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A Boolean shape operation algorithm which is based on triangulation of potentially intersecting faces is proposed. The essential part of the algorithm is a method for mutual processing of intersecting triangular pairs. This triangulation method is very effective in simplifying the algorithm and in reducing the system size. The method is suitable for hardware implementation because the simple routines for processing the intersecting pairs appear frequently in the algorithm. In determining points on an intersecting line loop, previous computational results can be utilized to calculate the next point, helping to speed up the algorithm.