Compressed piecewise-circular approximations of 3D curves

CAD Computer Aided Design

Volumn 35, Issue 6, 2003, Pages 533-547

  Safonova, Alla ^a   Rossignac, Jarek ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

3D curves; Approximation; Circular arcs; Compression; Fitting

Indexed keywords

ADAPTIVE SYSTEMS; ALGORITHMS; COMPUTER AIDED MANUFACTURING; CURVE FITTING; ERROR CORRECTION;

QUANTIZATION ERROR;

COMPUTER AIDED DESIGN;

EID: 0037408705     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4485(02)00073-8     Document Type: Review

References (44)

1. Farin G. Curves and surfaces for computer aided geometric design: a practical guide. 4th ed: 1997;Academic Press, San Diego.
2. Laurent P.J., Mehaute A.L., Schumaker L.L. Curves and surfaces. 1991;Academic Press, New York.
3. Heckbert P, Garland M. Survey of polygonal surface simplification algorithms. SIGGRAPH 97 course on multiresolution surface modeling.
4. McMaster R.B. The integration of simplification and smoothing algorithms in line generalization. Cartographica. 26:(1):1989;101-121.
5. Beard K. Theory of the cartographic line revisited. Cartographica. 28:(4):1991;32-58.
6. Cromley R.G., Campbell G.M. Integrating quantitative and qualitative aspects of digital line simplification. Cartograph J. 29:(1):1992;25-30.
7. Douglas D.H., Peucker T.K. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Can Cartograph. 10:(2):1973;112-122.
8. Ballard D.H. Strip trees: a hierarchical representation for curves. Commun ACM. 24:(5):1981;310-321.
9. McMaster R.B. The geometric properties of numerical generalization. Geograph Anal. 19:(4):1987;330-346.
10. Boxer L., Chang C.-S., Miller R., Rau-Chaplin A. Polygonal approximation by boundary reduction. Pattern Recogn Lett. 14:(2):1993;111-119.
11. Leu J.G., Chen L. Polygonal approximation of 2-D shapes through boundary merging. Pattern Recogn Lett. 7:(4):1988;231-238.
12. Imai H., Iri M. Computational-geometric methods for polygonal approximations of a curve. Comput Vision, Graph, Image Process. 36:1986;31-41.
13. Imai H., Iri M. Polygonal approximations of a curve-formulations and algorithms. Computational morphology. 1988;North-Holland, Amsterdam. p. 71-86.
14. Melkman A., O'Rourke J. On polygonal chain approximation. Computational morphology. 1988;North-Holland, Amsterdam
15. Chan W.S., Chin F. Approximation of polygonal curves with minimal number of line segments or minimum error. Int J Comput Geometr Appl. 6:(1):1996;59-77.
16. Chen D.Z., Daescu O. Space-efficient algorithms for approximating polygonal curves in two-dimensional space. Manuscript. 1997.
17. Varadarajan K.R. Approximating monotone polygonal curves using the uniform metric. Proc 12th Annu Acm Symp Comput Geometr, Philadelphia, PA. 1996;106-112.
18. Ihm I., Naylor B. Piecewise linear approximations of digitized space curves with applications. Patrikalakis N.M. Scientific visualization of physical phenomina. 1991;545-569 Springer, Tokyo.
19. Eu D., Toussaint G.T. On approximation of polygonal curves in two and three dimensions. CVGIP: Graph Model Image Process. 56:(3):1994;231-246.
20. Varadarajan K.R. Approximating monotone polygonal curves using the uniform metric. Proceedings of the 12th Annual ACM Symposium on Computational Geometry, Philadelphia, PA. 1996;106-112.
21. Guibas L.J., Hershberger J.E., Mitchell J.S.B., Snoeyink J.S. Approximating polygons and subdivisions with minimum-link paths. Int J Comput Geometr Appl. 3:(4):1993;383-415.
22. Saux E., Daniel M. Data reduction of polygonal curves using B-splines. Comput Aid Des. 31:(8):1999;507-515.
23. Pei S.C., Horns J.H. Optimum approximation of digital planar curves using circular arcs. Pattern Recogn. 29:(3):1996;383-388.
24. Pei S.C., Horns J.H. Fitting digital curves using circular arcs. Pattern Recogn. 28:(1):1995;107-116.
25. Yang S.N., Du W.C. Numerical methods for approximating digitized curves by piecewise circular arcs. J Comput Appl Math. 66:1996;557-569.
26. Yang S.N., Du W.C. Piecewise arcs approximation for digitized curves. Proceedings of the Computer Graphics International 1994 (CG194). Insight through computer graphics. 1996;. p. 291-302.
27. Rosin P.L., West G.A.W. Segmentation of edges into lines and arcs. Image Vision Comput. 7:(2):1989;109-114.
28. West G.A.W., Rosin P.L. Techniques for segmenting image curves into meaningful description. Pattern Recogn. 24:(7):1991;643-652.
29. Rossignac J.R., Requicha A.A.G. Piecewise-circular curves for geometric modeling. IBM J Res Dev. 31:(3):1987;296-313.
30. Tseng Y.J., Chen Y.D. Three dimensional biarc approximation of freeform surfaces for machining tool path generation. Int J Prod Res. 38:(4):2000;739-763.
31. Rossignac J. Blending and offsetting solid models. PhD Thesis, University of Rochester, NY. June 1985, Advisor: Dr Aristides Requicha.
32. 1 arc splines. Comput Aid Des. 24:(6):1992;301-306.
33. Hoschek J. Circular splines. Comput Aid Des. 24:(11):1992;611-618.
34. Walton D.J., Meek D.S. Approximation of quadratic Bezier curves by arc splines. J Comput Appl Math. 54:(1):1994;107-120.
35. Meek D.S., Walton D.J. Approximating quadratic NURBS curves by arc splines. Comput Aid Des. 25:(6):1993;371-376.
36. Eck M, Hadenfeld J. Knot removal for B-spline curves, Fachbereich Mathematik. Technische Hochschule Darmstadt. D-64289 Darmstadt, FRG. 1994.
37. Alt H., Godau M. Measuring the resemblance of polygonal curves. Proceedings of the Eighth Annual Symposium on Computational Geometry. 1992;102-109.
38. Godau M. Die Fréchet-Metric für Polygonzüge - Algorithmen zur Abstandsmessung und Approximation. Diplomarbeit. Fachbereich Mathematik. FU Berlin. 1991.
39. Barequet G., Chen D.Z., Daescu O., Goodrich M.T., Snoeyink J. Efficiently Approximating Polygonal Paths in Three and Higher Dimensions. Proceedings of the 14th Annual Symposium on Computational Geometry. 1998;317-326.
40. Taubin G., Rossignac J. Geometric compression through topological surgery. ACM Trans Graph. 17:(2):1998;84-115.
41. Rossignac J., Requicha A. Offsetting operations in solid modeling. Comput Aid Des. 3:1986;129-148.
42. de Berg M., van Kreveld M., Overmars M., Schwarzkopf O. Computational geometry. 2nd ed: 2000;Springer, Berlin.
43. Matheron G. Random sets and integral geometry. 1975;Wiley, New York.
44. Safonova A, Rossignac J. Compressed piecewise circular approximation of 3D curves. GVU, Report GIT-GVU-01-05, 2001, updated 2002. http://www.cc.gatech.edu/gvu/reports/2001/