Abstract
In the application of CAD/CAM, the target form of a curve, which is used for plotting or as the data supplied for CAM, is a set of points on (or near by) the curve. Using the subdivision algorithm, the procedure of curve generation fromControl points →Mathematical form of the curve →Points on (or near by) the curve which is used in most systems for curve design, is simplified in this paper toControl points →Points on (or near by,) the curve.
We also discuss the conditions of shape preserving, polynomial reproducing, continuity as well as the convergent properties of the target curve.
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References
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Cavaretta, A. et al., Subdivision Algorithms, Mathematical Methods in CAGD, Academic Press, New York, 1989, 543–581.
Dyn, N., et al., A 4-point interpolation subdivision scheme for curve desgin,Comput. Aided. Geom. Design,4 (1987), 257–268.
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Zongmin, W., Qing, Y. & Jianpin, L. The subdivision algorithm for generating curves and its properties. Appl. Math. 9, 169–176 (1994). https://doi.org/10.1007/BF02662070
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DOI: https://doi.org/10.1007/BF02662070