Abstract
Novel algorithms for the generation of conic sections whose axes are aligned to the coordinate axes are proposed in this paper. The algorithms directly calculate difference between the expressions satisfied by two adjacent points lied on curves, and then, a kind of iteration relation including residuals is established. Furthermore, according to the criterion of nearest to curve, a residual in 1/2 is employed to obtain an integer decision variable. The analyses and experimental results show that in the case of the ellipse, our algorithm is faster than basic mid-point algorithm and Agathos algorithm because constant term accumulated in every loop is eliminated, but its idea and derivation are at least as simple as basic mid-point algorithm. Moreover, our algorithm does not set erroneous pixels at region boundaries, and anti-aliasing is easily incorporated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bresenham, J.E.: A linear algorithm for incremental digital display of circular arcs. Commun. Assoc. Comput. Mach. 20, 100–106 (1977)
Van Aken, J.R.: An efficient ellipse-drawing algorithm. CG&A 4, 24–35 (1984)
Van Aken, J.R., Novak, M.: Curve-drawing algorithms for raster display. ACM Trans. Graph. 4, 147–169 (1985)
Pitteway, M.L.V.: Algorithm for drawing ellipse or hyperbolae with a digital plotter. Comput. J. 10, 282–289 (1985)
Foley, J.D.: Computer Graphics Principles and Practice. Addison Wesley Publishing Company, Reading Massachusetts (1990)
McIlroy, M.D.: Getting raster ellipses right. ACM Trans. Graph. 11, 259–275 (1992)
Kappel, M.R.: An ellipse-drawing algorithm for raster displays. In: Earnshaw, R. (ed.) Fundamental Algorithms for Computer Graphics, NATO ASI Series. Springer, Berlin (1985)
Fellner, D.W., Helmberg, C.: Robust rendering of general ellipses and elliptical arcs. ACM Trans. Graph. 12, 251–276 (1993)
Agathos, A., Theoharis, T., Boehm, A.: Efficient integer algorithms for the generation of conic sections. Comput. & Graph. 22, 621–628 (1998)
Wu, X., Rokne, J.G.: Double-step incremental generation of lines and circles. Comput. Vis., Graph. Image Process. 37, 331–344 (1987)
Cheng, J., Lu, G., Tan, J.: A fast arc drawing algorithm. Software J. 13, 2275–2280 (2002)
Niu, L., Xue, J., Zhu, T.: A run-length algorithm for fast circle drawing. J. Shenyang Univ. Technol. 32, 411–416 (2010)
Liu, Y., Shi, J.: Double-Step Circle Drawing Algorithm with and without Grey Scale. J. Comput. Aided Des. Comput. Graph. 17, 34–41 (2005)
Wu, X., Rokne, J.G.: Double-step generation of ellipse. CG&A 9, 376–388 (1989)
Hsu, S.Y., Chow, L.R., Liu, C.H.: A new approach for the generation of circles. Comput. Graph. Forum 12, 105–109 (1993)
Liu, K., Hou, B.H.: Double-step incremental generation of ellipse and its hardware implementation. J. Comput. Aid. Des. & Comput. Graph. 15, 393–396 (2003)
Yao, C., Rokne, J.G.: Hybrid scan-conversion of circles. IEEE Trans. Comput. Vis. Graph. 1, 31–318 (1995)
Yao, C., Rokne, J.G.: Run-length slice algorithms for the scan-conversion of ellipses. Comput. & Graph. 22, 463–477 (1998)
Wu, X.: An efficient antialiasing technique. Computer Graphics, Proceedings of SIGGRAPH’91, vol. 25. pp. 143–152 (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer India
About this paper
Cite this paper
Chen, X., Niu, L., Song, C., Li, Z. (2014). Novel Algorithms for Scan-Conversion of Conic Sections. In: Patnaik, S., Li, X. (eds) Proceedings of International Conference on Computer Science and Information Technology. Advances in Intelligent Systems and Computing, vol 255. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1759-6_73
Download citation
DOI: https://doi.org/10.1007/978-81-322-1759-6_73
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-1758-9
Online ISBN: 978-81-322-1759-6
eBook Packages: EngineeringEngineering (R0)