using PH-MPH transitive mappings공재훈, 김광일, 이현철대한수학회 · 대한수학회지2019 · 제56권 제3호Circle approximation using parametric polynomial curves of high degree in explicit formYoung Joon Ahn대한수학회 · 대한수학회논문집2022 · 제37권 제4호Implicitization of rational curves and polynomial surfacesJian-ping Yu, Yong-li Sun대한수학회 · 대한수학회보2007 · 제44권 제1호
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