Pipe surfaces with rational spine curve are rational

Computer Aided Geometric Design

Volumn 13, Issue 7, 1996, Pages 621-628

  Lü, Wei ^a,b   Pottmann, Helmut ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b ZHEJIANG UNIVERSITY   (China)

Author keywords

Blend surface; Normal ringed surface; Offset surface; Pipe surface; Pythagorean hodograph curve; Rational parameterization; Rational surface

Indexed keywords

ALGORITHMS; CURVE FITTING; FUNCTIONS; PIPE; POLYNOMIALS; SURFACES;

PIPE SURFACES; RATIONAL FUNCTIONS; RATIONAL SPINE CURVE;

COMPUTER AIDED DESIGN;

EID: 0030257440     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-8396(95)00051-8     Document Type: Article

References (17)

1. 2 approximation of an offset curve by Tschirnhausen quartics, in: M. Daehlen, T. Lyche and L.L. Schumaker, eds., Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, 1-10.
2. 2 Pythagorean-hodograph interpolating splines by the homotopy method, Advances in Comp. Math., to appear.
3. Aumann, G. (1995), Curvature continuous connections of cones and cylinders, Computer Aided Design 27, 293-310.
4. Farin, G. (1994), NURBS for Rational Curve and Surface Design, AK Peters, Wellesley, MA, 1994.
5. Farouki, R.T. (1992), Pythagorean-hodograph curves in practical use, in: R.E. Barnhill, ed., Geometry Processing for Design and Manufacturing, SIAM, Philadelphia, 3-33.
6. 2 of the hodograph plane, Computer Aided Geometric Design 11, 363-390.
7. Farouki, R.T. and Neff, C.A. (1995), Hermite interpolation by Pythagorean-hodograph quintics, Math. Comp. 64, 1589-1609.
8. Farouki, R.T. and Sakkalis, T. (1990), Pythagorean hodographs, IBM J. Res. Develop. 34, 736-752.
9. Farouki, R.T. and Sakkalis, T. (1994), Pythagorean-hodograph space curves, Advances in Comp. Math. 2, 41-66.
10. Fiorot, J.C. and Gensane, T. (1994), Characterizations of the set of rational paramatric curves with rational offsets, in: P.J. Laurent, A. LeMéhauté and L.L. Schumaker, eds., Curves and Surfaces in Geometric Design, AK Peters, Wellesley, MA, 153-160.
11. Hoschek, J. and Lasser, D. (1993), Fundamentals of Computer Aided Geometric Design, AK Peters, Wellesley, MA, 1993.
12. Lü, W. (1994), Rationality of the offsets to algebraic curves and surfaces, Applied Mathematics (Journal of Chinese Universities, Ser. B) 9, 265-278.
13. Lü, W. (1995), Offset-rational parametric plane curves, Computer Aided Geometric Design 12, 601-616.
14. Peternell, M. and Pottmann, H. (1995), Computing rational parametrizations of canal surfaces, Preprint.
15. Pottmann, H. (1994), Applications of the dual Bézier representation of rational curves and surfaces, in: P.J. Laurent, A. LeMéhauté and L.L. Schumaker, eds., Curves and Surfaces in Geometric Design, AK Peters, Wellesley, MA, 377-384.
16. Pottmann, H. (1995a), Rational curves and surfaces with rational offsets, Computer Aided Geometric Design 12, 175-192.
17. Pottmann, H. (1995b), Curve design with rational Pythagorean-hodograph curves, Advances in Comp. Math. 3, 147-170.