“…The angular spectrum branches of the edges of the left triangle, 1 L , 2 L , and 3 L are denoted by 1 A , 2 A , and 3 A , respectively, while in Step2 those of the right triangle, 4 L , 5 L , and 6 L , are denoted by 4 A , 5 A , and 6 A . In the analytic method, the angular spectrums of the shared edges are exactly removed in Step1 + Step2 which is mathematically expressed by 4 0, A A + = (10) meaning that the two shared edges represented by 2 L and 4 L precisely cancels each other out and the line artifact does not develop, as was proven in previous research [10,13]. However, in the FFT calculation, the angular spectrums of the shared edges do not precisely cancel each other out because of the considerable numerical errors induced by the discrete approximation of FFT, which causes the non-zero line artifact at the border of the two adjacent polygons.…”