Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves

Graphical Models

Volumn 64, Issue 6, 2002, Pages 382-395

  Farouki, Rida T ^a  

^a University of California   (United States)

Author keywords

Differential geometry; Frenet Serret frame; Pythagorean hodograph curves; Rational function integration; Rotation minimizing frame

Indexed keywords

ALGORITHMS; ANGLE MEASUREMENT; ANIMATION; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; INTEGRATION; POLYNOMIALS; ROBOT APPLICATIONS; ROTATION;

DIFFERENTIAL GEOMETRY;

COMPUTER GRAPHICS;

GEOMETRY;

EID: 0038137416     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1524-0703(03)00002-X     Document Type: Article

References (32)

1. 2 Pythagorean hodograph interpolating splines by the homotopy method, Adv. Comput. Math. 5 (1996) 417-442.
2. R.L. Bishop, There is more than one way to frame a curve, Am. Math. Monthly 82 (1975) 246-251.
3. H.I. Choi, C.Y. Han, Euler-Rodrigues frames on spatial Pythagorean-hodograph curves, Comput. Aided Geom. Design 19 (2002) 603-620.
4. H.I. Choi, D.S. Lee, H.P. Moon, Clifford algebra, spin representation, and rational parameterization of curves and surfaces, Adv. Comput. Math. 17 (2002) 5-48.
5. J.H. Davenport, Y. Siret, E. Tournier, Computer Algebra, Academic Press, London, 1988.
6. R. Dietz, J. Hoschek, B. Jüttler, An algebraic approach to curves and surfaces on the sphere and on other quadrics, Comput. Aided Geom. Design 10 (1993) 211-229.
7. R.T. Farouki, Pythagorean hodograph curves in practical use, in: R.E. Barnhill (Ed.), Geometry Processing for Design and Manufacturing, SIAM, Philadelphia, PA, 1992, pp. 3-33.
8. 2 of the hodograph plane, Comput. Aided Geom. Design 11 (1994) 363-390.
9. R.T. Farouki, M. al-Kandari, T. Sakkalis, Structural invariance of spatial Pythagorean hodographs, Comput. Aided Geom. Design 19 (2002) 395-407.
10. R.T. Farouki, M. al-Kandari, T. Sakkalis, Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves, Adv. Comput. Math. 17 (2002) 369-383.
11. R.T. Farouki, J. Manjunathaiah, D. Nicholas, G.-F. Yuan, S. Jee, Variable feedrate CNC interpolators for constant material removal rates along Pythagorean hodograph curves, Comput. Aided Design 30 (1998) 631-640.
12. R.T. Farouki, C.A. Neff, Hermite interpolation by Pythagorean hodograph quintics, Math. Comput. 64 (1995) 1589-1609.
13. R.T. Farouki, T. Sakkalis, Pythagorean hodographs, IBM J. Res. Develop. 34 (1990) 736-752.
14. R.T. Farouki, T. Sakkalis, Pythagorean hodograph space curves, Adv. Comput. Math. 2 (1994) 41-66.
15. R.T. Farouki, S. Shah, Real-time CNC interpolators for Pythagorean hodograph curves, Comput. Aided Geom. Design 13 (1996) 583-600.
16. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980.
17. H. Guggenheimer, Computing frames along a trajectory, Comput. Aided Geom. Design 6 (1989) 77-78.
18. E. Horowitz, Algorithm for symbolic integration of rational functions, Ph.D. Thesis, University of Wisconsin, 1969.
19. E. Horowitz, Algorithms for partial fraction decomposition and rational function integration, in: Proceedings of Second ACM Symposium on Symbolic and Algebraic Manipulation, 1971, pp. 441-457.
20. B. Jüttler, Generating rational frames of space curves via Hermite interpolation with Pythagorean hodograph cubic splines, in: Geometric Modeling and Processing '98, Bookplus Press, 1998, pp. 83-106.
21. B. Jüttler, C. Mäurer, Cubic Pythagorean hodograph spline curves and applications to sweep surface modelling, Comput. Aided Design 31 (1999) 73-83.
22. B. Jüttler, C. Mäurer, Rational approximation of rotation minimizing frames using Pythagorean-hodograph cubics, J. Geom. Graphics 3 (1999) 141-159.
23. F. Klok, Two moving coordinate frames for sweeping along a 3D trajectory, Comput. Aided Geom. Design 3 (1986) 217-229.
24. E. Kreyszig, Differential Geometry, University of Toronto Press, 1959.
25. J. Roe, Elementary Geometry, Oxford University Press, 1993.
26. M. Rothstein, Aspects of symbolic integration and simplification of exponential and primitive functions, Ph.D. Thesis, University of Wisconsin, 1976.
27. B.M. Trager, Algebraic factoring and rational function integration, in: Proceedings of 1976 ACM Symposium on Symbolic and Algebraic Computation, 1976, pp. 219-226.
28. Y.-F. Tsai, R.T. Farouki, B. Feldman, Performance analysis of CNC interpolators for time-dependent feedrates along PH curves, Comput. Aided Geom. Design 18 (2001) 245-265.
29. J. von zur Gathen, J. Gerhard, Modern Computer Algebra, Cambridge University Press, Cambridge, MA, 1999.
30. J.V. Uspensky, Theory of Equations, McGraw-Hill, New York, 1948.
31. M. Wagner, B. Ravani, Curves with rational Frenet-Serret motion, Comput. Aided Geom. Design 15 (1997) 79-101.
32. W. Wang, B. Joe, Robust computation of the rotation minimizing frame for sweep surface modelling, Comput. Aided Design 29 (1997) 379-391.