Helical polynomial curves and double Pythagorean hodographs I. Quaternion and Hopf map representations
Tài liệu tham khảo
Beltran, 2007, A characterization of quintic helices, J. Comput. Appl. Math., 206, 116, 10.1016/j.cam.2006.06.001
Choi, 2002, Clifford algebra, spin representation, and rational parameterization of curves and surfaces, Adv. Comput. Math., 17, 5, 10.1023/A:1015294029079
Dietz, 1993, An algebraic approach to curves and surfaces on the sphere and on other quadrics, Comput. Aided Geom. Design, 10, 211, 10.1016/0167-8396(93)90037-4
Farouki, 1994, The conformal map z→z2 of the hodograph plane, Comput. Aided Geom. Design, 11, 363, 10.1016/0167-8396(94)90204-6
Farouki, 2008
Farouki, 2002, Structural invariance of spatial Pythagorean hodographs, Comput. Aided Geom. Design, 19, 395, 10.1016/S0167-8396(02)00123-1
Farouki, 2002, Hermite interpolation by rotation-invariant spatial Pythagorean hodograph curves, Adv. Comput. Math., 17, 369, 10.1023/A:1016280811626
Farouki, 2008, Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures, Comput. Aided Geom. Design, 25, 274, 10.1016/j.cagd.2007.09.007
Farouki, R.T., Giannelli, C., Sestini, A., 2008. Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves, J. Symbolic Comput., in press (doi:10.1016/j.jsc.2008.07.003)
Farouki, 2004, Characterization and construction of helical polynomial space curves, J. Comput. Appl. Math., 162, 365, 10.1016/j.cam.2003.08.030
Farouki, 2001, Efficient solution of the complex quadratic tridiagonal system for C2 PH quintic splines, Numer. Algorithms, 27, 35, 10.1023/A:1016621116240
Farouki, 1995, Hermite interpolation by Pythagorean hodograph quintics, Math. Comput., 64, 1589, 10.1090/S0025-5718-1995-1308452-6
Farouki, 1990, Pythagorean hodographs, IBM J. Res. Dev., 34, 736, 10.1147/rd.345.0736
Farouki, 1994, Pythagorean-hodograph space curves, Adv. Comput. Math., 2, 41, 10.1007/BF02519035
Kreyszig, 1959
Kubota, 1972, Pythagorean triples in unique factorization domains, Amer. Math. Monthly, 79, 503, 10.2307/2317570
Monterde, J., 2008, A characterization of helical polynomial curves of any degree, Adv. Comput. Math. (in press)
Needham, 1997
Perwass, 2007, A geometric product formulation for spatial Pythagorean-hodograph curves with applications to Hermite interpolation, Comput. Aided Geom. Design, 24, 220, 10.1016/j.cagd.2007.01.002
Schwerdtfeger, 1979
Šír, 2005, Spatial Pythagorean hodograph quintics and the approximation of pipe surfaces, 364
Šír, 2007, C2 Hermite interpolation by Pythagorean hodograph space curves, Math. Comput., 76, 1373, 10.1090/S0025-5718-07-01925-4
Struik, 1961
Wagner, 1997, Curves with rational Frenet–Serret motion, Comput. Aided Geom. Design, 15, 79, 10.1016/S0167-8396(97)81786-4