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Construction of C 2 Pythagorean-hodograph interpolating splines by the homotopy method. (English) Zbl 0866.65008
C 2 Pythagorean-hodograph interpolating splines are investigated. The authors demonstrate how to set up a system of quadratic equations that insure the prescribed continuity of the spline interpolant. The analysis of the solution set of this system is presented in detail. Numerical examples are included.

65D07Splines (numerical methods)
65D05Interpolation (numerical methods)
41A15Spline approximation
[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, inGeometry Processing for Design and Manufacturing (R.E. Barnhill, ed.), (SIAM, Philadelphia, 1992) 3–33.
[6]R.T. Farouki, The conformal mapz 2 of the hodograph plane, Comput. Aided Geom. Design 11 (1994) 363–390. · Zbl 0806.65005 · doi:10.1016/0167-8396(94)90204-6
[7]R.T. Farouki, The elastic bending energy of Pythagorean-hodograph curves, Comput. Aided Geom. Design 13 (1996) 227–241. · Zbl 0875.68861 · doi:10.1016/0167-8396(95)00024-0
[8]R.T. Farouki and C.A. Neff, Hermite interpolation by Pythagorean-hodograph quintics, Math. Comp. 64 (1995) 1589–1609. · doi:10.1090/S0025-5718-1995-1308452-6
[9]R.T. Farouki and T. Sakkalis, Pythagorean hodographs, IBM J. Res. Develop. 34 (1990) 736–752. · doi:10.1147/rd.345.0736
[10]W. Gröbner,Algebraische Geometrie I (Bibliographisches Institut, Mannheim, 1968).
[11]W. Gröbner,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 respectsm-homogeneous structures, Appl. Math. Comp. 24 (1987) 101–113. · Zbl 0635.65057 · doi:10.1016/0096-3003(87)90063-4
[15]A.P. Morgan and A. Sommese, Computing all solutions to polynomial systems using homotopy continuation, Appl. Math. Comp. 24 (1987) 115–138. · Zbl 0635.65058 · doi:10.1016/0096-3003(87)90064-6
[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. · Zbl 0626.65049 · doi:10.1145/29380.214343
[17]W. Zulehner, A simple homotopy method for determining all isolated solutions to polynomial systems, Math. Comp. 181 (1988) 167–177. · doi:10.1090/S0025-5718-1988-0917824-7