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New Geomatics Technologies and Applications

5) By LS, the edge L2 is fitted to the nodes of set A2.
6) If the distance of the fitted edge to each node of set A2 is less than the value of T, the next node is added to set A 2
and the same operation is repeated. Otherwise, the last node is removed from set A 2 and the parameters a2 and b2
resulting from the fitting of the edge to the points of set A2 are stored as the parameters of the second line.
7) To measure the first node (N1) from several target lines, the equation of the second edge is equated with the equation
of the first edge.

8) The above operations will continue and each time a new edge is stored, which can be obtained by equating its equation
with the equation of the edge before itself, a new node of the target multiline.
9) This process will continue until the last node (due to the closed shape) is the same node that has coordinates equal to
the first node of the original multi-line, at which point node N1 will be included in the hypothetical set Ak to calculate
the parameters of the Lk edge.

There are two possible ways:
A. If the distance between all nodes in the set A k and the edge fitted to them is less than T, the edge is saved as the
final simplified multiple line edge, and node N1 and edge L1 are deleted. The Nk is obtained as the last node by
equating the equations of the edges L2 and Lk (also because it is closed as a multi-line as the first node).
B. Otherwise N1 is not added to Ak and the last edge is obtained from the fit on the A k nodes. Finally, by equating
the equations of the edges L1 and Lk, the node N k is obtained as the last node.

According to the proposed model model of this study, the proposed model was implemented for Zerivar Lake, and the
results of the Least Squares (LS) were compared to the Douglas-Poker (DP) and Viswalingam (VW) methods results in Fig. 2.

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