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Volumn 15, Issue 3, 1998, Pages 223-249

A Laguerre geometric approach to rational offsets

Author keywords

Geometrical optics; Laguerre geometry; NC milling; Offset; Principal curvature line; Principal patch; Rational curve; Rational offset: Pythagorean hodograph curve; Rational surface

Indexed keywords

ALGORITHMS; COMPUTER AIDED DESIGN; GEOMETRICAL OPTICS; MATHEMATICAL TRANSFORMATIONS; SURFACES;

EID: 0032027896     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(97)00024-1     Document Type: Article
Times cited : (96)

References (38)
  • 1
    • 0002799393 scopus 로고
    • 2 approximation of an offset curve by Tschirnhausen quartics
    • Daehlen, M., Lyche, T. and Schumaker, L.L., eds., Vanderbilt University Press
    • 2 approximation of an offset curve by Tschirnhausen quartics, in: Daehlen, M., Lyche, T. and Schumaker, L.L., eds., Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, 1-10.
    • (1995) Mathematical Methods for Curves and Surfaces , pp. 1-10
    • Ait Haddou, R.1    Biard, L.2
  • 2
    • 0039829557 scopus 로고    scopus 로고
    • 2 Pythagorean-hodograph interpolating splines by the homotopy method
    • to appear
    • 2 Pythagorean-hodograph interpolating splines by the homotopy method, Advances in Comp. Math., to appear.
    • (1996) Advances in Comp. Math.
    • Albrecht, G.1    Farouki, R.T.2
  • 3
    • 0029291510 scopus 로고
    • Curvature continuous connections of cones and cylinders
    • Aumann, G. (1995), Curvature continuous connections of cones and cylinders, Computer-Aided Design 27, 293-310.
    • (1995) Computer-Aided Design , vol.27 , pp. 293-310
    • Aumann, G.1
  • 4
    • 0038850557 scopus 로고
    • Untersuchungen über die geometrie der speere in der eukhdischen ebene
    • Blaschke, W. (1910), Untersuchungen über die Geometrie der Speere in der Eukhdischen Ebene, Monatshefte für Mathematik und Physik 21, 3-60.
    • (1910) Monatshefte für Mathematik und Physik , vol.21 , pp. 3-60
    • Blaschke, W.1
  • 6
    • 0041016242 scopus 로고
    • An introduction to Padé approximations
    • Laurent, P.J., Le Méhauté A. and Schumaker, L.L., eds., A K Peters, Boston
    • Brezinski, C. (1993), An Introduction to Padé Approximations, in: Laurent, P.J., Le Méhauté A. and Schumaker, L.L., eds., Curves and Surfaces II, A K Peters, Boston, 1-10.
    • (1993) Curves and Surfaces II , pp. 1-10
    • Brezinski, C.1
  • 8
    • 0039237736 scopus 로고
    • Rational Bézier curves and surfaces on projective domains
    • Farin, G., ed., SIAM, Philadelphia
    • DeRose, T.D. (1991), Rational Bézier curves and surfaces on projective domains, in: Farin, G., ed., NURBS for Curve and Surface Design, SIAM, Philadelphia, 35-45.
    • (1991) NURBS for Curve and Surface Design , pp. 35-45
    • DeRose, T.D.1
  • 10
    • 0027640669 scopus 로고
    • An algebraic approach to curves and surfaces on the sphere and on other quadrics
    • Dietz, R., Hoschek, J. and Jüttler, B. (1993), An algebraic approach to curves and surfaces on the sphere and on other quadrics, Computer Aided Geometric Design 10, 211-229.
    • (1993) Computer Aided Geometric Design , vol.10 , pp. 211-229
    • Dietz, R.1    Hoschek, J.2    Jüttler, B.3
  • 11
    • 0002452294 scopus 로고
    • Pythagorean-hodograph curves in practical use
    • Barnhill, R.E., ed., SIAM, Philadelphia
    • Farouki, R.T. (1992), Pythagorean-hodograph curves in practical use, in: Barnhill, R.E., ed., Geometry Processing for Design and Manufacturing, SIAM, Philadelphia, 3-33.
    • (1992) Geometry Processing for Design and Manufacturing , pp. 3-33
    • Farouki, R.T.1
  • 13
    • 21844514153 scopus 로고
    • Hermite interpolation by Pythagorean-hodograph quintics
    • Farouki, R.T. and Neff, C.A. (1995), Hermite interpolation by Pythagorean-hodograph quintics, Math. Comp. 64, 1589-1609.
    • (1995) Math. Comp. , vol.64 , pp. 1589-1609
    • Farouki, R.T.1    Neff, C.A.2
  • 16
    • 0028743805 scopus 로고
    • Offset curves in layered manufacturing
    • Manufacturing Science and Engineering Book No. G0930B
    • Farouki, R.T. et al. (1994), Offset curves in layered manufacturing. ASME PED, Vol. 68-2, Manufacturing Science and Engineering Book No. G0930B, 557-568.
    • (1994) ASME PED , vol.68 , Issue.2 , pp. 557-568
    • Farouki, R.T.1
  • 17
    • 0001952424 scopus 로고
    • Characterization of the set of rational parametric curves with rational offsets
    • Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., A K Peters, Wellesley, MA
    • Fiorot, J.C. and Gensane, T. (1994), Characterization of the set of rational parametric curves with rational offsets, in: Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., Curves and Surfaces in Geometric Design, A K Peters, Wellesley, MA, 153-160.
    • (1994) Curves and Surfaces in Geometric Design , pp. 153-160
    • Fiorot, J.C.1    Gensane, T.2
  • 18
    • 0039237600 scopus 로고
    • Geometric constraints for CAGD
    • M, Daehlen, T. Lyche and Schumaker, L.L., eds.
    • Hoffmann, Ch. M. and Peters, J. (1995), Geometric Constraints for CAGD, in: M, Daehlen, T. Lyche and Schumaker, L.L., eds., Mathematical Methods in CAGD III, 1-16.
    • (1995) Mathematical Methods in CAGD III , pp. 1-16
    • Hoffmann, Ch.M.1    Peters, J.2
  • 19
    • 0030169416 scopus 로고    scopus 로고
    • Computer aided design with spatial rational B-spline motions
    • Jüttler, B. and Wagner, M. (1996), Computer aided design with spatial rational B-spline motions. ASME J. of Mechanical Design 118, 193-201.
    • (1996) ASME J. of Mechanical Design , vol.118 , pp. 193-201
    • Jüttler, B.1    Wagner, M.2
  • 20
    • 51249168031 scopus 로고
    • Rationality of the offsets to algebraic curves and surfaces
    • Ser. B
    • Lü, W. (1994), Rationality of the offsets to algebraic curves and surfaces, Applied Mathematics 9 (Ser. B), 265-278.
    • (1994) Applied Mathematics , vol.9 , pp. 265-278
    • Lü, W.1
  • 21
    • 0002928828 scopus 로고
    • Offset-rational parametric plane curves
    • Lü, W. (1995), Offset-rational parametric plane curves, Computer Aided Geometric Design 12, 601-616.
    • (1995) Computer Aided Geometric Design , vol.12 , pp. 601-616
    • Lü, W.1
  • 22
    • 0030394157 scopus 로고    scopus 로고
    • Rational parameterization of quadrics and their offsets
    • Lü, W. (1996), Rational parameterization of quadrics and their offsets. Computing 57, 135-147.
    • (1996) Computing , vol.57 , pp. 135-147
    • Lü, W.1
  • 23
    • 0030257440 scopus 로고    scopus 로고
    • Pipe surfaces with rational spine curve are rational
    • Lü, W. and Pottmann, H. (1996), Pipe surfaces with rational spine curve are rational, Computer Aided Geometric Design 13, 621-628.
    • (1996) Computer Aided Geometric Design , vol.13 , pp. 621-628
    • Lü, W.1    Pottmann, H.2
  • 25
    • 0003301752 scopus 로고    scopus 로고
    • Designing rational surfaces with rational offsets
    • Fontanella, F., Jetter, K. and Laurent, P.J., eds., World Scientific
    • Peternell, M. and Pottmann, H. (1996), Designing rational surfaces with rational offsets, in: Fontanella, F., Jetter, K. and Laurent, P.J., eds., Advanced Topics in Multivariate Approximation, World Scientific, 275-286.
    • (1996) Advanced Topics in Multivariate Approximation , pp. 275-286
    • Peternell, M.1    Pottmann, H.2
  • 26
    • 0031073214 scopus 로고    scopus 로고
    • Computing rational parametrizations of canal surfaces
    • Peternell, M. and Pottmann, H. (1997), Computing rational parametrizations of canal surfaces, J. Symbolic Computation 23, 255-266.
    • (1997) J. Symbolic Computation , vol.23 , pp. 255-266
    • Peternell, M.1    Pottmann, H.2
  • 27
    • 0000182266 scopus 로고
    • Applications of the dual Bézier representation of rational curves and surfaces
    • Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., A K Peters, Wellesley, MA
    • Pottmann, H. (1994), Applications of the dual Bézier representation of rational curves and surfaces, in: Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., Curves and Surfaces in Geometric Design, A K Peters, Wellesley, MA, 377-384.
    • (1994) Curves and Surfaces in Geometric Design , pp. 377-384
    • Pottmann, H.1
  • 28
    • 0029271014 scopus 로고
    • Rational curves and surfaces with rational offsets
    • Pottmann, H. (1995a), Rational curves and surfaces with rational offsets, Computer Aided Geometric Design 12, 175-192.
    • (1995) Computer Aided Geometric Design , vol.12 , pp. 175-192
    • Pottmann, H.1
  • 29
    • 0001383351 scopus 로고
    • Curve design with rational Pythagorean-hodograph curves
    • Pottmann, H. (1995b). Curve design with rational Pythagorean-hodograph curves, Advances in Comp. Math. 3, 147-170.
    • (1995) Advances in Comp. Math. , vol.3 , pp. 147-170
    • Pottmann, H.1
  • 30
    • 0029357520 scopus 로고
    • Developable rational Bézier and B-spline surfaces
    • Pottmann, H. and Farin, G. (1995), Developable rational Bézier and B-spline surfaces. Computer Aided Geometric Design 12, 513-531.
    • (1995) Computer Aided Geometric Design , vol.12 , pp. 513-531
    • Pottmann, H.1    Farin, G.2
  • 33
    • 0039829556 scopus 로고    scopus 로고
    • Principal surfaces
    • T.N.T. Goodman (ed.), Information Geometers Ltd., to appear
    • Pottmann, H., and Wagner, M. (1997), Principal Surfaces, in: T.N.T. Goodman (ed.), The Mathematics of Surfaces VII, Information Geometers Ltd., to appear.
    • (1997) The Mathematics of Surfaces VII
    • Pottmann, H.1    Wagner, M.2
  • 34
    • 0040422201 scopus 로고
    • Methodus curvas determinandi, quae formantur a radiis reflectis, quorum incidentes ut paralleli considerantur
    • Febr. 1690
    • Tschirnhaus, W. von (1690), Methodus curvas determinandi, quae formantur a radiis reflectis, quorum incidentes ut paralleli considerantur, Acta Eruditorum, Febr. 1690, 68-75.
    • (1690) Acta Eruditorum , pp. 68-75
    • Von Tschirnhaus, W.1
  • 35
    • 0040422198 scopus 로고    scopus 로고
    • Computer aided design of robot trajectories using rational Frenet-Serret motions
    • J. Lenarcic and V. Parenti-Castelli (eds.) Kluwer Academic Publishers, Dordrecht
    • Wagner, M. and Ravani, B. (1996), Computer aided design of robot trajectories using rational Frenet-Serret motions, in: J. Lenarcic and V. Parenti-Castelli (eds.) Recent Advances in Robot Kinematics, Kluwer Academic Publishers, Dordrecht, 151-158.
    • (1996) Recent Advances in Robot Kinematics , pp. 151-158
    • Wagner, M.1    Ravani, B.2
  • 37
    • 0040422197 scopus 로고
    • Spiegelung am elliptischen Paraboloid
    • Wunderlich, W. (1948), Spiegelung am elliptischen Paraboloid, Monatsh. Math, 52, 13-37.
    • (1948) Monatsh. Math , vol.52 , pp. 13-37
    • Wunderlich, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.