Download e-book for iPad: Analytic theory of continued fractions Proc. Loen by W. B. Jones

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3 developed is applied on the same digital curves. The digital curves and their polygonal approximations are shown in Figures 2 through 5. The data are processed in the clockwise direction. Since, this procedure is sequential and one-pass hence we compare the experimental results of this procedure with those of the Williams’ algorithm [184] and the Wall-Danielsson algorithm [180]. As we have already seen this procedure controls the maximum error indirectly, so the maximum error that is obtained by applying this procedure on each of the four digital curves are used to run the Williams’ and the Wall-Danielsson algorithm.

But the choice of this critical value is problematic. If we set it to 1, we get many redundant vertices and if we set it to 2 we miss many important vertices and so we lose the shape of the curve. So it is not effective to use 2A only as a measure of collinearity. In the following we introduce as an alternative measure of collinearity. 9) The significance of r is that it gives the in-radius of the triangle pi pj pk (op`j p`k). This is an indirect approach to the problem but is justified by the following proposition.

The origin is again translated to the point jj and the same computation is carried out in the same fashion as already described. The procedure is carried on along the entire digital curve beyond the starting point till the vertex generated last coincides with one of the vertices already generated. At this point we note that Williams’ [184] and Wall-Danielsson [180] too looked for the maximal possible line segments. But in their procedure it is necessary to specify the error. In Williams’ technique the error is specified directly whereas in the WallDanielsson technique the error is specified in terms of area deviation per unit length.

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