String Actuated Curved Folded Surfaces

Abstract

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

Semi‐Automatic Conversion of 3D Shape into Flat‐Foldable Polygonal Model

“…Although allowing concave components will increase the designing and folding labor, the labor might be alleviated if we can actuate a foldable model mechanically [KMM17]. Although allowing concave components will increase the designing and folding labor, the labor might be alleviated if we can actuate a foldable model mechanically [KMM17].…”

State of the Art on Stylized Fabrication

“…Taking time into account as an additional dimension, the process of printing structures that can transform in a pre‐programmed way in response to a stimulus is called 4D printing [Tib14]. Several recent works in computer graphics investigated the design of surfaces fabricated with pre‐stretched elastic materials that deploy into complex, 3D shapes [GMB17, POT17, KMM17]. Other methods optimize shapes to offer a pre‐defined elastic [CLMK17] or dynamic behaviour [UKSI14, BWBSH14].…”

“…Addressing this problem, Killian et al . [KMM17] introduced string‐actuated, curved folded surfaces that can be shaped by pulling a network of strings. The concept of foldable strips has been extended by Takezawa et al .…”

Modeling curved folding with freeform deformations

“…The design of a curved folded surface is manual and time consuming and is usually done using an empirical trial and error approach [Demaine et al 2011a,c]. The known theory on curved folds is conned to a narrow set of folds, and contrary to classical origami, bending and folding instructions are hard to write down and multiple creases must be folded simultaneously [Kilian et al 2017]. Artists generally pre-crease the paper using a ball burnisher or a CNC plotter before carefully folding and bending, making the process of shape exploration even slower.…”

“…Although manual and slow, playing with paper is still the predominant approach for curved folded surface design. Existing works on modeling such surfaces are either limited to previously discovered surfaces [Kilian et al 2008[Kilian et al , 2017 or model a small, partial set of folded surfaces generated by re ections or rotational sweeps [Mitani 2009;Mitani and Igarashi 2011]. Modeling the folding process of novel forms remains a challenge [Demaine et al 2011c].…”