[Paper Review] Surface2Volume: Surface Segmentation Conforming Assemblable Volumetric Partition

Chrystiano Araújo, Daniela Cabiddu+4 more|arXiv (Cornell University)|Apr 23, 2019

Additive Manufacturing and 3D Printing Technologies4 citations

TL;DR

Surface2Volume introduces a novel algorithm for partitioning 3D models with multi-attribute surfaces into assemblable, single-attribute volumetric parts that strictly conform to surface segmentation. By sequentially computing assembly trajectories, interface topology, and interface geometry, the method enables robust, efficient fabrication of complex multi-material objects using standard single-material 3D printing or milling, validated through physical prototypes and comparisons to prior work.

ABSTRACT

Users frequently seek to fabricate objects whose outer surfaces consist of regions with different surface attributes, such as color or material. Manufacturing such objects in a single piece is often challenging or even impossible. The alternative is to partition them into single-attribute volumetric parts that can be fabricated separately and then assembled to form the target object. Facilitating this approach requires partitioning the input model into parts that conform to the surface segmentation and that can be moved apart with no collisions. We propose Surface2Volume, a partition algorithm capable of producing such assemblable parts, each of which is affiliated with a single attribute, the outer surface of whose assembly conforms to the input surface geometry and segmentation. In computing the partition we strictly enforce conformity with surface segmentation and assemblability, and optimize for ease of fabrication by minimizing part count, promoting part simplicity, and simplifying assembly sequencing. We note that computing the desired partition requires solving for three types of variables: per-part assembly trajectories, partition topology, i.e. the connectivity of the interface surfaces separating the different parts, and the geometry, or location, of these interfaces. We efficiently produce the desired partitions by addressing one type of variables at a time: first computing the assembly trajectories, then determining interface topology, and finally computing interface locations that allow parts assemblability. We algorithmically identify inputs that necessitate sequential assembly, and partition these inputs gradually by computing and disassembling a subset of assemblable parts at a time. We demonstrate our method....

Motivation & Objective

• To address the challenge of fabricating 3D objects with complex, non-uniform surface attributes (e.g., color, material, opacity) using standard single-attribute fabrication methods.
• To generate assemblable volumetric partitions that strictly conform to input surface segmentation and allow collision-free assembly.
• To minimize part count, promote geometric simplicity, and simplify assembly sequencing while preserving surface attribute fidelity.
• To overcome limitations of prior methods that fail on free-form or irregularly segmented models by enabling robust partitioning for diverse geometries.

Proposed method

• The method computes part assembly trajectories first, using a discrete mesh labeling approach to identify feasible, non-colliding motion paths for each part.
• It then determines the topological connectivity of internal interfaces between parts, ensuring that each part is associated with a single surface attribute.
• Finally, it computes the precise geometric location of these interfaces to guarantee assemblability and minimal part complexity.
• The algorithm iteratively extracts subsets of assemblable parts in sequence when full simultaneous disassembly is not possible, enabling handling of complex models.
• It uses a combined discrete-continuous optimization framework: discrete labeling for approximate solution, followed by geometric optimization to produce the final partition.
• The method assumes that newly exposed interfaces after part extraction can be attributed to adjacent regions, which holds for most practical cases.

Experimental results

Research questions

• RQ1 Can we automatically generate assemblable volumetric partitions that strictly conform to a given surface segmentation for multi-attribute 3D models?
• RQ2 How can we ensure that the resulting parts are geometrically simple, minimize part count, and allow for straightforward assembly sequencing?
• RQ3 What algorithmic strategy enables robust partitioning of complex, free-form models where prior methods fail?
• RQ4 How can we sequentially decompose models requiring non-simultaneous disassembly while maintaining assemblability and segmentation fidelity?

Key findings

• Surface2Volume successfully partitions a wide range of complex models—including free-form and man-made geometries—into assemblable, single-attribute parts that conform exactly to the input surface segmentation.
• The method produces physically fabricated parts that assemble correctly, as validated through 3D printing and milling of prototypes, including challenging cases like the wooden puzzle and bench components.
• The algorithm outperforms prior approaches in terms of input coverage, robustness, and efficiency, particularly on models requiring non-regular, free-form interfaces.
• The approach enables fabrication of multi-material objects using standard single-material processes, such as FDM 3D printing and CNC milling, by decomposing them into compatible, independently manufacturable parts.
• The method is limited by volumetric mesh resolution and mesh quality, particularly for models requiring extrusion of very small features (e.g., <0.5% of bounding box), where it fails due to insufficient resolution.
• Pathological cases—such as models where newly exposed interfaces cannot be attributed to adjacent regions—cannot be partitioned, though such cases are rare in practice.