Nonsmooth Developable Geometry for Interactively Animating Paper Crumpling

Schreck, Camille; Rohmer, Damien; Hahmann, Stéfanie; Cani, Marie-Paule; Jin, Shuangshuang; Wang, Charlie C. L.; Bloch, Jean‐Francis

doi:10.1145/2829948

Cited by 28 publications

(24 citation statements)

References 37 publications

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“…There have been past efforts to model and analyze surfaces that exhibit bent and creased folding. Origami-based bent and creased surfaces have been simulated using collections of developable surface subdomains [47][48][49][50][51]. Such advancements allow for the realistic animation and rendering of curved folds and combinations of creases and bent regions.…”

Section: Introductionmentioning

confidence: 99%

“…Such advancements allow for the realistic animation and rendering of curved folds and combinations of creases and bent regions. However, none of the aforementioned works [47][48][49][50][51] have considered constraints on the geometry and deformation of the bent folded regions that are required to preserve rigid faces as in analogous rigid origami models, which are essential when fold intersections or holes are present in the sheet. In view of this, a novel model for the kinematic response of rigid origami-based structures having smooth folds is presented in this work.…”

Section: Introductionmentioning

confidence: 99%

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Kinematics of Origami Structures With Smooth Folds

Hernandez

Hartl

Lagoudas

2016

Journal of Mechanisms and Robotics

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Origami provides both inspiration and potential solutions to the fabrication, assembly, and functionality of various structures and devices. Kinematic modeling of origamibased objects is essential to their analysis and design. Models for rigid origami, in which all planar faces of the sheet are rigid and folds are limited to straight creases having only zeroth-order geometric continuity, are available in the literature. Many of these models include constraints on the fold angles to ensure that any initially closed strip of faces is not torn during folding. However, these previous models are not intended for structures with non-negligible fold thickness or with maximum curvature at the folds restricted by material or structural limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate idealizations of structural response, and a new approach is needed. In this work, a novel model analogous to those for rigid origami with creased folds is presented for sheets having realistic folds of nonzero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of smooth folds and constraints on their associated shape variables are presented. A numerical implementation of the model allowing for kinematic simulation of sheets having arbitrary fold patterns is also described. Simulation results are provided showing the capability of the model to capture realistic kinematic response of origami sheets with diverse fold patterns.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kinematics of Origami Structures With Smooth Folds

Hernandez

Hartl

Lagoudas

2016

Journal of Mechanisms and Robotics

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“…They model a material's behavior through energy minimization, simulating the physical shape when applying forces. The focus of these works is the physics of an object, such as an elastic simulation [Burgoon et al 2006], or paper crumpling and tearing [Narain et al 2013;Schreck et al 2017Schreck et al , 2015, rather than the geometry of developable surfaces. As such, these works do not deal with defining a precise notion of a discrete developable surface, nor do they aim at the exploration of the entire shape space of developable surfaces without straying off constraints.…”

Section: Modeling With Developable Surfacesmentioning

confidence: 99%

Discrete Geodesic Nets for Modeling Developable Surfaces

2018

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We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be parameterized through orthogonal geodesics. Our model is simple, local, and, unlike previous works, it does not directly encode the surface rulings. This allows us to model continuous deformations of discrete developable surfaces independently of their decomposition into torsal and planar patches or the surface topology. We prove and experimentally demonstrate strong ties to smooth developable surfaces, including a theorem stating that every sampling of the smooth counterpart satisfies our constraints up to second order. We further present an extension of our model that enables a local definition of discrete isometry. We demonstrate the effectiveness of our discrete model in a developable surface editing system, as well as computation of an isometric interpolation between isometric discrete developable shapes.

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“…Recently, modeling deformation behavior of paper in the context of thin shells has been explored by Narain et al [2013]. Schreck et al [2015] propose a hybrid surface model to support crumpling behavior for interactive paper simulation while explicitly accounting for isometric deformations. However, such methods do not help in predicting a folded shape starting only from an input crease pattern, as is our goal.…”

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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Nonsmooth Developable Geometry for Interactively Animating Paper Crumpling

Cited by 28 publications

References 37 publications

Kinematics of Origami Structures With Smooth Folds

Kinematics of Origami Structures With Smooth Folds

Discrete Geodesic Nets for Modeling Developable Surfaces

String Actuated Curved Folded Surfaces

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