A new stitching algorithm named ARSA (Approximated Reference Shape Algorithm) that connects multiple partial measurements and combines them into a whole shape is proposed. Compared to the conventional stitching method, the advantages of the new algorithm are that there is no need to precisely find the overlap area and no need to interpolate three dimensional point data. These are essential conditions in order to apply the method to a free form measurement machine whose measured data are sparse and three dimensional points. The performance of the algorithm is verified by simulation of a TMT (30 m telescope) segmented mirror.
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