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Brian A. Barsky, Tony D. DeRose, "Parametric Curves, Part Two," IEEE Computer Graphics and Applications, vol. 10, no. 1, pp. 6068, January/February, 1990.  
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@article{ 10.1109/38.45811, author = {Brian A. Barsky and Tony D. DeRose}, title = {Parametric Curves, Part Two}, journal ={IEEE Computer Graphics and Applications}, volume = {10}, number = {1}, issn = {02721716}, year = {1990}, pages = {6068}, doi = {http://doi.ieeecomputersociety.org/10.1109/38.45811}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  MGZN JO  IEEE Computer Graphics and Applications TI  Parametric Curves, Part Two IS  1 SN  02721716 SP60 EP68 EPD  6068 A1  Brian A. Barsky, A1  Tony D. DeRose, PY  1990 VL  10 JA  IEEE Computer Graphics and Applications ER   
Some observations are made concerning the source and nature of shape parameters. It is then described how Bezier curve segments can be stitched together with G/sup 1/ or G/sup 2/ continuity, using geometric constructions. These constructions lead to the development of geometric constructions for quadratic G/sup 1/ and cubic G/sup 2/ Betasplines. A geometrically continuous subclass of CatmullRom splines based on geometric continuity and possessing shape parameters is discussed.
1. B.A. Barsky and T.D. DeRose, "Geometric Continuity of Parametric Curves: Three Equivalent Characterizations,"CG&A, Vol. 9, No. 6, Nov. 1989, pp. 6068.
2. B.A. Barsky, "A Description and Evaluation of Various 3D Models,"CG&A, Vol. 4, No. 1, Jan. 1984, pp. 3852.
3. 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, Los Altos, Calif., 1987.
4. P.E. Bezier,Emploi des machines a commande numerique, Masson et Cie., Paris, 1970; trans. A.R. Forrest and A.F. Pankhurst,Numerical ControlMathematics and Applications, John Wiley, London, 1972.
5. P.E. Bezier, "Mathematical and Practical Possibilities of UNISURF," inComputer Aided Geometric Design, R.E. Barnhill and R.F. Riesenfeld, eds., Academic Press, New York, 1974, pp. 127152.
6. P.E. Bezier,Essai de definition numerique des courbes et des surfaces experimentales [An Attempt to Define Experimental Curves and Surfaces Numerically], doctoral dissertation, Pierre and Marie Curie University, Paris, 1977.
7. W. Boehm, G. Farin, and J. Kahmann, "A survey of curve and surface methods in CAGD,"Comput. Aided Geometric Des., vol. 1, no. 1, pp. 160, July 1984.
8. G. Farin,Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston, 1988.
9. A. Fournier and B.A. Barsky, "Geometric Continuity with Interpolating Bezier Curves" (extended summary),Proc. Graphics Interface, Canadian Information Processing Soc., Toronto, 1985, pp. 337341; revised forComputerGenerated Images: The State of the Art, N. MagnenatThalmann and D. Thalmann, eds., SpringerVerlag, Tokyo, 1985, pp. 153158.
10. G. Farin, "Visually C2 Cubic Splines,"ComputerAided Design, Vol. 14, No. 3, May 1982, pp. 137139.
11. W. Boehm, "Curvature Continuous Curves and Surfaces,"Computer Aided Geometric Design, Vol. 2, No. 4, Dec. 1985, pp. 313323.
12. T.D. DeRose, "Composing Bezier Simplexes,"ACM Trans. Graphics, Vol. 7, No. 3, Jan. 1988, pp. 198221.
13. B.A. Barsky, "The betaspline: A local representation based on shape parameters and fundamental geometric measures," Ph.D. dissertation, Univ. of Utah, Salt Lake City, Dec. 1981.
14. B.A. Barsky,Computer Graphics and Geometric Modeling Using BetaSplines, SpringerVerlag, Heidelberg, W. Germany, 1988.
15. B.A. Barsky and J.C. Beatty, "Local Control of Bias and Tension in BetaSplines,"ACM Trans. Graphics, Vol. 2, No. 2, Apr. 1983, pp. 109134; also published inComputer Graphics(Proc. SIGGRAPH), Vol. 17, No. 3, July 1983, pp. 193218.
16. B.A. Barsky and T.D. DeRose, "The Beta 2Spline: A Special Case of the BetaSpline Curve and Surface Representation,"CG&A, Vol. 5, No. 9, Sept. 1985, pp. 4658; correction published in Letter to the Editor,CG&A, Vol. 7, No. 3, Mar. 1987, p. 15.
17. B.A. Barsky, T.D. DeRose, and M.D. Dippe, "An Adaptive Subdivision Method with Crack Prevention for Rendering BetaSpline Objects," Tech. Report UCB/CSD 87/348, Computer Science Div., Dept. of Electrical Eng. and Computer Sciences, Univ. of California, Berkeley, Calif., 1987.
18. R.H. Bartels and J.C. Beatty, "BetaSplines with a Difference," Tech. Report CS8340, Dept. of Computer Science, Univ. of Waterloo, Waterloo, Canada, 1984.
19. E. Cohen, "A New Local Basis for Designing with Tensioned Splines,"ACM Trans. Graphics, Vol. 6, No. 2, Apr. 1987, pp. 81122.
20. T.N.T. Goodman, "Properties of BetaSplines,"J. Approximation Theory, Vol. 44, No. 2, June 1985, pp. 132153.
21. T.N.T. Goodman and K. Unsworth, "Generation of BetaSpline Curves Using a Recurrence Relation," inFundamental Algorithms for Computer Graphics, R.A. Earnshaw, ed., NATO Advanced Study Inst. Series, Ser. F, Vol. 17, pp. 325357.
22. T.N.T. Goodman and K. Unsworth, "Manipulating Shape and Producing Geometric Continuity inβSpline Curves,"CG&A, Vol. 6, No. 2, Feb. 1986, pp. 5056.
23. B. Joe, "Rational BetaSpline Curves and Surfaces and Discrete BetaSplines," Tech. Report TR8704, Dept. of Computing Science, Univ. of Alberta, Edmonton, Canada, 1987.
24. B. Joe, "Discrete BetaSplines,"Computer Graphics(Proc. SIGGRAPH), Vol. 21, No. 4, July 1987, pp. 137144.
25. B.A. Barsky and T.D. DeRose, "Geometric Continuity of Parametric Curves," Tech. Report UCB/CSD 84/205, Computer Science Div., Dept. of Electrical Eng. and Computer Sciences, Univ. of California, Berkeley, Calif., 1984.
26. J.M. Lane and R.F. Riesenfeld, "A Theoretical Development for the Computer Generation of Piecewise Polynomial Surfaces,"IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 2, No. 1, Jan. 1980, pp. 3546.
27. N. Dyn and C.A. Micchelli, "Piecewise Polynomial Spaces and Geometric Continuity of Curves," Research Report 11390, IBM T.J. Watson Research Ctr., Yorktown Heights, N.Y., 1985.
28. E.E. Catmull and R.J. Rom, "A Class of Local Interpolating Splines," inComputer Aided Geometric Design, R.E. Barnhill and R.F. Riesenfeld, eds., Academic Press, New York, 1974, pp. 317326.
29. T.D. DeRose and B.A. Barsky, "Geometric Continuity and Shape Parameters for CatmullRom Splines" (extended abstract),Proc. Graphics Interface, Canadian Information Processing Soc., Toronto, 1984, pp. 5764.
30. T.D. DeRose and B.A. Barsky, "Geometric Continuity, Shape Parameters, and Geometric Constructions for CatmullRom Splines,"ACM Trans. Graphics, Vol. 7, No. 1, Jan. 1988, pp. 141.