Construction of C2 Pythagorean - Hodograph interpolating splines by the homotopy method

Advances in Computational Mathematics

Volumn 5, Issue 4, 1996, Pages 417-442

  Albrecht, Gudrun ^a   Farouki, Rida T ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039829557     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02124754     Document Type: Article

References (17)

1. E.L. Allgower and K. Georg, Numerical Continuation Methods: An Introduction (Springer, Berlin, 1990).
2. E.L. Allgower and K. Georg, Continuation and path following, Acta Numerica (1993) 1-64.
3. J.F. Canny, The Complexity of Robot Motion Planning (MIT Press, Cambridge, MA, 1988).
4. G. Dahlquist and A. Björck, Numerical Methods (Prentice - Hall, Englewood Cliffs, NJ, 1974).
5. R.T. Farouki, Pythagorean - hodograph curves in practical use, in Geometry Processing for Design and Manufacturing (R.E. Barnhill, ed.), (SIAM, Philadelphia, 1992) 3-33.
6. 2 of the hodograph plane, Comput. Aided Geom. Design 11 (1994) 363-390.
7. R.T. Farouki, The elastic bending energy of Pythagorean-hodograph curves, Comput. Aided Geom. Design 13 (1996) 227-241.
8. R.T. Farouki and C.A. Neff, Hermite interpolation by Pythagorean-hodograph quintics, Math. Comp. 64 (1995) 1589-1609.
9. R.T. Farouki and T. Sakkalis, Pythagorean hodographs, IBM J. Res. Develop. 34 (1990) 736 - 752.
10. W. Gröbner, Algebraische Geometrie I (Bibliographisches Institut, Mannheim, 1968).
11. W. Grobner, Algebraische Geometrie II (Bibliographisches Institut, Mannheim, 1970).
12. T. Lyche, There's always more room in the "Spline Zoo," personal communication (1989).
13. A.P. Morgan, Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems (Prentice - Hall, Englewood Cliffs, NJ, 1987).
14. A.P. Morgan and A. Sommese, A homotopy for solving general polynomial systems that respects m-homogeneous structures, Appl. Math. Comp. 24 (1987) 101-113.
15. A.P. Morgan and A. Sommese, Computing all solutions to polynomial systems using homotopy continuation, Appl. Math. Comp. 24 (1987) 115-138.
16. L.T. Watson, S.C. Billups, and A.P. Morgan, ALGORITHM 652 HOMPACK: A suite of codes for globally convergent homotopy algorithms, ACM Trans. Math. Software 13 (1987) 281-310.
17. W. Zulehner, A simple homotopy method for determining all isolated solutions to polynomial systems, Math. Comp. 181 (1988) 167-177.