@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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {149--176}, publisher = {AFCET - Gauthier-Villars}, address = {Paris}, volume = {26}, number = {1}, year = {1992}, mrnumber = {1155005}, zbl = {0752.65008}, language = {en}, url = {http://archive.numdam.org/item/M2AN_1992__26_1_149_0/} }

TY - JOUR AU - Seidel, H.-P. TI - New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1992 SP - 149 EP - 176 VL - 26 IS - 1 PB - AFCET - Gauthier-Villars PP - Paris UR - http://archive.numdam.org/item/M2AN_1992__26_1_149_0/ LA - en ID - M2AN_1992__26_1_149_0 ER -

%0 Journal Article %A Seidel, H.-P. %T New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree %J ESAIM: Modélisation mathématique et analyse numérique %D 1992 %P 149-176 %V 26 %N 1 %I AFCET - Gauthier-Villars %C Paris %U http://archive.numdam.org/item/M2AN_1992__26_1_149_0/ %G en %F M2AN_1992__26_1_149_0

Seidel, H.-P. New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree. ESAIM: Modélisation mathématique et analyse numérique, Volume 26 (1992) no. 1, pp. 149-176. http://archive.numdam.org/item/M2AN_1992__26_1_149_0/

[1] 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] Local control of bias and tension in Beta-splines, ACM Trans. Graph. 2, 109-134, 1983. | Zbl

and ,[3] Computer Graphics and Geometric Modelling Using Beta-splines, Springer, 1988. | MR | Zbl

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

,[5] Geometric continuity of parametric curves : Three equivalent characterizations, IEEE Comput. Graph. Appl 9(5), 60-68, 1989.

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

and ,[7] Beta-splines with a difference, Technical Report CS-83-40, Dept. of Computer Science, Univ. of Waterloo, 1983.

and ,[8] An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann Publishers, 1987. | MR | Zbl

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

,[10] A survey of curve and surface methods in CAGD, Comput. Aided Geom. Design 1, 1-60, 1984. | Zbl

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

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

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

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

,[15] A Pratical Guide to Splines, Springer, New York, 1978. | MR | Zbl

,[16] Formes à pôles, Hermes, Paris, 1985. | Zbl

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

,[18] Maple Reference Manual, 5th ed., Watcom Publ. Ltd, Waterloo, 1988.

et al.,[19] Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics, Comput. Graph. Image Process. 14, 87-111, 1980.

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

,[21] Introductin to Geometry, Wiley, New York, 1961. | MR | Zbl

,[22] Geometric continuity : a parametrization independent measure of continuity for computer aided geometric design, PhD Dissertation, UC Berkeley, Berkeley, U.S.A., 1985.

,[23] Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines, ACM Trans. Graph. 7, 1-41, 1988. | Zbl

and ,[24] 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 | Zbl

and ,[25] Generating the Bezier points of a β-spline curve, Comput. Aided. Geom. Design 6, 279-291, 1989. | MR | Zbl

and ,[26] A locally supported basis function for the representation of geometrically continuous curves, Analysis 7, 313-341, 1987. | MR | Zbl

, and ,[27] 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

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

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

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

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

,[32] Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 1988. | MR | Zbl

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

,[34] 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 | Zbl

and ,[35] 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 | Zbl

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

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

,[38] Generation of Beta-spline curves using a recurrence relation, in : Earnashaw, R. (ed.), Fundamental Algorithms for Computer Graphics, 325-357, Springer, 1985.

and ,[39] 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

and ,[40] Manipulating shape and producing geometric continuity in Beta-spline curves, IEEE Comput. Graph. Appl. 6(2), 50-56, 1986.

and ,[41] Constructing piecewise rational curves with Frenet frame continuity, to appear, in Comput. Aided. Geom. Design. | MR | Zbl

,[42] Geometric continuity, in : Lyche, T. and Schumaker, L. L. (eds.), Mathematical Methods in Computer Aided Geom. Design, Academic Press, 1989. | MR | Zbl

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

,[44] Rational Continuity : Parametric, Geometric, and Frenet Frame Continuity of Rational Curves, ACM Trans. Graph. 8(4), 1989. | Zbl

and ,[45] Grundlagen der geometrischen Datenverarbeitung, Teubner, 1989. | MR | Zbl

and ,[46] Rational Beta-spline curves and surfaces and discrete Beta-splines, Technical Report TR 87-04, Dept. of Computing Science, Univ. of Alberta, 1987.

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

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

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

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

and ,[51] 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

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

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

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

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

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

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

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

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

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

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

,[62] 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] A geometric characterization of parametric cubic curves, ACM Trans. Graph. 8, 147-163, 1989. | Zbl

and ,