G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics

Computer Aided Geometric Design

Volumn 23, Issue 5, 2006, Pages 401-418

  Kosinka, Jiří ^a   Jüttler, Bert ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Hermite interpolation; Minkowski Pythagorean hodograph curves; Space like vector; Taylor expansion

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTER AIDED DESIGN; GRAPH THEORY;

HERMITE INTERPOLATION; MINKOWSKI PYTHAGOREAN HODOGRAPH CURVES; SPACE-LIKE VECTOR; TAYLOR EXPANSION;

INTERPOLATION;

EID: 33646822993     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2006.01.004     Document Type: Article

References (15)

1. Blaschke W. Vorlesungen über Differentialgeometrie III (1929), Springer, Berlin
2. Cho H.Ch., Choi H.I., Kwon S.-H., Lee D.S., and Wee N.-S. Clifford algebra, Lorentzian geometry and rational parametrization of canal surfaces. Computer Aided Geometric Design 21 (2004) 327-339
3. Choi H.I., Choi S.W., and Moon H.P. Mathematical theory of medial axis transform. Pacific J. Math. 181 1 (1997) 57-88
4. Choi H.I., Han Ch.Y., Moon H.P., Roh K.H., and Wee N.S. Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves. Computer-Aided Design 31 (1999) 59-72
5. Choi H.I., Lee D.S., and Moon H.P. Clifford algebra, spin representation and rational parameterization of curves and surfaces. Adv. Comput. Math. 17 (2002) 5-48
6. Degen W.L.F. Exploiting curvatures to compute the medial axis for domains with smooth boundary. Computer Aided Geometric Design 21 (2004) 641-660
7. Ekmekci N., and Ilarslan K. Higher curvatures of a regular curve in Lorentzian space. J. Inst. Math. Comp. Sci. 11 2 (1998) 97-102
8. Farouki R.T. Pythagorean-hodograph curves. In: Hoschek J., Farin G., and Kim M.-S. (Eds). Handbook of Computer Aided Geometric Design (2002), Elsevier, Amsterdam 405-427
9. Farouki R.T., and Sakkalis T. Pythagorean hodographs. IBM J. Res. Develop. 34 (1990) 736-752
10. 1 Hermite interpolation using MPH quartic. Computer Aided Geometric Design 20 (2003) 469-492
11. Kosinka, J., 2006. Algorithms for Minkowski Pythagorean hodograph curves. Doctoral thesis, Faculty of Mathematics and Physics, Charles University, Prague, in preparation
12. Kosinka, J., Jüttler, B., 2006. Cubic helices in Minkowski space, Sitzungsber. Österr. Akad. Wiss., Math.-Nat. Kl., in press
13. Moon H.P. Minkowski Pythagorean hodographs. Computer Aided Geometric Design 16 (1999) 739-753
14. Pottmann H., and Peternell M. Applications of Laguerre geometry in CAGD. Computer Aided Geometric Design 15 (1998) 165-186
15. Walrave, J., 1995. Curves and surfaces in Minkowski space. Doctoral thesis, K.U. Leuven, Fac. of Science, Leuven