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Double- and Triple-Step Incremental Linear Interpolation
May/June 1994 (vol. 14 no. 3)
pp. 49-53

Incremental linear interpolation determines the set of n+1 equidistant points on an interval [a,b] where all variables involved (n, a, b, and the set of equidistant points) are integers and n<0. Our method of linear interpolation generalizes the findings of a variable-step line-drawing algorithm. The resulting interpolation algorithm has as many loops as the line-drawing algorithm, but fewer restrictions on its input variables. Furthermore, its benefits over the fixed-step interpolation algorithms are similar to those of the variable-step line-drawing algorithm. That is, the double- and triple-step interpolation algorithm can reduce the number of loop iterations of the double-step interpolation algorithm (by 12.5% on average) while keeping the code complexity, initialization costs, and worst-case performance the same. The improvement in speed over the single-step B5 algorithm is even greater.

1. D. Field, "Incremental Linear Interpolation,"ACM Trans. Graphics, Vol. 4, No. 1, Jan. 1985, pp. 1-11.
2. T.R.H. Sizer,The Digital Differential Analyser, Chapman and Hall, London, 1968.
3. J.E. Bresenham, "Incremental Line Compaction,"Computer J., Vol. 25, No. 1, Feb. 1982, pp. 116-120.
4. J. Rokne and Y. Rao, "Double-Step Incremental Linear Interpolation,"ACM Trans. Graphics, Vol. 11, No. 2, Apr. 1992, pp. 183-192.
5. X. Wu and J. Rokne, "Double-Step Incremental Generation of Lines and Circles, "Computer Vision, Graphics, and Image Processing, Vol. 37, No. 3, Mar. 1987, pp. 331-344.
6. P. Bao and J. Rokne, "Quadruple-Step Line Generation,"Computers&Graphics, Vol. 13, No. 4, 1989, pp. 461-469.
7. P. Graham and S.S. Iyengar, "Double- and Triple-Step Incremental Generation of Lines,"Proc. 1993 ACM Computer Science Conf., ACM Press, New York, 1993.

Phil. Graham, S. Sitharama Iyengar, "Double- and Triple-Step Incremental Linear Interpolation," IEEE Computer Graphics and Applications, vol. 14, no. 3, pp. 49-53, May-June 1994, doi:10.1109/38.279045
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