Axis-aligned height-field block decomposition of 3D shapes

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

Research output: Contribution to journalArticle

Abstract

We propose a novel algorithm for decomposing general three-dimensional 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 fabrication settings. Computing our desired decomposition requires solving 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, then 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.

Original languageEnglish (US)
Article number169
JournalACM Transactions on Graphics
Volume37
Issue number5
DOIs
StatePublished - Nov 1 2018

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Decomposition
Fabrication
Constrained optimization
Sorting
Geometry

Keywords

  • Fabrication
  • Shape decomposition

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

Cite this

Axis-aligned height-field block decomposition of 3D shapes. / Muntoni, Alessandro; Livesu, Marco; Scateni, Riccardo; Sheffer, Alla; Panozzo, Daniele.

In: ACM Transactions on Graphics, Vol. 37, No. 5, 169, 01.11.2018.

Research output: Contribution to journalArticle

Muntoni, Alessandro ; Livesu, Marco ; Scateni, Riccardo ; Sheffer, Alla ; Panozzo, Daniele. / Axis-aligned height-field block decomposition of 3D shapes. In: ACM Transactions on Graphics. 2018 ; Vol. 37, No. 5.
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