Topologically reliable approximation of composite Bézier curves

Computer Aided Geometric Design

Volumn 13, Issue 6, 1996, Pages 497-520

  Cho, Wonjoon ^a   Maekawa, Takashi ^a   Patrikalakis, Nicholas M ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Bucketing technique; Homeomorphism; Interval B zier curves; Piecewise linear approximation; Significant points; Subdivision method

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; ERRORS; FINITE ELEMENT METHOD; PIECEWISE LINEAR TECHNIQUES; TOPOLOGY;

APPROXIMATION ERROR; BUCKETING TECHNIQUE; COMPOSITE BEZIER CURVES; HOMEOMORPHISM; LINEAR APPROXIMATING SEGMENTS; SUBDIVISION METHOD;

COMPUTER AIDED DESIGN;

EID: 0030215146     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-8396(95)00042-9     Document Type: Article

References (27)

1. Agoston, M.K. (1976), Algebraic Topology, Marcel Dekker Inc., New York.
2. Asano, T., Edahiro, M., Imai, H., Iri, M. and Murota, K. (1985), Practical use of bucketing technique in computational geometry, in: G. Toussaint, ed., Computational Geometry, Machine Intelligence and Pattern Recognition, 2, North-Holland, 153-195.
3. Bardis, L. and Patrikalakis, N.M. (1989), Approximate conversion of rational B-spline patches, Computer Aided Geometric Design 6, 189-204.
4. Brown, R. (1988), Topology: A Geometric Account of General Topology, Homotopy Types and the Fundamental Groupoid, Ellis Horwood Ltd., Chichester, England.
5. Chinn, W.G. and Steenrod, N.E. (1966), First Concepts of Topology: the Geometry of Mappings of Segments, Curves, Circles, and Disks, Mathematical Association of America Inc., Washington DC.
6. Cormen, T.H., Leiserson, C.E. and Rivest, R.L. (1990), Introduction to Algorithms, MIT Press, Cambridge, MA.
7. do Carmo, M.P. (1976), Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, NJ.
8. Eck, M. (1993), Degree reduction of Bézier curves, Computer Aided Geometric Design 10, 237-251.
9. Fahn, C., Wang, J. and Lee, J. (1989), An adaptive reduction procedure for the piecewise linear approximation of digitized curves, IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 967-973.
10. Farin, G. (1993), Curves and Surfaces for Computer Aided Geometric Design-A Practical Guide, 3rd ed., Academic Press, Inc., San Diego, CA.
11. Farouki, R.T. (1989), Hierarchical segmentations of algebraic curves and some applications, in: T. Lyche and L.L. Schumaker, eds., Mathematical Methods in Computer Aided Geometric Design, 239-248.
12. Hamann, B. and Chen, J. (1994), Data point selection for piecewise linear curve approximation, Computer Aided Geometric Design 11, 289-301.
13. Hoschek, J. and Schneider, F.-J. (1992), Approximate spline conversion for integral and rational Bézier and B-spline surfaces, in: R.E. Barnhill, ed., Geometry Processing for Design and Manufacturing, SIAM, Philadelphia, 45-86.
14. Hu, C.-Y., Maekawa, T., Sherbrooke, E.C. and Patrikalakis, N.M. (1995), Robust interval algorithm for curve intersections, Computer-Aided Design, to appear.
15. Ihm, I. and Naylor, B. (1991), Piecewise linear approximations of digitized space curves with applications, in: N.M. Patrikalakis, ed., Scientific Visualization of Physical Phenomena, Proceedings of the 9th International Conference on Computer Graphics, CGI '91, Springer-Verlag, 545-569.
16. Kehtarnavaz, N. and deFigueiredo, R.J.P. (1988), A 3-D contour segmentation scheme based on curvature and torsion, IEEE Transactions on Pattern Analysis and Machine Intelligence 10, 707-713.
17. Kreyszig, E. (1959), Differential Geometry, University of Toronto Press.
18. Maekawa, T. and Patrikalakis, N.M. (1993), Computation of singularities and intersections of offsets of planar curves, Computer Aided Geometric Design 10, 407-429.
19. Maekawa, T. and Patrikalakis, N.M. (1994), Interrogation of differential geometry properties for design and manufacture, The Visual Computer 10, 216-237.
20. Moore, R.E. (1966), Interval Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ.
21. Patrikalakis, N.M. (1989), Approximate conversion of rational splines, Computer Aided Geometric Design 6, 155-165.
22. Pratt, M.J., Goult, R.J. and Ye, L. (1993), On rational parametric curve approximation, Computer Aided Geometric Design 10, 363-377.
23. Sederberg, T.W. and Farouki, R.T. (1992), Approximation by interval Bézier curves, IEEE Computer Graphics and Applications 15, 87-95.
24. Sederberg, T.W. and Buehler, D.B. (1992), Offsets of polynomial Bézier curves: Hermite approximation with error bounds, in: T. Lyche and L.L. Schumaker, eds., Mathematical Methods in Computer Aided Geometric Design, vol. II, Academic Press, 549-558.
25. Sherbrooke, E.C. and Patrikalakis, N.M. (1993), Computation of the solutions of nonlinear polynomial systems, Computer Aided Geometric Design 10, 379-405.
26. Tuohy, S.T. and Patrikalakis, N.M. (1993), Representation of geophysical maps with uncertainty, in: N. Magnenat-Thalmann and D. Thalmann, eds., Communicating with Virtual Worlds, Proceedings of CG International '93, Springer, Tokyo, 179-192.
27. Wolter, F.E. and Tuohy, S.T. (1992), Approximation of high degree and procedural curves, Engineering with Computers 8, 61-80.