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| Jin J. Chou, Les A. Piegl, "Data Reduction Using Cubic Rational B-Splines," IEEE Computer Graphics and Applications, vol. 12, no. 3, pp. 60-68, May/June, 1992. | |||
| BibTex | x | ||
| @article{ 10.1109/38.135914, author = {Jin J. Chou and Les A. Piegl}, title = {Data Reduction Using Cubic Rational B-Splines}, journal ={IEEE Computer Graphics and Applications}, volume = {12}, number = {3}, issn = {0272-1716}, year = {1992}, pages = {60-68}, doi = {http://doi.ieeecomputersociety.org/10.1109/38.135914}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - MGZN JO - IEEE Computer Graphics and Applications TI - Data Reduction Using Cubic Rational B-Splines IS - 3 SN - 0272-1716 SP60 EP68 EPD - 60-68 A1 - Jin J. Chou, A1 - Les A. Piegl, PY - 1992 VL - 12 JA - IEEE Computer Graphics and Applications ER - | |||
A geometric method for fitting rational cubic B-spline curves to data representing smooth curves, such as intersection curves or silhouette lines, is presented. The algorithm relies on the convex hull and on the variation diminishing properties of Bezier/B-spline curves. It is shown that the algorithm delivers fitting curves that approximate the data with high accuracy even in cases with large tolerances. The ways in which the algorithm computes the end tangent magnitudes and inner control points, fits cubic curves through intermediate points, checks the approximate error, obtains optimal segmentation using binary search, and obtains appropriate final curve form are discussed.
1. C. de Boor,A Practical Guide to Splines, Springer-Verlag, New York, 1978.
2. M. Kallay, "Approximating a Composite Cubic Curve with One Fewer Pieces,"Computer-Aided Design, Vol. 19, No. 10, Dec. 1987, pp 539-543.
3. L. Piegl, "A Technique for Smoothing Scattered Data with Conic Sections,"Computers in Industry, Vol. 9, No. 3, Nov. 1987, pp. 223-237.
4. L. Piegl, "On NURBS: A Survey,"IEEE CG&A, Vol. 19, No. 1, Jan. 1991, pp. 55-26.
5. L. Piegl and W. Tiller, "Curve and Surface Constructions Using Rational B-Splines,"Computer-Aided Design, Vol. 19, No. 9, Nov. 1987, pp. 485-498.
6. D. F. Rogers and J. A. Adams,Mathemational Elements for Computer Graphics, 2nd ed. New York: McGraw-Hill, 1990.
7. P. de Casteljau,Shape Mathematics and CAD, Kogan Page, London, 1985.
8. A.R. Forrest,Curves and Surfaces for Computer-Aided Design, PhD thesis, University of Cambridge, Cambridge, UK, 1968.
9. E.T.Y. Lee, "The Rational Quadratic Bezier Representation for Conies," inGeometric Modeling: Algorithms and New Trends, G. Farin, ed., SIAM, Philadelphia, Penn., 1987, pp. 3-19.
10. E.T.Y. Lee, "Choosing the Nodes in Parametric Curve Interpolation,"Computer-Aided Design, Vol. 21, No. 6, July/Aug. 1989, pp. 363-370.
11. R.R. Patterson, "Projective Transformations of the Parameter of a Bernstein-Bezier Curve," ACM Trans. Graphics, Vol. 4, No. 4, Oct. 1985, pp. 276-290.