The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.05 - May (1987 vol.7)
pp: 31-43
Jack Bresenham , IBM Communication Products Division
ABSTRACT
In implmenting rater grahic algorithms, it is impotant to toroughly understand behavior and implicit defaults inherent in each algorithm. Design choices must balance performance with respect to drawing speed, circult count, code space, picture fidelity, system complexity, and system consistency. For example, "close" may sound appealing when describing the match of the rastered representation to a geometirc line. An implementation, however, must quantily an error metric?such as minimum normal distance between candidate raster grid points and the geometric line?and resolve "ties" in which two candidate grid points have an equal error metric. Equal error metric ambiguity can permit algorithimic selection of raster points for a line from (X0, Y0) to (X1, Y1) to differ from points selected rastering the same line back from (X1, Y1) to (X0, Y0). Modilying a rastering algorithm to provide an exactly reversibie path, though, will cause problems when lines are rastered in a context of approximating a circle with a polygon. Only by fully understanding any algorithm can designers determine whether such pel-level anomalies are worth the code space or circuit count necessary to provide explicit user resolution, or whether a fixed default must suffice. This article discusses implementation considerations relevant to selecting and customizing incremental line-drawing algorithms to cope with such anomalies as equal error metric instances, perturbation effects of clipping, interesections in raster space, EXOR interpretations for polylines, reversibility, and fractional endpoint rounding.
INDEX TERMS
null
CITATION
Jack Bresenham, "Ambiguities in Incremental Line Rastering", IEEE Computer Graphics and Applications, vol.7, no. 5, pp. 31-43, May 1987, doi:10.1109/MCG.1987.276986
REFERENCES
1. J.E.Bresenham, "An Incremental Algorithm for Digital Plotting," ACM Nat'l Conf. Aug. 1963 unpublished talk given at
2. J.E.Bresenham, "Algorithm for Computer Control of a Digital Plotter,"pp. 25-30 Jan. 1965 IBM Systems J.
3. J.Boothroyd and P.A.Hamilton, "Exactly Reversible Plotter Paths," Australian Computer J. Vol. 2, No. 1, pp. 20-21 1970
4. Tran-Thong, "A Symmetric Linear Algorithm for Line Segment Generation," Computers & Graphics Vol. 6, No. 1, pp. 15-17 1982
5. M.D.McLlroy, "Best Approximate Circles on Integer Grids,"pp. 237-263 Oct. 1983 ACM Trans. Graphics
6. J.E.Bresenham, "Incremental Line Compaction,"pp. 116-120 Feb. 1982 The Computer J.
7. P.L.Gardner, "Modification of Bresenham's Algorithm for Displays,"pp. 1595-1596 Oct. 1975 IBM Tech. Disclosure Bull.
8. R.D.Hersch, IEEE CG&A , July 1986pp. 61-70
9. A.R.Forrest, R.A.Earnshaw, Fundamental Algorithms for Computer Graphics , Springer-Verlag 1985pp. 707-724
21 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool