Interactive Design of Developable Surfaces

Tang, Chengcheng; Bo, Pengbo; Wallner, Johannes; Pottmann, Helmut

doi:10.1145/2832906

Cited by 108 publications

(95 citation statements)

References 37 publications

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“…Our system thus moves vertex v 1 to v ′ 1 and vertex v 3 to v ′ 3 after the annotation is specified. If the shape before folding is an n-gon (n > 3) ( Figure 6(b)), our system moves v 3 and v 5 so that they are aligned with the ideal mirror image, while keeping the lengths of the line segments connected to v 3 and v 5 .…”

Section: Constraint-based Polygon Rectificationmentioning

confidence: 99%

Single‐View Modeling of Layered Origami with Plausible Outer Shape

Kato

Tanaka

Kanamori

et al. 2019

Computer Graphics Forum

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Modeling 3D origami pieces using conventional software is laborious due to the geometric constraints imposed by the complicated layered structure. Targeting origami models used in visual content such as CG illustrations and movies, we propose an interactive system that dramatically simplifies the modeling of 3D origami pieces with plausible outer shapes, while omitting accurate inner structures. By focusing on flat origami models with a front‐and‐back symmetry commonly found in traditional artworks, our system realizes easy and quick modeling via single‐view interface; given a reference image of the target origami piece, the user draws polygons of planar faces onto the image, and assigns annotations indicating the types of folding operations. Our system automatically rectifies the manually‐specified polygons, infers the folded structures that should yield the user‐specified polygons with reference to the depth order of layered polygons, and generates a plausible 3D model while accounting for gaps between layers. Our system is versatile enough for modeling pseudo‐origami models that are not realizable by folding a single sheet of paper. Our user study demonstrates that even novice users without the specialized knowledge and experience on origami and 3D modeling can create plausible origami models quickly.

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Section: Constraint-based Polygon Rectificationmentioning

confidence: 99%

Single‐View Modeling of Layered Origami with Plausible Outer Shape

Kato

Tanaka

Kanamori

et al. 2019

Computer Graphics Forum

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“…Static soundness has been explored in the context of 3D printing [Langlois et al 2016;Prévost et al 2013;, furniture [Umetani et al 2012], gridshell structures [Pietroni et al 2015], and selfsupporting surfaces [Block and Ochsendorf 2007;de Goes et al 2013;Panozzo et al 2013;Vouga et al 2012]. To reduce manufacturing cost, researchers looked at the use of o -the-shelf parts [Schulz et al 2014], simpli cation of geometric components [Liu et al 2006;Tang et al 2016], and construction using repetitive elements [Fu et al 2010;Huard et al 2014;. In line with these two themes, we study the design of statically sound space structures of minimal volume to reduce production cost.…”

Section: Previous Workmentioning

confidence: 99%

Design and volume optimization of space structures

et al. 2017

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Fig. 1. Le : A statically sound space structure designed and optimized with our framework, motivated by the real architectural project shown in Figure 2. Right: The space structure is constructed with six types of customized beams to minimize the total volume of the material used for beams while maintaining moderate manufacturing complexity. Here, a ho er color indicates a larger beam cross-section area. Our framework automatically determines the optimal cross-section areas of the six types of beams as well as the assignment of beam types.We study the design and optimization of statically sound and materially e cient space structures constructed by connected beams. We propose a systematic computational framework for the design of space structures that incorporates static soundness, approximation of reference surfaces, boundary alignment, and geometric regularity. To tackle this challenging problem, we rst jointly optimize node positions and connectivity through a nonlinear continuous optimization algorithm. Next, with xed nodes and connectivity, we formulate the assignment of beam cross sections as a mixed-integer programming problem with a bilinear objective function and quadratic constraints. We solve this problem with a novel and practical alternating direction method based on linear programming relaxation. The capability and e ciency of the algorithms and the computational framework are validated by a variety of examples and comparisons.

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“…Later, Solomon et al [2012] presented a subdivision based modeling approach involving curved folds assuming the crease pattern and corresponding crease angles as input. Tang et al [2015] encode developability conditions as nonlinear constraints and solve for curved folded surfaces using a projection-based efficient constraint solver for interactive modeling. These efforts typically assume access to target shapes, which are analyzed to initialize direction of rulings, estimate the crease angles, or tessellate the planar domain.…”

Section: Related Workmentioning

confidence: 99%

String Actuated Curved Folded Surfaces

2017

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e e e e e e e e e e e e e e e e e Fig. 1: The top row shows a crease pattern together with the strings S = {a, b, c, d, e} computed by our algorithm and simulation of the induced, string driven folding motion. The bottom row shows a physical realization of the same crease pattern as a thin aluminum sheet. Each string is realized as a strand of colored thread. Strings are collected at a single anchor point and folding is driven by pulling the threads.Curved folded surfaces, given their ability to produce elegant freeform shapes by folding flat sheets etched with curved creases, hold a special place in computational Origami. Artists and designers have proposed a wide variety of different fold patterns to create a range of interesting surfaces. The creative process, design as well as fabrication, is usually only concerned with the static surface that emerges once folding has completed. Folding such patterns, however, is difficult as multiple creases have to be folded simultaneously to obtain a properly folded target shape. We introduce string actuated curved folded surfaces that can be shaped by pulling a network of strings thus vastly simplifying the process of creating such surfaces and making the folding motion an integral part of the design. Technically, we solve the problem of which surface points to string together and how to actuate them by locally expressing a desired folding path in the space of isometric shape deformations in terms of novel string actuation modes. We demonstrate the validity of our apMartin Kilian was supported by the Erwin Schrödinger fellowship J-3678-N25 awarded by the Austrian Science Fund (FWF), ERC StG-2013-335373, and the DFGCollaborative Research Center, TRR 109, 'Discretization in Geometry and Dynamics' through grant I-706-N26 of FWF. Aron Monszpart was supported by a Google PhD Fellowship, the ERC Starting Grant SmartGeometry (StG-2013-335373), and Adobe Research. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. proach by computing string actuation networks for a range of well known crease patterns and testing their effectiveness on physical prototypes. All the examples in this paper can be downloaded for personal use from

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Interactive Design of Developable Surfaces

Cited by 108 publications

References 37 publications

Single‐View Modeling of Layered Origami with Plausible Outer Shape

Single‐View Modeling of Layered Origami with Plausible Outer Shape

Design and volume optimization of space structures

String Actuated Curved Folded Surfaces

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