Hull algorithms are the most efficient and closest methods to be redesigned for connecting vertices for geometric shape reconstruction. The vertices are the input points representing the original object shape. Our objective is to reconstruct the shape and edges but with no information on any pattern, it is challenging to reconstruct the lines to resemble the original shape. By comparing our results to recent concave hull based algorithms, two performance measures were conducted to evaluate the accuracy and time complexity of the proposed method. Besides achieving the most acceptable accuracy which is 100%, the time complexity of the proposed algorithm is evaluated to be O(wn). All results have shown a competitive and more effective algorithm compared to the most efficient similar ones. The algorithm is shown to be able to solve the problems of vertices connection in an efficient way by devising a new approach.