This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Curvature and the fairness of curves and surfaces
March/April 1989 (vol. 9 no. 2)
pp. 52,53,54,55,56,57
The use of curvature plots for the design of curves that have to meet aesthetic requirements is discussed. The aim is to emphasize the usefulness of curvature as a measure for curve fairness. A local method to optimize the curvature plot of a given cubic spline curve is presented. It automatically determines where the curve is to be faired and can be applied repeatedly. A straightforward generalization to surfaces is easy to formulate.<>

1. J.C. Dill, "An Applicatiun of Color Graphics to the Display of Surface Curvature,"Computer Graphics(Proc. SIGGRAPH), Vol. 15, No. 3, Aug. 1981, pp. 153-161.
2. G.D. Birkhoff,Aesthetic Measure, Harvard Univ. Press, Cambridge, Mass., 1933.
3. F. Crow, "The Origins of the Teapot,"CG&A, Vol. 7, No. 1, Jan. 1987, pp. 8-19.
4. J.A. Kjellander, "Smoothing of Cubic Parametric Splines,"Computer-Aided Design, Vol. 15, No. 3, May 1983, pp. 175-179.
5. W. Boehm, "Inserting New Knots into B-spline Curves,"Computer-Aided Design, Vol. 12, No. 4, Aug. 1980, pp. 199-201.
6. E. Cohen, T. Lyche, and R. Riesenfeld, "Discrete B-Splines and Subdivision Techniques in CAGD and Computer Graphics,"Computer Graphics and Image Processing, Vol. 14, No. 2, 1980, pp. 87-111.
7. G. Farin,Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston, 1988.
8. G. Farin et al., "Fairing Cubic B-Spline Curves,"Computer Aided Geometric Design, Vol. 4, No. 1-2, July 1987, pp. 91-103.
9. N. Sapidis,Algorithms for Locally Fairing B-Spline Curves, master's thesis, Univ. of Utah., 1987.
10. N. Sapidis and G. Farin, "An Automatic Fairing Algorithm for B-Spline Curves," submitted toComputer-Aided Design.
11. C. de Boor,A Practical Guide to Splines, Springer-Verlag, Berlin, 1978.
12. R. Klass, "Correction of Local Surface Irregularities Using Reflection Lines,"Computer-Aided Design, Vol. 12, No. 2, Feb. 1980, pp. 73-76.
13. J. Beck, R. Farouki, and J. Hinds, "Surface Analysis Methods,"CG&A, vol. 6, No. 12, Dec. 1986, pp. 18-36.
14. F. Munchmeyer, "Shape Interrogation: A Case Study," inGeometric Modeling, G. Farin, ed., SIAM, Philadelphia, 1987, pp. 291-301.

Index Terms:
splines (mathematics),computational geometry,curve fitting,cubic spline curve,computational geometry,curvature plots,aesthetic requirements,curve fairness,curvature plot,Shape control,Spline,Design automation,Production,Inspection,Process design,Computer graphics,Application software,Computer aided manufacturing,CADCAM
Citation:
"Curvature and the fairness of curves and surfaces," IEEE Computer Graphics and Applications, vol. 9, no. 2, pp. 52,53,54,55,56,57, March-April 1989, doi:10.1109/38.19051
Usage of this product signifies your acceptance of the Terms of Use.