Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves

Advances in Computational Mathematics

Volumn 17, Issue 4, 2002, Pages 369-383

  Farouki, Rida T ^a   Al Kandari, Mohammad ^a   Sakkalis, Takis ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b AGRICULTURAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Hermite interpolation; Pythagorean hodograph curves; Quaternions

Indexed keywords

EID: 0001476854     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016280811626     Document Type: Article

References (17)

1. 2 Pythagorean hodograph interpolating splines by the homotopy method, Adv. Comput. Math. 5 (1996) 417-442.
2. H.I. Choi, D.S. Lee and H.P. Moon, Clifford algebra, spin representation, and rational parameterization of curves and surfaces, Adv. Comput. Math. (2002) to appear.
3. M.J. Crowe, A History of Vector Analysis (Dover, New York, 1967).
4. R. Dietz, J. Hoschek and B. Jüttler, An algebraic approach to curves and surfaces on the sphere and on other quadrics, Comput. Aided Geom. Design 10 (1993) 211-229.
5. 2 of the hodograph plane, Comput. Aided Geom. Design 11 (1994) 363-390.
6. R.T. Farouki, The elastic bending energy of Pythagorean hodograph curves, Comput. Aided Geom. Design 13 (1996) 227-241.
7. R.T. Farouki, M. al-Kandari and T. Sakkalis, Structural invariance of spatial Pythagorean hodographs, Comput. Aided Geom. Design (2002) to appear.
8. 2 PH quintic splines, Numer. Algorithms 27 (2001) 35-60.
9. R.T. Farouki, J. Manjunathaiah, D. Nicholas, G.-F. Yuan and S. Jee, Variable feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves, Comput. Aided Design 30 (1998) 631-640.
10. R.T. Farouki and C.A. Neff, Hermite interpolation by Pythagorean hodograph quintics, Math. Comp. 64 (1995) 1589-1609.
11. R.T. Farouki and T. Sakkalis, Pythagorean-hodograph space curves, Adv. Comput. Math. 2 (1994) 41-66.
12. R.T. Farouki and S. Shah, Real-time CNC interpolators for Pythagorean-hodograph curves, Comput. Aided Geom. Design 13 (1996) 583-600.
13. B. Jüttler, Hermite interpolation by Pythagorean hodograph curves of degree seven, Math. Comp. 70 (2001) 1089-1111.
14. E. Kreyszig, Differential Geometry (Univ. of Toronto Press, Toronto, 1959).
15. H.P. Moon, R.T. Farouki and H.I. Choi, Construction and shape analysis of PH quintic Hermite interpolants, Comput. Aided Geom. Design 18 (2001) 93-115.
16. J. Roe, Elementary Geometry (Oxford Univ. Press, Oxford, 1993).
17. Y-F. Tsai, R.T. Farouki and B. Feldman, Performance analysis of CNC interpolators for time-dependent feedrates along PH curves, Comput. Aided Geom. Design 18 (2001) 245-265.