Double- and triple-step incremental linear interpolation

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.<>