Curvatures of the Quadratic Rational Bézier Curves

Computers and Mathematics with Applications

Volumn 36, Issue 9, 1998, Pages 71-83

  Ahn, Y J ^a   Kim, H O ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Fairing curves; Local extrema of curvature; Monotone curvature; Offset curves; Quadratic rational B zier curves

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DIFFERENTIATION (CALCULUS); GEOMETRY; POLYNOMIALS;

CURVATURES; FAIRING CURVES; LOCAL EXTREMA OF CURVATURE; OFFSET CURVES; QUADRATIC RATIONAL BEZIER CURVES;

CURVE FITTING;

EID: 0032205257     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00193-X     Document Type: Article

References (19)

1. Y.J. Ahn and H.O. Kim, Approximation of circular arcs by Bézier curves, J. Computational and Applied Mathematics 81, 145-163, (1997).
2. C. de Boor, K. Höllig and M. Sabin, High accuracy geometric Hermite interpolation, Computer Aided Geometric Design 4, 169-178, (1987).
3. J. Hoschek, Approximate conversion of spline curves, Computer Aided Geometric Design 4, 59-66, (1987).
4. G. Farin and N. Sapidis, Fairing curve. Curvature and the fairness of curves and surfaces, IEEE Computer Graphics Application, 52-57, (1987).
5. N. Sapidis and W.H. Frey, Controlling the curvature of a quadratic Bézier curve, Computer Aided Geometric Design 9, 85-91, (1992).
6. H. Nowacki, D. Liu and X. Lú, Fairing Bézier curves with constraints, Computer Aided Geometric Design 7, 43-55, (1990).
7. R.T. Farouki and C.A. Neff, Analytic properties of plane offset curves, Computer Aided Geometric Design 7, 83-99, (1990).
8. G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, San Diego, CA, (1993).
9. T. Pavlidis, Curve fitting with conic splines, ACM Trans. Graph. 2, 1-31, (1983).
10. T. Pratt, Techniques for conic splines, In Proceedings of SIGGRAPH 85, pp. 151-159, ACM, (1985).
11. G. Farin, Curvature continuity and offsets for piecewise conics, ACM Trans. Graph., 89-99, (1989).
12. R. Schaback, Planar curve interpolation by piecewise conics of arbitrary type, Constructive Approximation 9, 373-389, (1993).
13. E.T. Lee, The rational Bézier representation for conics, In Geometric Modeling: Algorithms and New Trends, pp. 3-19, SIAM, Academic Press, Philadelphia, PA, (1987).
14. G. Geise and B. Jüttler, A geometric approach to curvature continuous joints of rational curves, Computer Aided Geometric Design 10, 109-122, (1993).
15. 2n) Hermite approximation for conic sectons, Computer Aided Geometric Design 14, 135-151, (1997).
16. W.H. Frey and D.A. Field, Designing Bézier conic segments with monotone curvature, Computer Aided Geometric Design 14 (to appear).
17. 1 curves containing conic segments, Computer and Graphics 8, 177-182, (1984).
18. H.E. Bez, An analysis of symmetry for plane curves and plane curve algorithms, Computer Aided Geometric Design 9, 125-142, (1992).
19. L. Piegl and W. Tiller, Curves and surfaces constructions using rational B-splines, Computer Aided Design 19, 485-498, (1987).