New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree
Seidel, H.-P.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 26 (1992), p. 149-176 / Harvested from Numdam
@article{M2AN_1992__26_1_149_0,
     author = {Seidel, H.-P.},
     title = {New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {26},
     year = {1992},
     pages = {149-176},
     mrnumber = {1155005},
     zbl = {0752.65008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1992__26_1_149_0}
}
Seidel, H.-P. New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 26 (1992) pp. 149-176. http://gdmltest.u-ga.fr/item/M2AN_1992__26_1_149_0/

[1] 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.

[2] 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

[3] B. A. Barsky, Computer Graphics and Geometric Modelling Using Beta-splines, Springer, 1988. | MR 949915 | Zbl 0648.65008

[4] B. A. Barsky, Introducing the rational Beta-spline, Proc. 3rd Int. Conf. Eng. Graphics Descr. Geometry, Vienna, 1988. | MR 1011496

[5] B. A. Barsky and T. D. Derose, Geometric continuity of parametric curves : Three equivalent characterizations, IEEE Comput. Graph. Appl 9(5), 60-68, 1989.

[6] B. A. Barsky and T. D. Derose, Geometric continuity of parametric curves : Constructions of geometrically continuous splines, IEEE Comput. Graph. Appl. 60-68, 1990.

[7] 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.

[8] 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

[9] W. Boehm, Inserting new knots into a B-spline curve, Comput. Aided Design, 12, 50-62, 1980.

[10] 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

[11] W. Boehm, Curvature continuous curves and surfaces, Comput. Aided Geom. Design 2, 313-323, 1985. | MR 824102 | Zbl 0645.53002

[12] W. Boehm, Smooth curves and surfaces, in : Farin, G. (ed.), Geometric Modeling, Algorithms and New Trends, SIAM, 1987. | MR 936453

[13] W. Boehm, Rational geometric splines, Comput. Aided Geom. Design 4, 67-77, 1987. | MR 898024 | Zbl 0632.65005

[14] C. De Boor, On calculating with B-splines, J. Approx. Theory 6, 50-62, 1972. | MR 338617 | Zbl 0239.41006

[15] C. De Boor, A Pratical Guide to Splines, Springer, New York, 1978. | MR 507062 | Zbl 0406.41003

[16] P. De Casteljau, Formes à pôles, Hermes, Paris, 1985. | Zbl 0655.41001

[17] P. De Casteljau, Shape Mathematics and CAD, Kogan Page Ltd, London, 1986.

[18] B. W. Char et al., Maple Reference Manual, 5th ed., Watcom Publ. Ltd, Waterloo, 1988.

[19] 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.

[20] E. Cohen, A new local basis for designing with tensioned splines, ACM Trans. Graph. 6(2), 81-122, 1987.

[21] H. S. M. Coxeter, Introductin to Geometry, Wiley, New York, 1961. | MR 178389 | Zbl 0095.34502

[22] 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.

[23] 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

[24] 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

[25] 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

[26] 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

[27] 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

[28] M. Eck and D. Lasser, B-spline-Bezier representation of geometric spline curves, Preprint 1254, FB. Mathematik, TH. Darmstadt, 1989. | Zbl 0762.65004

[29] M. Eck, Algorithms for geometric spline curves, Preprint 1309, FB Mathematik, TH. Darmstadt, 1990. | MR 1170133 | Zbl 0799.41011

[30] G. E. Farin, Visually C2-cubic splines, Comput. Aided Design. 14, 137-139, 1982.

[31] G. E. Farin, Some remarks on V2-splines, Comput. Aided Geom. Design 2, 325-328, 1985. | MR 824103 | Zbl 0598.41015

[32] G. E. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 1988. | MR 974109 | Zbl 0694.68004

[33] G. Geise, Über berührende kegelschnitte einer ebenen Kurve, Z. Angew Math. Mech. 42(7/8), 297-304, 1962. | Zbl 0105.14801

[34] 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

[35] 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

[36] R. N. Goldman, Blossoming and knot algorithms for B-spline curves, to appear in Comput. Aided Geom. Design. | MR 1074600

[37] T. N. T. Goodman, Properties of Beta-splines, J. Approx. Theory 44, 132-153, 1985. | MR 794596 | Zbl 0569.41010

[38] 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.

[39] 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

[40] 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.

[41] T. N. T Goodman, Constructing piecewise rational curves with Frenet frame continuity, to appear, in Comput. Aided. Geom. Design. | MR 1074596 | Zbl 0709.65010

[42] 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

[43] H. Hagen, Geometric spline curves, Comput. Aided Geom. Design 2, 223-227, 1985. | MR 828548 | Zbl 0577.65006

[44] 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

[45] J. Hoschek and D. Lasser, Grundlagen der geometrischen Datenverarbeitung, Teubner, 1989. | MR 1055828 | Zbl 0682.68002

[46] 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.

[47] B. Joe, Quatric Beta-splines, Technical Report TR 87-11, Dept. of Computing Science, Univ. of Alberta, 1987.

[48] B. Joe, Discrete Beta-splines, Computer Graphics 21(4) (Proc. SIG-GRAPH'87), 137-144, 1987. | MR 987652

[49] B. Joe, Multiple-knot and rational cubic β-splines, ACM Trans. Graph. 8(2), 100-120, 1989. | Zbl 0746.68096

[50] D. Lasser and M. Eck, Bézier representation of geometric spline curves, Technical Report NPS-53-88-004, Naval Postgraduate Schoo, Monterey, 1988.

[51] 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

[52] H. Pottmann, Curves and tensor product surfaces with third order geometric continuity, Proc. 3rd Int. Conf. Eng. Graphics Descr. Geometry, Vienna, 1988. | MR 1011527

[53] H. Pottmann, Projectively invariant classes of geometric continuity, Comput. Aided Geom. Design 6, 307-322, 1989. | MR 1030617 | Zbl 0684.65011

[54] H. Prautzsch, A round trip to B-splines via de Casteljau, ACM Trans. Graph. 8(3), 243-254, 1989. | Zbl 0746.68099

[55] L. Ramshaw, Blossoming : A connect-the-dots approach to splines, Digital Systems Research Center, Palo Alto, 1987.

[56] L. Ramshaw, Béziers and B-splines as multiaffine maps, in : Theoretical Foundations of Computer Graphics and CAD, 757-776, Springer, 1988. | MR 944723

[57] L. Ramshaw, Blossoms are polar forms, Comput. Aided Geom. Design 6, 323-358, 1989. | MR 1030618 | Zbl 0705.65008

[58] L. L. Schumaker, Spline Functions : Basic Theory, John Wiley & Sons, New York, 1981. | MR 606200 | Zbl 0449.41004

[59] H.-P. Seidel, Knot insertion from a blossoming point of view, Comput. Aided Geom. Design 5, 81-86, 1988. | MR 945308 | Zbl 0665.65009

[60] H.-P. Seidel, A new multiaffine approach to B-splines, Comput. Aided Geom. Design 6, 23-32, 1989. | MR 983469 | Zbl 0666.65011

[61] H.-P. Seidel, Polynome, Splines und symmetrische rekursive Algorithmen im Computer Aided Geometric Design, Habilitationsschrift, Tübingen, 1989.

[62] 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.

[63] M. C. Stone and T. D. Derose, A geometric characterization of parametric cubic curves, ACM Trans. Graph. 8, 147-163, 1989. | Zbl 0746.68102