Rational approximation of rotation minimizing frames using Pythagorean-hodograph cubics

Journal for Geometry and Graphics

Volumn 3, Issue 2, 1999, Pages 141-159

  Mäurer, Christoph ^a   Jüttler, Bert ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Moulding surface; Profile surface; Pythagorean hodograph curves; Rotation minimizing frame; Sweeping surface

Indexed keywords

EID: 0001335040     PISSN: 14338157     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. M. Eriksson, Hermite interpolation with spatial Pythagorean hodograph curves. Master thesis, TU Darmstadt / KTH Stockholm 1999
2. G. Farin, Curves and surfaces for computer aided geometric design. 3rd ed., Academic Press, Orlando FL 1992
3. R.T. Farouki, T. Sakkalis, Pythagorean-hodograph space curves. Adv. Comput. Math. 2, 41-66 (1994)
4. H.W. Guggenheimer, Computing frames along a trajectory. Comput. Aided Geom. Design 6, 77-78 (1989)
5. J. Hoschek, D. Lasser, Fundamentals of Computer Aided Geometric Design. AK Peters, Wellesley Mass. 1993
6. B. Jüttler, Generating Rational Frames of Space curves via Hermite Interpolation with Pythagorean Hodograph Cubic Splines. In: Differential/Topological Techniques in Geo-metric Modeling and Processing'98, eds. D.P. Choi, H.I. Choi, M.S. Kim and R.R. Martin, Bookplus press, Seoul, South Korea, 1998, pp. 83-106
7. B. Jüttler, Rotation Minimizing Spherical Motions. In: Advances in Robot Kinematics: Analysis and Control, eds. J. Lenarcic and M. Husty, Kluwer, Dordrecht 1998, pp. 413-422
8. B. Jüttler, C. Máurer, Cubic Pythagorean Hodograph Spline Curves and Applica-tions to Sweep Surface Modeling. Comput.-Aided Design 31, 73-83 (1999)
9. P.D. Kaklis, G.D. Koras, A Quadratic-Programming Method for Removing Shape-Failures from Tensor-Product B-Spline Surfaces. Computing [Suppl] 13, 177-188 (1998)
10. M.-S. Kim, E.-J. Park, H.-Y. Lee, Modelling and animation of generalized cylinders with variable offset space curves. The Journal of Visualization and Computer Animation 5, 189-207 (1994)
11. F. Klok, Two moving coordinate frames for sweeping along a 3D trajectory. Comput. Aided Geom. Design 3, 217-229 (1986)
12. E. Kreyszig, Differential geometry, Oxford University Press, London 1964
13. R.R. Martin, Principal Patches for Computational Geometry, Ph.D. thesis, Cambridge University Engineering Department, 1982
14. D.S. Meek, D.J. Walton, Geometric Hermite interpolation with Tschirnhausen cu-bics. J. Comput. Appl. Math. 81, 299-309 (1997)
15. H. Pottmann, M. Wagner, Principal Surfaces. In: The Mathematics of Surfaces VII, eds. T.N.T. Goodman and R.R. Martin, Information Geometers, Winchester 1997, pp. 337-362
16. H. Pottmann, M. Wagner, Contributions to Motion Based Surface Design. Int. J. of Shape Modeling 4, 183-196 (1998)
17. K. Strubecker, Differentialgeometrie I-III. 2nd ed., de Gruyter (Sammlung Góschen), Berlin 1964-1969
18. D.J. Struik, Lectures on classical differential geometry. 2nd ed., Addison-Wesley, Read-ing (Mass.) 1961
19. M. Wagner, B. Ravani, Curves with Rational Frenet-Serret motion. Comput. Aided Geom. Design 15, 79-101 (1997)
20. W. Wang, B. Joe, Robust computation of the rotation minimizing frame for sweep surface modeling. Comput.-Aided Design 29, 379-391 (1997)
21. W. Wunderlich, Algebraische Bóschungslinien dritter und vierter Ordnung. Sitzungs-ber., Abt. II, ósterr. Akad. Wiss., Math.-Naturw. Kl. 181, 353-376 (1973)