Dapper：3D打印的分解与打包技术

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Dapper是一项针对3D打印技术的重要研究成果，发表于2015年的ACM Transactions on Graphics（TOG）第34卷第6期，文章编号为213。这篇名为《Dapper：分解与打包，面向3D打印》的论文由陈(X.)、张(H.)等人共同完成，探讨了如何有效地优化3D打印过程中的数据处理和模型转换。作者们提出了一种新颖的方法，旨在通过将复杂的3D模型分解并打包，提高打印效率，减少材料浪费，从而推动3D打印技术在工业和设计领域的应用。论文的主要贡献在于开发了一种名为"Dapper"的技术，它能够将大尺寸或高细节的3D模型分解成一系列更小、更易于处理的部分，这些部分能够在打印过程中独立生成，然后在完成后重新组装成原始模型。这种分解策略考虑了3D打印设备的物理限制，如层厚和打印速度，确保在保持模型完整性的同时，最大化打印效率。 Dapper的核心是它的分解算法，它基于模型的拓扑结构和几何特性，智能地分割模型，同时保留重要的连接性和支持结构，以便于打印过程中的顺利进行。此外，论文还讨论了打包策略，即如何组织和存储这些分解后的部分，以优化打印路径规划，减少重叠区域，进一步节省材料。该论文的研究成果对于提升3D打印的生产效率和降低成本具有显著意义，特别是在大规模生产和定制化制造领域。同时，Dapper方法也展示了如何利用计算机图形学和算法在现实世界的应用中解决实际问题，体现了跨学科研究的价值。为了确保学术公正和尊重版权，作者提供了关于复制和分发此作品的规定。未经许可，个人或课堂用途可以免费制作或复制，但商业目的或未经明确许可的网络发布和分发则需事先获得许可。有兴趣的读者可以通过ACM官方邮箱permissions@acm.org申请相应权限。《Dapper：分解与打包，面向3D打印》是一篇深入研究了3D打印技术瓶颈并提供创新解决方案的论文，它代表了3D打印领域的一个关键里程碑，对推动该行业向更高效率和灵活性迈进有着重要影响。

3D Packing. In engineering and manufacturing domains, some

methods pack 3D parts for efﬁcient layered fabrication [Dickinson

and Knopf 2002] and rapid prototyping [Gogate and Pande 2008].

The general packing problem has many variants in many appli-

cation settings, including packing/loading, scheduling, and rout-

ing [Crainic et al. 2012]. Most instances of the packing problem

are NP-hard, hence heuristic-driven exhaustive or stochastic search

including branch-and-bound, simulated annealing, and genetic al-

gorithms are frequently adopted [Cagan et al. 2002].

The key difference between Dapper and these previous works is

that in our problem, the shapes to be packed are not given a priori;

they are the result of a simultaneous shape decomposition and are

modiﬁed on-the-ﬂy. The coupling not only changes the nature of

the problem but also increases the search space signiﬁcantly.

Decomposition for 3D printing. The problem of decomposing

3D objects into solid parts for efﬁcient fabrication has drawn inter-

ests from graphics researchers recently. Perhaps the ﬁrst attempt

was made by Luo et al. [2012], where they develop a tool to parti-

tion a 3D model so that each part can ﬁt in the printing volume. Fac-

tors including low part count, assemblability, and aesthetics of the

cuts are taken into consideration, but the method is oblivious to sup-

port material or build time. The work by Hildebrand et al. [2013] is

motivated by the direction bias of additive manufacturing. It poses

the interesting problem of decomposing a 3D shape into few pieces

so that each piece can be consistently sliced with small geometric

error along one of three orthogonal slicing directions. Recent work

by Hu et al. [2014] decomposes a 3D object into a small number

of approximately pyramidal parts so that each can be printed by an

FDM printer with low cost in time and material.

Dapper also computes solid decompositions in 3D and seeks low

part counts. However, we add packing, a new dimension, to the

decompose-to-print problem. Smart packing strategies allow print-

ing multiple parts at a time, leading to better utilization of the print

volume while incurring small time and material cost.

Boxelization. Recent work by Zhou et al. [2014] “boxelizes” a

3D shape by voxelizing it, computing a tree linkage structure over

the voxels, and folding the linkage structure into a box. There is

slight resemblance between boxelization and Dapper: voxelization

and unlinking of voxels can be seen as a special form of decompo-

sition; folding into a box is a special form of packing. The resem-

blance would stop there though as the two problems have different

goals and operate on completely different primitives (linked voxels

vs. discrete set of polycubes) and constraints.

Discrete scissor congruence. More closely related to DAP is

the intriguing Scissoring Congruence problem, which disects two

shapes into identical sets of segments. Note that this problem is

identical to DAP if its target container has the same area/volume as

the input shape. Zhou and Wang [2012] discretize the problem on

a grid and solve Discrete Scissoring Congruence (DSC) by recur-

sive co-disection of the two input shapes. Our DAP problem has a

different goal: it decompose-and-packs an input shape into an open-

ended volume as tightly as possible while minimizing part count. In

contrast, DSC works with a ﬁxed target container and seeks exact

congruence without setting an objective to minimize the number of

segments. Both problems require difﬁcult global optimization. To

counter local minima, the DSC solution applies random exploration

of hundreds of pairs of initial seeds for the co-disection.

PackMerger. PackMerger [Vanek et al. 2014] appears to be the

ﬁrst work which considers improving a decomposition for better

packing. The method ﬁrst converts an input 3D object into shells,

while Dapper works with solid decomposition. Moreover, Pack-

Merger works with terahedralized input and imposes additional re-

strictions on the input object, possibly leading to uneven gluing

boundaries. Dapper, on the other hand, only makes planar cuts.

Algorithmically, while Dapper follows a top-down search, Pack-

Merger is bottom-up. In PackMerger, the initial set of segments is

obtained with packing in mind, e.g., larger cut areas are preferred.

However, the consideration of packing is only implicit, the decom-

position is not coupled with any packing process. After the initial

decomposition, PackMerger executes a merge-and-pack step which

again decouples the two tasks; it corresponds to a “merge-and-then-

pack” process. Speciﬁcally, this step randomly explores mergings

between segments, and for each merging, recomputes a tight pack-

ing with a ﬁxed set of segments. The search merely amounts to

a random sampling of packing solutions. The ﬁnal solution is se-

lected as the merging conﬁguration leading to the best packing.

In our work, we adhere to the true spirit of DAP, emphasizing the

strong coupling, rather than interleaving the solution by solving a

decomposition and then a packing, independently.

The main potential advantage of PackMerger over our algorithm is

that it searches over arbitrary rotations of the shape pieces during

packing. Dapper could allow this as well. However, the coupling

of decompose and pack signiﬁcantly increases the search space

over any decoupled approach, making a reﬁned discretization of the

space of rotations prohibitive. As the experimental comparison re-

sults would later reveal, the quality and computational advantages

afforded by Dapper with only axial rotations appear to outweight

any gains offered by PackMerger with the consideration of arbi-

trary rotations. Indeed, the difference is mainly in the optimization

or search strategy, not the discretization of search spaces.

3 Decompose-and-pack pyramidal shapes

Our goal is to optimally decompose-and-pack a 3D input object into

a container, the printing volume, for efﬁcient fabrication. The input

to the Dapper algorithm is a solid 3D object, along with a target

container which is a rectangular cuboid. In our coverage, to ease

understanding of the algorithm, we mainly illustrate it in 2D. We

assume that the container has sufﬁcient height to admit a packing

of all the decomposed parts. However, the horizontal dimensions of

the container are limiting, so that the input shape cannot ﬁt inside

without being cut into smaller pieces. The challenge is to efﬁciently

pack the input using a small number of pieces.

3.1 Overview

Dapper starts with an initial partitioning of the input shape into few

pyramidal parts. The parts are voxelized into pyramidal polycubes.

Dapper then applies a global DAP optimization over the polycubes.

After packing the polycubes into the container, the positions of the

enclosed shape parts are locally reﬁned to obtain a lower and tighter

packing. Figure 3 outlines the major steps of Dapper.

In the global optimization phase (Section 4.1), we decompose and

pack pyramidal polycubes. We pictorially regard the container as a

pile of packed polycubes. Each pile corresponds to a partial DAP

solution and a complete solution is reached when all polycubes are

packed. Our solution search is top-down and iterative. At each iter-

ation, we generate a set of candidate moves, each of which involves

packing a part onto the pile, possibly after a part decomposition.

Iterative selection of candidate moves advances the DAP solution

and forms a search tree. Expansion and pruning of the search tree

are based on a priority score we deﬁne for each candidate move and

a global objective function we deﬁne for each DAP solution.

Dapper: Decompose-and-Pack for 3D Printing • 213:3

ACM Transactions on Graphics, Vol. 34, No. 6, Article 213, Publication Date: November 2015

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