Axis-Aligned Height-Field Block Decomposition of 3D Shapes

Alessandro Muntoni, Marco Livesu, Riccardo Scateni, Alla Sheffer, Daniele Panozzo

ACM Transactions on Graphics (TOG), 2018


We propose a novel algorithm for decomposing general 3D geometries into a small set of overlap-free height-field blocks, volumes enclosed by a flat base and a height-field surface defined with respect to this base. This decomposition is useful for fabrication methodologies such as 3-axis CNC milling, where a single milling pass can only carve a single height-field surface defined with respect to the machine tray, but can also benefit other fabricationsettings. Computingourdesireddecompositionrequiressolving a highly constrained discrete optimization problem, variants of which are known to be NP-hard. We effectively compute a high-quality decomposition by using a two-step process that leverages the unique characteristics of our setup. Specifically, we notice that if the height-field directions are constrained to the major axes we can always produce a valid decomposition starting from a suitable surface segmentation. Our method first produces a compact set of large, possibly overlapping, height-field blocks that jointly cover the model surface by recasting this discrete constrained optimization problem as an unconstrained optimization of a continuous function, which allows for an efficient solution. We then cast the computation of an overlap-free, final decomposition as an ordering problem on a graph, and solve it via a combination of cycle elimination and topological sorting. The combined algorithm produces a compact set of height-field blocks that jointly describe the input model within a user given tolerance. We demonstrate our method on a range of inputs, and showcase a number of real life models manufactured using our technique.


Paper Code Data
(paper)               (code)               (data)


Milling Max Planck (wood, 3-axis milled)

Assemblage of Max Planck (wood, 3-axis milled)

Assemblage of Lion (plastic, 3d printed without supports)

Assemblage of Moai statue (wood, 3-axis milled)


            author    = {Muntoni, Alessandro and Livesu, Marco and Scateni, Riccardo and Sheffer, Alla and Panozzo, Daniele},
            title     = {Axis-Aligned Height-Field Block Decomposition of 3D Shapes},
            journal   = {ACM Transactions on Graphics},
            year      = {2018},
            volume    = {37},
            number    = {5},
            doi       = {10.1145/3204458}}