自支撑结构的3D打印技术

3D打印

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Deuss, M., Panozzo, D., Whiting, E., Liu, Y., Block, P., Sorkine-Hornung, O., Pauly, M. 2014. Assembling

Self-Supporting Structures. ACM Trans. Graph. 33, 6, Article 214 (November 2014), 10 pages.

DOI = 10.1145/2661229.2661266 http://doi.acm.org/10.1145/2661229.2661266.

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DOI: http://doi.acm.org/10.1145/2661229.2661266

Assembling Self-Supporting Structures

Mario Deuss

Daniele Panozzo

Emily Whiting

2,3

Yang Liu

Philippe Block

Olga Sorkine-Hornung

Mark Pauly

EPF Lausanne

ETH Zurich

Dartmouth College

Microsoft Research

Figure 1:

We propose a construction method for self-supporting structures that uses chains, instead of a dense formwork, to support the blocks

during the intermediate construction stages. Our algorithm ﬁnds a work-minimizing sequence that guides the construction of the structure,

indicating which chains are necessary to guarantee stability at each step. From left to right: a self-supporting structure, an intermediate

construction stage with dense formwork, an intermediate construction stage with our method and the assembled model.

Abstract

Self-supporting structures are prominent in historical and contem-

porary architecture due to advantageous structural properties and

efﬁcient use of material. Computer graphics research has recently

contributed new design tools that allow creating and interactively

exploring self-supporting freeform designs. However, the physical

construction of such freeform structures remains challenging, even

on small scales. Current construction processes require extensive

formwork during assembly, which quickly leads to prohibitively

high construction costs for realizations on a building scale. This

greatly limits the practical impact of the existing freeform design

tools. We propose to replace the commonly used dense formwork

with a sparse set of temporary chains. Our method enables gradual

construction of the masonry model in stable sections and drastically

reduces the material requirements and construction costs. We an-

alyze the input using a variational method to ﬁnd stable sections,

and devise a computationally tractable divide-and-conquer strategy

for the combinatorial problem of ﬁnding an optimal construction se-

quence. We validate our method on 3D printed models, demonstrate

an application to the restoration of historical models, and create

designs of recreational, collaborative self-supporting puzzles.

CR Categories:

I.3.5 [Computer Graphics]: Computational Ge-

ometry and Object Modeling—Curve, surface, solid, and object

representations;

Keywords:

masonry models, static equilibrium analysis, self-

supporting surfaces, optimization, sparsity, assembly order

Links:

DL PDF WEB

1 Introduction

The majority of man-made objects are composed of multiple inter-

locking parts, kept together by glue, bolts or other connections. The

division into components is often necessary to achieve a certain

purpose (computers, cars) or to make the fabrication of large models

feasible or cheaper (buildings, furniture, roads, railways, large 3D

printed models, etc.).

In this work, we focus on the construction of self-supporting struc-

tures that are composed of bricks or stone blocks without any mortar

to bind them together. Most of the world’s architectural heritage

consist of self-supporting masonry structures that require no support-

ing framework, since the entire structure is in a static equilibrium

conﬁguration.

The design of modern, freeform self-supporting structures has re-

cently received a lot of interest in computer graphics [Vouga et al

2012; Liu et al

2013; de Goes et al

2013; Panozzo et al

2013], but

their physical construction has only been addressed for small-scale

models. The method proposed in [Panozzo et al

2013] relies on

dense formwork (Figure 1) to support all the blocks until the entire

construction is completed; after the last piece is put in place, the

structure is in equilibrium and the formwork can be carefully re-

moved. This method is difﬁcult to apply to large scale structures,

because a dense formwork able to sustain the weight of large stone

blocks is too expensive and not practical, especially considering that

the formwork has to be dismantled after all the blocks are in place.

Also, removing the formwork demands technically complex and

expensive solutions: the formwork has to be lowered evenly to avoid

failures due to redistribution of forces. Due to the lack of an econom-

ically feasible construction strategy, freeform masonry structures are

currently rarely built, despite their advantageous structural proper-

ties and unique aesthetics. Additionally, the majority of the cost is

associated with the foundations necessary to support the formwork.

We propose a different approach, replacing the dense formwork

with a sparse set of chains that are connected to ﬁxed anchor points.

While chains have been used for construction before, our method

speciﬁcally aims at ﬁnding a work-minimizing assembly sequence,

requiring as few chains to be rehung as possible. Our solution

leverages the internal force distribution of the partially assembled

structure and only provides the minimally required additional sup-

ports to keep the structure in static equilibrium at all stages of the

assembly. The use of chains has been pioneered in modern construc-

ACM Transactions on Graphics, Vol. 33, No. 6, Article 214, Publication Date: November 2014

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