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The conditions for appearance of the isoscattering points of one- and two-dimensional systems have been theoretically derived using the ideal models of oriented membranes and fibers. The position s* of the isoscattering point of a one-dimensional system is given by s* = n/(2R0), where n is a positive integer and 2R0 is the thickness of the membrane. For a two-dimensional system, the position s* is given by J1(2πs*R0) = 0, where J1 is the first-order Bessel function and R0 is the radius of the fiber.