Free Access
Issue |
ESAIM: M2AN
Volume 26, Number 1, 1992
Topics in computer aided geometric design
|
|
---|---|---|
Page(s) | 149 - 176 | |
DOI | https://doi.org/10.1051/m2an/1992260101491 | |
Published online | 31 January 2017 |
- B. A. BARSKY, The Beta-spline : a local représentation based on shape parameters and fundamental geometric measures, PhD Dissertation, Univ. of Utah, Salt Lake City, USA, 1981. [Google Scholar]
- B. A. BARSKY and J. C. BEATTY, Local control of bias and tension in Beta-splines, ACM Trans. Graph. 2, 109-134, 1983. [Zbl: 0584.65004] [Google Scholar]
- B. A. BARSKY, Computer Graphics and Geometric Modelling Using Beta-splines, Springer, 1988. [MR: 949915] [Zbl: 0648.65008] [Google Scholar]
- B. A. BARSKY, Introducing the rational Beta-spline, Proc. 3rd Int. Conf. Eng. Graphics Descr. Geometry, Vienna, 1988. [MR: 1011496] [Google Scholar]
- B. A. BARSKY and T. D. DEROSE, Geometric continuity of parametric curves : Three equivalent characterizations, IEEE Comput. Graph. Appl 9(5), 60-68, 1989. [Google Scholar]
- B. A. BARSKY and T. D. DEROSE, Geometric continuity of parametric curves : Constructions of geometrically continuous splines, IEEE Comput. Graph. Appl. 60-68, 1990. [Google Scholar]
- R. H. BARTELS and J. C. BEATTY, Beta-splines with a difference, Technical Report CS-83-40, Dept. of Computer Science, Univ. of Waterloo, 1983. [Google Scholar]
- R. H. BARTELS, J. C. BEATTY and B. A. BARSKY, An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann Publishers, 1987. [MR: 919732] [Zbl: 0682.65003] [Google Scholar]
- W. BOEHM, Inserting new knots into a B-spline curve, Comput. Aided Design, 12, 50-62, 1980. [Google Scholar]
- W. BOEHM, G. FARIN and J. KAHMANN, A survey of curve and surface methods in CAGD, Comput. Aided Geom. Design 1, 1-60, 1984. [Zbl: 0604.65005] [Google Scholar]
- W. BOEHM, Curvature continuous curves and surfaces, Comput. Aided Geom. Design 2, 313-323, 1985. [MR: 824102] [Zbl: 0645.53002] [Google Scholar]
- W. BOEHM, Smooth curves and surfaces, in : Farin, G. (ed.), Geometric Modeling, Algorithms and New Trends, SIAM, 1987. [MR: 936453] [Google Scholar]
- W. BOEHM, Rational geometric splines, Comput. Aided Geom. Design 4, 67-77, 1987. [MR: 898024] [Zbl: 0632.65005] [Google Scholar]
- C. DE BOOR, On calculating with B-splines, J. Approx. Theory 6, 50-62, 1972. [MR: 338617] [Zbl: 0239.41006] [Google Scholar]
- C. DE BOOR, A Pratical Guide to Splines, Springer, New York, 1978. [MR: 507062] [Zbl: 0406.41003] [Google Scholar]
- P. DE CASTELJAU, Formes à pôles, Hermes, Paris, 1985. [Zbl: 0655.41001] [Google Scholar]
- P. DE CASTELJAU, Shape Mathematics and CAD, Kogan Page Ltd, London, 1986. [Google Scholar]
- B. W. CHAR et al., Maple Reference Manual, 5th ed., Watcom Publ. Ltd, Waterloo, 1988. [Google Scholar]
- E. COHEN, T. LYCHE and R. F. RIESENFELD, Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics, Comput. Graph. Image Process. 14, 87-111, 1980. [Google Scholar]
- E. COHEN, A new local basis for designing with tensioned splines, ACM Trans. Graph. 6(2), 81-122, 1987. [Google Scholar]
- H. S. M. COXETER, Introductin to Geometry, Wiley, New York, 1961. [MR: 178389] [Zbl: 0095.34502] [Google Scholar]
- T. D. DEROSE, Geometric continuity : a parametrization independent measure of continuity for computer aided geometric design, PhD Dissertation, UC Berkeley, Berkeley, U.S.A., 1985. [Google Scholar]
- T. D. DEROSE and B. A. BARSKY, Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines, ACM Trans. Graph. 7, 1-41, 1988. [Zbl: 0646.65010] [Google Scholar]
- P. DIERCKX and B. TYTGAT, Inserting new knots into Beta-spline curves, in : Lyche, T. and Schumaker, L. L. (eds.), Mathematical Methods in Computer Aided Geometric Design 195-206, Academic Press, 1989. [MR: 1022708] [Zbl: 0693.41014] [Google Scholar]
- P. DIERCKX and B. TYTGAT, Generating the Bezier points of a β-spline curve, Comput. Aided. Geom. Design 6, 279-291, 1989. [MR: 1030615] [Zbl: 0682.65004] [Google Scholar]
- N. DYN, A. EDELMANN and C. A. MICCHELLI, A locally supported basis function for the representation of geometrically continuous curves, Analysis 7, 313-341, 1987. [MR: 928645] [Zbl: 0633.41005] [Google Scholar]
- N. DYN and C. A. MICCHELLI, Piecewise polynomial spaces and geometric continuity of curves, IBM Res. Rep. Mathematical Sciences Dept., IBM T. J. Watson Research Center, Yorktown Heights, N.Y., 1985. [Zbl: 0638.65010] [Google Scholar]
- M. ECK and D. LASSER, B-spline-Bezier representation of geometric spline curves, Preprint 1254, FB. Mathematik, TH. Darmstadt, 1989. [Zbl: 0762.65004] [Google Scholar]
- M. ECK, Algorithms for geometric spline curves, Preprint 1309, FB Mathematik, TH. Darmstadt, 1990. [MR: 1170133] [Zbl: 0799.41011] [Google Scholar]
- G. E. FARIN, Visually C2-cubic splines, Comput. Aided Design. 14, 137-139, 1982. [Google Scholar]
- G. E. FARIN, Some remarks on V2-splines, Comput. Aided Geom. Design 2, 325-328, 1985. [MR: 824103] [Zbl: 0598.41015] [Google Scholar]
- G. E. FARIN, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 1988. [MR: 974109] [Zbl: 0694.68004] [Google Scholar]
- G. GEISE, Über berührende kegelschnitte einer ebenen Kurve, Z. Angew Math. Mech. 42(7/8), 297-304, 1962. [Zbl: 0105.14801] [Google Scholar]
- R. N. GOLDMAN and C. A. MICCHELLI, Algebraic aspects of geometric continuity, in Lyche, T. And Schumarker, L. L. (eds.), Mathematical Methods in Computer Aided Geometric Design, 313-332, Academic Press, 1989. [MR: 1022716] [Zbl: 0679.65006] [Google Scholar]
- R. N. GOLDMAN and B. A. BARSKY, On Beta-continuous functions and their application to the construction of geometrically continuous curves and surfaces, in : Lyche, T. and Schumaker, L. L. (eds.), Mathematical Methods in Computer Aided Geometric Design, 299-312, Academic Press, 1989. [MR: 1022715] [Zbl: 0692.41018] [Google Scholar]
- R. N. GOLDMAN, Blossoming and knot algorithms for B-spline curves, to appear in Comput. Aided Geom. Design. [MR: 1074600] [Google Scholar]
- T. N. T. GOODMAN, Properties of Beta-splines, J. Approx. Theory 44, 132-153, 1985. [MR: 794596] [Zbl: 0569.41010] [Google Scholar]
- T. N. T GOODMAN and K. UNSWORTH, Generation of Beta-spline curves using a recurrence relation, in : Earnashaw, R. (ed.), Fundamental Algorithms for Computer Graphics, 325-357, Springer, 1985. [Google Scholar]
- T. N. T GOODMAN and C. A. MICCHELLI, Corner cutting algorithms for the Bézier representation of free from curves, IBM Research Report RC 12139, IBM T. J. Watson Research Center, Yorktown Heights, N. Y., 1986. [Zbl: 0652.41003] [Google Scholar]
- T. N. T GOODMAN and K. UNSWORTH, Manipulating shape and producing geometric continuity in Beta-spline curves, IEEE Comput. Graph. Appl. 6(2), 50-56, 1986. [Google Scholar]
- T. N. T GOODMAN, Constructing piecewise rational curves with Frenet frame continuity, to appear, in Comput. Aided. Geom. Design. [MR: 1074596] [Zbl: 0709.65010] [Google Scholar]
- J. GREGORY, Geometric continuity, in : Lyche, T. and Schumaker, L. L. (eds.), Mathematical Methods in Computer Aided Geom. Design, Academic Press, 1989. [MR: 1022718] [Zbl: 0675.41023] [Google Scholar]
- H. HAGEN, Geometric spline curves, Comput. Aided Geom. Design 2, 223-227, 1985. [MR: 828548] [Zbl: 0577.65006] [Google Scholar]
- M. E. HOHMEYER and B. A. BARSKY, Rational Continuity : Parametric, Geometric, and Frenet Frame Continuity of Rational Curves, ACM Trans. Graph. 8(4), 1989. [Zbl: 0746.68095] [Google Scholar]
- J. HOSCHEK and D. LASSER, Grundlagen der geometrischen Datenverarbeitung, Teubner, 1989. [MR: 1055828] [Zbl: 0682.68002] [Google Scholar]
- B. JOE, Rational Beta-spline curves and surfaces and discrete Beta-splines, Technical Report TR 87-04, Dept. of Computing Science, Univ. of Alberta, 1987. [Google Scholar]
- B. JOE, Quatric Beta-splines, Technical Report TR 87-11, Dept. of Computing Science, Univ. of Alberta, 1987. [Google Scholar]
- B. JOE, Discrete Beta-splines, Computer Graphics 21(4) (Proc. SIG-GRAPH'87), 137-144, 1987. [MR: 987652] [Google Scholar]
- B. JOE, Multiple-knot and rational cubic β-splines, ACM Trans. Graph. 8(2), 100-120, 1989. [Zbl: 0746.68096] [Google Scholar]
- D. LASSER and M. ECK, Bézier representation of geometric spline curves, Technical Report NPS-53-88-004, Naval Postgraduate Schoo, Monterey, 1988. [Zbl: 0762.65004] [Google Scholar]
- G. M. NIELSON, Some piecewise polynomial alternatives to splines under tension, in : Barnhill, R. E. and Riesenfeld, R. F. (eds.), Computer Aided Geometric Design, Academic Press, 1974. [MR: 371012] [Google Scholar]
- H. POTTMANN, Curves and tensor product surfaces with third order geometric continuity, Proc. 3rd Int. Conf. Eng. Graphics Descr. Geometry, Vienna, 1988. [MR: 1011527] [Google Scholar]
- H. POTTMANN, Projectively invariant classes of geometric continuity, Comput. Aided Geom. Design 6, 307-322, 1989. [MR: 1030617] [Zbl: 0684.65011] [Google Scholar]
- H. PRAUTZSCH, A round trip to B-splines via de Casteljau, ACM Trans. Graph. 8(3), 243-254, 1989. [Zbl: 0746.68099] [Google Scholar]
- L. RAMSHAW, BLOSSOMING : A connect-the-dots approach to splines, Digital Systems Research Center, Palo Alto, 1987. [Google Scholar]
- L. RAMSHAW, Béziers and B-splines as multiaffine maps, in : Theoretical Foundations of Computer Graphics and CAD, 757-776, Springer, 1988. [MR: 944723] [Google Scholar]
- L. RAMSHAW, Blossoms are polar forms, Comput. Aided Geom. Design 6, 323-358, 1989. [MR: 1030618] [Zbl: 0705.65008] [Google Scholar]
- L. L. SCHUMAKER, Spline Functions : Basic Theory, John Wiley & Sons, New York, 1981. [MR: 606200] [Zbl: 0449.41004] [Google Scholar]
- H.-P. SEIDEL, Knot insertion from a blossoming point of view, Comput. Aided Geom. Design 5, 81-86, 1988. [MR: 945308] [Zbl: 0665.65009] [Google Scholar]
- H.-P. SEIDEL, A new multiaffine approach to B-splines, Comput. Aided Geom. Design 6, 23-32, 1989. [MR: 983469] [Zbl: 0666.65011] [Google Scholar]
- H.-P. SEIDEL, Polynome, Splines und symmetrische rekursive Algorithmen im Computer Aided Geometric Design, Habilitationsschrift, Tübingen, 1989. [Google Scholar]
- H.-P. SEIDEL, Geometric Constructions and Knot Insertion for Geometrically Continuous Spline Curves of Arbitrary Degree, Research Report CS-90-24, Department of Computer Science, University of Waterloo, Waterloo, 1990. [Google Scholar]
- M. C. STONE and T. D. DEROSE, A geometric characterization of parametric cubic curves, ACM Trans. Graph. 8, 147-163, 1989. [Zbl: 0746.68102] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.