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[Fig. 6] (For simplicity exact geometrical figures are assumed, the original networks are usually distorted enough)
The case of hypothetical diagonals will be dealt after the present case of next network.
THE CASE OF
HYPOTHETICAL DIAGONALS/VIRTUAL SEGMENTS
572
573
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Again we may have the shortest route between the points one more query arises. We may join any two points and consider a hypothetical diagonal. Then we may join the nearest points to this hypothetical diagonal and calculate the whole mesh if it comes lower than previous we take this hypothetical route as a new shortest route. The process is repeated for all points and we arrive at the shortest possible route between the points.
THE SEGMENT CONNECTION
The route which we got so far may be the shorter route but it may not be the shortest. The route which we have got so far is no doubt the shorter route as compared to many other routes but it is still possible that some changes may result in a further shorter route.
Let us examine what these changes could be. The route which we got till now has one property that all the points are joined to the nearest branches to them, but it is still possible that some segment may have been joined to a segment which may not be nearest to it .For that we must do a segment to segment check via similar rule which we used for joining points to the nearest branches to them. This rule may be cal