Application of Generalized NAUT B-Spline Curveon Circular Domain to Generate Circle Involute
In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design.
[1] A.Ganguly, P.Arondekar 2007: Generalized hyperbolic class of B-Spline
curves. Far East J. of Mathematical Science(FJMS),26(3)579-590.
[2] A.Ganguly , P. Arondekar2009, A Study Related to interval B-Spline
curve, Far East Journal of Applied Mathematics, Vol 34, number 2,
,pages 151-167.
[3] A. Ganguly, P. Arondekar 2010: least square approximation of to fit
scattered data using B-Spline curve on circular domain, International
Journal of Applied Mathematics & Eng. Sciences (To be published vol
1, 2010).
[4] Devid F.Roger, J.Alan Adams. 1990: Mathematical Elements for Computer
Graphics. Tata McGraw-Hill, New York ,Edition II, pp 309-349.
[5] E Bugimghum 1928: Spur gear, McGraw hill book company, New York.
[6] Farin G. Curves and surfaces in computer Aided Geometric Design1993.,
3rd ed.San Diego: Academic press.
[7] Fumitaka Higuchi et al. Dec 2006: Approximation of involute curve for
CAD processing, YNU digital engineering laboratory.
[8] Gitin M maitra: Handbook of gear design2005, 2nd edition tata McGraw
hill, New Delhi, pp 1.10-1.13,2.1-2.11 .
[9] Germain E. Randriambelosa 2004: Space curve approximation using G1
ball-spline Curve Applied mathematical research Express No 5, 153-167.
[10] G. Wang,Q. Chen,M.Zhou,2004 :NAUT B-Spline curves . Computer
Aided Geometric Design,21,193-205.
[11] L├╝ ,Y.G.X, 2002, Uniform hyperbolic polynomial B-Spline curves.
Computer Aided Geometric Design, 19,379-393.
[12] Lin Q. Rokne J G., July 1998, Disk Bézier curve (J). Computer Aided
Geometric Design,15(7):721-737
[13] Pe..
na, J.M.,1997: Shape preserving representation for trigonometric
polynomial curves. Computer Aided Geometric Design, 14,5-11.
[14] Q. Chen, G. Wang, 2003: A class of Bézier like curves, Computer Aided
Geometric Design, 20, 29-39.
[15] Sederberg T.W., Farouki R.T. 1992: Approximation by interval Bézier
curves. IEEE compute. Graph Appl, 15(2):87-95.
[16] Shen G and Patrikalakis N M 1998: Numerical and geometric properties
of interval B-Spline . International Journal of Shape Modeling,
4(1/2):35-62.
[17] S. Barone 2001: Gear Geometric Design by B-Spline Curve Fitting and
Sweep Surface Modelling Engineering with Computers, 17(1):66-74.
[18] Tuohy S.T., Maekawa T., Shen G., Patrikalakis N.M., 1997, Approximation
of measured data with interval B-splines. Computer-Aided Design
29 (11), 791-799.
[1] A.Ganguly, P.Arondekar 2007: Generalized hyperbolic class of B-Spline
curves. Far East J. of Mathematical Science(FJMS),26(3)579-590.
[2] A.Ganguly , P. Arondekar2009, A Study Related to interval B-Spline
curve, Far East Journal of Applied Mathematics, Vol 34, number 2,
,pages 151-167.
[3] A. Ganguly, P. Arondekar 2010: least square approximation of to fit
scattered data using B-Spline curve on circular domain, International
Journal of Applied Mathematics & Eng. Sciences (To be published vol
1, 2010).
[4] Devid F.Roger, J.Alan Adams. 1990: Mathematical Elements for Computer
Graphics. Tata McGraw-Hill, New York ,Edition II, pp 309-349.
[5] E Bugimghum 1928: Spur gear, McGraw hill book company, New York.
[6] Farin G. Curves and surfaces in computer Aided Geometric Design1993.,
3rd ed.San Diego: Academic press.
[7] Fumitaka Higuchi et al. Dec 2006: Approximation of involute curve for
CAD processing, YNU digital engineering laboratory.
[8] Gitin M maitra: Handbook of gear design2005, 2nd edition tata McGraw
hill, New Delhi, pp 1.10-1.13,2.1-2.11 .
[9] Germain E. Randriambelosa 2004: Space curve approximation using G1
ball-spline Curve Applied mathematical research Express No 5, 153-167.
[10] G. Wang,Q. Chen,M.Zhou,2004 :NAUT B-Spline curves . Computer
Aided Geometric Design,21,193-205.
[11] L├╝ ,Y.G.X, 2002, Uniform hyperbolic polynomial B-Spline curves.
Computer Aided Geometric Design, 19,379-393.
[12] Lin Q. Rokne J G., July 1998, Disk Bézier curve (J). Computer Aided
Geometric Design,15(7):721-737
[13] Pe..
na, J.M.,1997: Shape preserving representation for trigonometric
polynomial curves. Computer Aided Geometric Design, 14,5-11.
[14] Q. Chen, G. Wang, 2003: A class of Bézier like curves, Computer Aided
Geometric Design, 20, 29-39.
[15] Sederberg T.W., Farouki R.T. 1992: Approximation by interval Bézier
curves. IEEE compute. Graph Appl, 15(2):87-95.
[16] Shen G and Patrikalakis N M 1998: Numerical and geometric properties
of interval B-Spline . International Journal of Shape Modeling,
4(1/2):35-62.
[17] S. Barone 2001: Gear Geometric Design by B-Spline Curve Fitting and
Sweep Surface Modelling Engineering with Computers, 17(1):66-74.
[18] Tuohy S.T., Maekawa T., Shen G., Patrikalakis N.M., 1997, Approximation
of measured data with interval B-splines. Computer-Aided Design
29 (11), 791-799.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51204", author = "Ashok Ganguly and Pranjali Arondekar", title = "Application of Generalized NAUT B-Spline Curveon Circular Domain to Generate Circle Involute", abstract = "In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design.
", keywords = "Bézier,Circle Involute, NAUT B-Spline, Spur Gear.", volume = "3", number = "11", pages = "909-7", }
