Abstract: Aiming at the problem of 3 D printing for a given image, this paper proposes an algorithm for generating approximating lines, which is geometrically and topologically optimized, so that the lines satisfy the conditions that can be used for 3 D printing. Firstly, an initialization is performed on the input image, that is, generating an initial line drawing that keeps the tone variations and boundary features of the original image by partition sampling on image, connecting points and extracting the boundaries. Secondly, the position of the line drawing points is corrected by geometric optimization, so that their connected lines are smoothed and the sharp-turns are reduced. Thirdly, adopting topology optimization to change the connection of the points in local areas, eliminating the self-intersection problem caused by geometric optimization and connecting the boundaries with the inner lines. Finally, the connection order of the points is made as a printing path that can be used by a 3 D printer. A variety of experiments have been demonstrated the feasibility and effectiveness of our proposed method.