Abstract
Filleting and rounding operations are very useful in solid modeling. The most popular means of producing a fillet surface is by means of the so-called ``rolling ball blend.'' A new method, inspired by the rolling ball blend, which overcomes both of its serious drawbacks is presented in this paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions with formulas, graphs, and mathematical tables. U. S. National Bureau of Standards 1964.
M. I. G. Bloor M. J. Wilson (1989) ArticleTitleGenerating blend surfaces using partial differential equations Comput. Aided Des. 21 165–171 Occurrence Handle0669.65006 Occurrence Handle10.1016/0010-4485(89)90071-7
M. I. G. Bloor M. J. Wilson (2000) ArticleTitleGenerating blend surfaces using a perturbation method Math. Comput. Model 31 1–13 Occurrence Handle1042.65516 Occurrence Handle10.1016/S0895-7177(99)00212-5 Occurrence Handle1748685
M. P. do Carmo (1976) Differential geometry of curves and surfaces Prentice-Hall Englewood Cliffs, NJ Occurrence Handle0326.53001
I. D. Faux M. J. Pratt (1979) Computational geometry for design and manufacture Ellis Horwood Chichester, West Sussex 190–191 Occurrence Handle0395.51001
R. A. M. Farouki R. Sverrisson (1996) ArticleTitleApproximation of rolling-ball blends for free-form parametric surfaces Comput. Aided Des. 28 871–878 Occurrence Handle10.1016/0010-4485(96)00008-5
A. Gray (1997) Clothoids. Modern differential geometry of curves and surfaces with mathematica, 2nd ed., sect. 3.7 CRC Press Boca Raton 64–66
J. D. Lawrence (1972) A catalog of special plane curves Dover New York 190–191 Occurrence Handle0257.50002
D. S. Meek D. J. Walton (1989) ArticleTitleThe use of Cornu spirals in drawing planar curves of controlled curvature J. Comput. Appl. Math. 25 69–78 Occurrence Handle0662.65008 Occurrence Handle10.1016/0377-0427(89)90076-9 Occurrence Handle977886
D. S. Meek D. J. Walton (1991) ArticleTitlePlanar spirals that match G 2 Hermite data Comput. Aided Geom. Des. 15 103–126 Occurrence Handle10.1016/S0167-8396(97)00020-4 Occurrence Handle1605362
D. S. Meek D. J. Walton (2004) ArticleTitleA note on finding clothoids J. Comput. Appl. Math. 170 433–453 Occurrence Handle1050.65017 Occurrence Handle10.1016/j.cam.2003.12.047 Occurrence Handle2075020
J. Pegna F.-E. Wolter (1992) ArticleTitleGeometrical criteria to guarantee curvature continuity of blend surfaces J. Mech. Des. ASME Trans. 114 201–210 Occurrence Handle10.1115/1.2916918
D. Seggern Particlevon (1993) CRC standard curves and surfaces CRC Press Boca Raton Occurrence Handle0772.00001
W. Snyder ParticleVan (1993) ArticleTitleAlgorithm 723: Fresnel integrals ACM Trans. Math. Softw. 19 452–456 Occurrence Handle0890.65017 Occurrence Handle10.1145/168173.168193
J. Vida R. Martin T. Varady (1994) ArticleTitleA survey of blending methods that use parametric surfaces Comput. Aided Des. 26 341–365 Occurrence Handle0802.65005 Occurrence Handle10.1016/0010-4485(94)90023-X
D. J. Walton D. S. Meek (1990) ArticleTitleClothoidal splines Comput. Graph. 14 95–100 Occurrence Handle10.1016/0097-8493(90)90013-N
J. J. Zhang L. You (2004) ArticleTitleAnalytical C 2 smooth blending surfaces Future Gener. Comput. Systems 20 1317–1326 Occurrence Handle10.1016/j.future.2004.05.023
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grandine, T.A., Hogan, T.A. C 2 pseudo rolling ball filleting. Computing 79, 163–173 (2007). https://doi.org/10.1007/s00607-006-0195-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00607-006-0195-x