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[Answered] algorithms: which method or operator must i use??

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VTwin:
Indeed winni. Very nice, that looks like a great start.

As you say, there is more here. The lower left pulleys don't make physical sense. Perhaps the OP can fix this.

speter:
Calculate the centre of the whole; then to work out whether the "rope" goes out or in, "draw a line" between the pullies on either side, if the middle pully is "inside" this line the "rope" will be "inside"...

cheers
S.

speter:
Further to my previous post, look at the diagram below.

In the top-left corner, the line between the adjoining pullies crosses the line from the centre - so the "rope" should be outside.

In the bottom-left corner, the line between the adjoining pullies does NOT cross the line from the centre - so the "rope" goes on the inside...

cheers
S.

ADMGNS:
hello again,

1) i want to thank everbody.

2) this is not a homework. this is an kind of experiment on smoothing polylines. recently, i sent an article to CodeProject site https://www.codeproject.com/Articles/5301415/HotPoints-A-New-Method-for-2D-Polyline-Vertex-Smoo so, i'm trying to find another simple methods.

3) about speter's solution.. think that the order of cirles not circular-ish, maybe linear-ish.. so, this is not a general solution, i think.

4) probably we need a new operator, like cross product..

5) i,m gonna working on it.. ;)

thanks

ADMGNS:
sorry, i,ve forgotten to attach the new picture

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