Optimal discrete slicing

Slicing is the procedure necessary to prepare a shape for layered manufacturing. There are degrees of freedom in this process, such as the starting point of the slicing sequence and the thickness of each slice. The choice of these parameters influences the manufacturing process and its result: The number of slices significantly affects the time needed for manufacturing, while their thickness affects the error. Assuming a discrete setting, we measure the error as the number of voxels that are incorrectly assigned due to slicing. We provide an algorithm that generates, for a given set of available slice heights and a shape, a slicing that is provably optimal. By optimal, we mean that the algorithm generates sequences with minimal error for any possible number of slices. The algorithm is fast and flexible, that is, it can accommodate a user driven importance modulation of the error function and allows the interactive exploration of the desired quality/time tradeoff. We demonstrate the practical importance of our optimization on several three-dimensional-printed results.