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Curved-line folding, the act of folding paper along a pattern of curved lines to obtain a 3D shape, is an interesting starting-point for the design of innovative pliable structures. There exists a kinematic connection between two surfaces linked through a curved crease that can be used to generate a folding motion. However, due to the interdependency of geometry, forces and material properties the design of pliable structures based on curved-line folding is very complex. To facilitate the design process, adequate computational modelling methods are essential. This paper presents two ways of modelling: a geometric modelling method based on discretisation of the crease pattern and a method based on Finite Element Analysis (FEA). The proposed methods are validated by means of a case study in which a physical model is compared to digital ones. It can be concluded that the method based on FEA corresponds very well with the physical model, proving its potential. The accuracy of the geometric modelling is improved by the introduction of a set of guidelines based on the direction of the principal bending moments in the pliable structure. Furthermore, the case study exposes how the material-dependent behaviour of pliable structures increases the complexity of the design and should certainly be part of future research. [ABSTRACT FROM AUTHOR]

The research on the conversion from 2D paper drawings to 3D computer feature models has been stuck in low-level coding. One of the reasons for it is that the three phases of understanding process has been isolated and people have been doing their research on only one of the phases since the whole conversion is very complicated and more difficult. For instance, the vectorization methods for the first phase were developed only for getting straight lines, arcs, circles, etc. so that much information contained in the drawing has been lost after the vectorization. This paper develops a holo-extraction method of information from paper drawings, the networks of single closed regions (SCRs), which can not only provide a unified base for recognizing both the annotations and the outlines of projections of parts, but also build the holo-relationships among SCRs so that it is convenient to extract lexical, syntactic and semantic information in the subsequent phases for 3D reconstruction. [Copyright &y& Elsevier]

As a ubiquitous paper folding art, origami has promising applications in science and engineering. Many software and parameterized methods have been proposed to draw, analyze and design origami patterns. Here we focus on the shape grammar formalism and the Shape Machine, a shape grammar interpreter that has managed to automate the seamless shape calculations that the shape grammar formalism advocates. Different from other origami pattern generation methods, shape grammars generate origami patterns through recursive applications of shape rewriting rules using lines and curves. Based on this concept, the transformations between some common origami patterns are reorganized following visual cues and reasoning. Four examples of generating origami pattern are presented to show the capability of Shape Machine in origami design, including construction, modification and programming of an origami pattern. The new origami designs inspired by this work prove that shape grammars and Shape Machine provide a perspective and modeling technique for creating origami tessellation patterns. • Rational method for generating origami patterns. • Modeling technique for designing origami tessellations. • Shape Machine, new shape grammar interpreter that automates shapes calculation to create new patterns. • Origami pattern considered as a combination of different shapes. [ABSTRACT FROM AUTHOR]

Motivated by the art of curved crease origami we study mathematical models for folding ideal paper along curved creases. We approach the problem of finding mathematical descriptions in terms of developable surfaces of those shapes which can be folded from real paper but where its rigorous description is very often unknown. For that we investigate a particular one-parameter family of surfaces isometric to a given planar surface patch. For each such surface we parametrize the crease curves which fold those surfaces into cylinders and cones. We apply our methods to explore curved crease origami designs, such as tessellations of the plane and cylinders. • We compute explicit isometric deformations of developable surfaces that are guided by sliding on planes. • We give explicit parametrizations of crease curves between developable surfaces and cylinders and cones. • We illustrate our methods on examples such as curved crease tessellations of cylinders and planes. [ABSTRACT FROM AUTHOR]

Creating developable surfaces from sparse design curves finds important applications in industrial design and modeling. Existing methods aim at finding a quasi-developable surface with as large developability as possible to interpolate design curves. Even so, the fabrication of industrial products with inextensible materials puts a higher request for surface developability. We propose a method to explore the space of developable surfaces whose boundaries are restricted in the close neighborhood of input design curves and aim at obtaining a smooth surface of a high degree of developability bounded by smooth curves perturbed from input curves. This is achieved by computing a developable surface with approximate boundaries, which is obtained by solving a geometric optimization problem. The performance of the proposed method is demonstrated by a number of experiments of design and fabrication of some industrial products with paper. • We propose a method to create seamless multi-strip smooth developable surfaces from an array of design curves. • We achieve high accuracy of developability with the controllable error in curve modification. • Original curves are modified and extended automatically when necessary which is driven by the surface developability. [ABSTRACT FROM AUTHOR]