Prof. Alexa has been awarded an ERC Advanced Grant for his research project “EMERGE” (“Geometry Processing as Inference”). The European Research Council will finance the project with 2.5 million euros over the next five years. They exclusively fund groundbreaking, innovative and pioneering basic research. The applicants’ scientific excellence and the projects are the sole selection criterion.
EMERGE aims to use the methods of geometry processing also for the processing of higher-dimensional structures. The hope and central thesis of the project is that the refinement of methods in geometry processing over the last decades will still be successful when extended to higher dimensions and exploit potentials that are complementary to developments in machine intelligence and classical digital signal processing.
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, it can accommodate a user driven importance modulation of the error function and allows the interactive exploration of the desired quality/time tradeoff.
