PN surfaces and their convolutions with rational surfaces

Computer Aided Geometric Design

Volumn 25, Issue 9, 2008, Pages 763-774

  Lávička, Miroslav ^a   Bastl, Bohumír ^a  

^a UNIVERSITY OF WEST BOHEMIA   (Czech Republic)

Author keywords

Convolution surfaces; Offsets; PN surfaces; Proper parameterizations; Rational parameterizations; Square root parameterizations

Indexed keywords

FUNCTIONS; VECTORS;

CONVOLUTION SURFACES; OFFSETS; PN SURFACES; PROPER PARAMETERIZATIONS; RATIONAL PARAMETERIZATIONS; SQUARE-ROOT PARAMETERIZATIONS;

CONVOLUTION;

EID: 54449087735     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2008.06.011     Document Type: Article

References (40)

1. Arrondo E., Sendra J., and Sendra J.R. Parametric generalized offsets to hypersurfaces. Journal of Symbolic Computation 23 (1997) 267-285
2. Aubin J.P., and Frankowska H. Set-Valued Analysis (1990), Birkhäuser, Boston
3. Bastl B., Kosinka J., Jüttler B., and Lávička M. Computing exact rational offsets of quadratic triangular Bézier surface patches. Computer-Aided Design 40 (2008) 197-209
4. Becker T., and Weispfenning V. Gröbner Bases-A Computational Approach to Commutative Algebra. Graduate Texts in Mathematics (1993), Springer-Verlag, New York
5. Cox D., Little J., and O'Shea D. Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics (1992), Springer-Verlag, New York
6. Farouki R.T., and Sakkalis T. Pythagorean hodographs. IBM Journal of Research and Development 34 5 (1990) 736-752
7. Farouki R.T. Pythagorean-hodograph curves in practical use. In: Barnhill R.E. (Ed). Geometry Processing for Design and Manufacturing (1992), SIAM, Philadelphia 3-33
8. Farouki R.T., and Sakkalis T. Pythagorean hodograph space curves. Advances in Computational Mathematics 2 1 (1994) 41-66
9. Farouki R.T., and Neff C.A. Hermite interpolation by Pythagorean-hodograph quintics. Mathematics of Computation 64 212 (1995) 1589-1609
10. Farouki R.T. Pythagorean-hodograph curves. In: Farin G., Hoschek J., and Kim M.-S. (Eds). Handbook of Computer Aided Geometric Design (2002), North-Holland 405-427
11. 2 PH quintic splines. In: Lynche T., Mazure M.L., and Schumaker L.L. (Eds). Curve and Surface Design. St. Malo 2002 (2003), Nashboro Press 147-156
12. Farouki R.T., and Sakkalis T. Rational space curves are not "unit speed". Computer Aided Geometric Design 24 (2007) 238-240
13. Gravesen J., Jüttler B., and Šír Z. On rationally supported surfaces. Computer Aided Geometric Design 25 (2008) 320-331
14. Jüttler B. Triangular Bézier surface patches with linear normal vector field. In: Cripps R. (Ed). The Mathematics of Surfaces VIII (1998), Information Geometers 431-446
15. Jüttler B., and Sampoli M.L. Hermite interpolation by piecewise polynomial surfaces with rational offsets. Computer Aided Geometric Design 17 (2000) 361-385
16. Jüttler B. Hermite interpolation by Pythagorean hodograph curves of degree seven. Mathematics of Computation 70 (2001) 1089-1111
17. 1 Hermite interpolation by Minkowski Pythagorean hodograph cubics. Computer Aided Geometric Design 23 (2006) 401-418
18. Krasauskas R. PN-surfaces for blending applications. In: Electronic Proceedings of Effective Methods in Algebraic Geometry (MEGA) [cit. 2007/08/11]. http://www.ricam.oeaw.ac.at/mega2007/electronic/44.pdf
19. Lávička M., and Bastl B. Rational hypersurfaces with rational convolutions. Computer Aided Geometric Design 24 (2007) 410-426
20. Lü W. Rationality of the offsets to algebraic curves and surfaces. Applied Mathematics, A Journal of Chinese Universities, Series B 9 (1994) 265-277
21. Lü W. Offset-rational parametric plane curves. Computer-Aided Design 12 (1995) 601-616
22. Lü W., and Pottmann H. Pipe surfaces with rational spine curve are rational. Computer Aided Geometric Design 13 (1996) 621-628
23. Lü W., and Pottmann H. Rational parameterization of quadrics and their offsets. Computing 57 (1996) 135-147
24. Maekawa T. An overview of offset curves and surfaces. Computer-Aided Design 31 (1999) 165-173
25. Moon H.P. Minkowski Pythagorean hodographs. Computer Aided Geometric Design 16 (1999) 739-753
26. 2 PH quintic spline curves. Computer Aided Geometric Design 24 (2007) 28-52
27. Pérez-Díaz S. On the problem of proper reparametrization for rational curves and surfaces. Computer Aided Geometric Design 23 (2006) 307-323
28. Pérez-Díaz S., Schicho J., and Sendra J.R. Properness and inversion of rational parametrizations of surfaces. Applicable Algebra in Engineering Communication and Computing 13 (2002) 29-51
29. Peternell M., and Pottmann H. A Laguerre geometric approach to rational offsets. Computer Aided Geometric Design 15 (1998) 223-249
30. Peternell M., and Manhart F. The convolution of a paraboloid and a parametrized surface. Journal for Geometry and Graphics 7 (2003) 157-171
31. Peternell M., and Odehnal B. Convolution surfaces of quadratic triangular Bézier surfaces. Computer Aided Geometric Design 25 (2008) 116-129
32. Pham B. Offset curves and surfaces: A brief survey. Computer-Aided Design 24 (1992) 223-229
33. Piegl L.A., and Tiller W. Computing offsets of NURBS curves and surfaces. Computer-Aided Design 31 (1999) 147-156
34. Pottmann H. Rational curves and surfaces with rational offsets. Computer Aided Geometric Design 12 (1995) 175-192
35. Pottmann H., and Peternell M. Applications of Laguerre geometry in CAGD. Computer Aided Geometric Design 15 (1998) 165-186
36. Sampoli M.L., Peternell M., and Jüttler B. Rational surfaces with linear normals and their convolutions with rational surfaces. Computer Aided Geometric Design 23 (2006) 179-192
37. Sendra J.R., and Sendra J. Algebraic analysis of offsets to hypersurfaces. Mathematische Zeitschrift 234 (2000) 697-719
38. Šír Z., Feichtinger R., and Jüttler B. Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics. Computer-Aided Design 38 (2006) 608-618
39. Šír Z., Gravesen J., and Jüttler B. Computing convolutions and Minkowski sums via support functions. In: Chenin P., Lyche T., and Schumaker L.L. (Eds). Curve and Surface Design. Avignon 2006 (2007), Nashboro Press 244-253
40. 2 Hermite interpolation by Pythagorean hodograph space curves. Mathematics of Computation 76 (2007) 1373-1391