针对给定的图像3D打印问题, 提出一种基于线型图逼近的打印路径生成算法, 并对打印路径进行几何与拓扑优化, 使得生成的路径可以满足 3D 打印的条件. 首先对给定图像进行初始化, 即通过对图片进行分块采样. 点的连通与边界提取来得到保持原图片色调变化与轮廓特征的初始的线型图; 然后通过几何优化修正组成线型图点的位置, 使得它们的连线平滑且尖锐的拐点减少; 再通过拓扑优化改变局部区域中的点的连接关系, 消除因几何优化带来的连线自交问题, 同时将边界与内部线连接起来; 最后将点的连接顺序作为 3D 打印的路径, 通过 3D 打印机进行制造. 实验结果表明, 该方法能够有效且高效地给图像生成线型图并用于3D打印.%Aiming at the problem of 3D printing for a given image, this paper proposes an algorithm for gen-erating approximating lines, which is geometrically and topologically optimized, so that the lines satisfy the conditions that can be used for 3D 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 con-necting 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 3D printer. A variety of experiments have been demonstrated the feasibility and effectiveness of our proposed method.
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