Origami Crease Pattern ((LINK)) Download
Diana Fisher
A crease pattern (commonly referred to as a CP)[1] is an origami diagram that consists of all or most of the creases in the final model, rendered into one image. This is useful for diagramming complex and super-complex models, where the model is often not simple enough to diagram efficiently.
The use of crease patterns originated with designers such as Neal Elias, who used them to record how their models were made. This allowed the more prolific designers to keep track of all their models, and soon crease patterns began to be used as a means for communication of ideas between designers. After a few years of this sort of use, designers such as Robert J. Lang, Meguro Toshiyuki, Jun Maekawa and Peter Engel began to design using crease patterns. This allowed them to create with increasing levels of complexity, and the art of origami reached unprecedented levels of realism. Now most higher-level models are accompanied by crease patterns.
Although not intended as a substitute for diagrams, folding from crease patterns is starting to gain in popularity, partly because of the challenge of being able to 'crack' the pattern, and also partly because the crease pattern is often the only resource available to fold a given model, should the designer choose not to produce diagrams. For example, an algorithm for the automatic development of crease patterns for certain polyhedra with discrete rotational symmetry by composing right frusta has been implemented via a CAD program.[2] The program allows users to specify a target polyhedron and generate a crease pattern that folds into it. Still, there are many cases in which designers wish to sequence the steps of their models but lack the means to design clear diagrams. Such origamists occasionally resort to the sequenced crease pattern (SCP) which is a set of crease patterns showing the creases up to each respective fold. The SCP eliminates the need for diagramming programs or artistic ability while maintaining the step-by-step process for other folders to see. Another name for the sequenced crease pattern is the progressive crease pattern (PCP).
I previously posted images of these crimp-bent tubes that I designed earlier this year, and here are the crease patterns. The top and bottom edge of each bend are based on sine waves. The angles of the internal crimps on each vertical gore use the same math as the diagonal shifts, where each diagonal fold is angled toward one convergence point.
I recently posted photos of several large-scale origami pieces I folded. These pieces incorporate painted diagonal elements, but the folded patterns are not much more complicated than the ones from the series of tutorials I wrote a while back.
The bottom half of this crease pattern is identical to the crease patterns I posted before. Just above the middle, the diagonal lines only go partway past the middle of each gore, and the top section forms a narrower tube. This crease pattern gives something similar to the central part of this model.
Recently I have folded several test pieces and a finished model incorporating a diagonal shift element. Here are several crease patterns showing how that element works, along with some notes and folding hints below:
One of the biggest challenges in designing these forms is figuring out how far apart the two sine curves need to be. I wrote an Excel spreadsheet to automatically calculate the correct distance based on the angles and distances in the crease pattern.
Another great thing about crease patterns is that it is always possible to two-color them. If you cannot color in a crease pattern without the same color touching itself, there is an error in the crease pattern; it is a nice way of checking whether or not you have done it correctly.
I used the two-colorability here to overlay two different textures over the crease pattern. Both are actually pictures I took of paper. One has a focal point in the center and the other goes upwards towards a horizon line. If you change your focus and swap the figure-ground of the piece, you can see these altering perspectives. I like that it has these two additional views in addition to viewing the piece as a whole. (3 in 1!)
Usually, origami-based morphing structures are designed on the premise of 'rigid folding', i.e. the facets and fold lines of origami can be replaced with rigid panels and ideal hinges, respectively. From a structural mechanics viewpoint, some rigid-foldable origami models are overconstrained and have negative degrees of freedom (d.f.). In these cases, the singularity in crease patterns guarantees their rigid foldability. This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by 'holes' such that the systems become a 1-d.f. mechanism. These perforated origami models can be folded and unfolded similar to rigid-foldable (without misalignment) models because of their d.f. focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.
To promote the progressive collapse of thin-walled vehicle structures and improve their energy-absorbing capabilities, designers allocate collapse initiators such as holes, grooves, humps, and creases. The use of some traditional origami patterns in pre-folded tubes has been particularly effective in this task. However, selecting the optimal origami pattern is a complex multidimensional combinatorial problem. This paper introduces a new origami pattern that triggers an extensional progressive collapse mode in a wide range of thin-walled tubes with a square cross-section. The parameters of the proposed pattern are optimized using a multi-objective Bayesian optimization algorithm to minimize the peak crushing force and maximize the mean crushing force. The crash simulations are supported by the commercial finite element solver Radioss. The optimized pre-folded origami structure depicts extensional progressive collapse under axial loads. Compared to alternative designs, results demonstrate significant improvement in crashworthiness indicators.
Hi BVR
I saw these videos, but none of these mentioned how to create yoshimura origami. I Completly followed the instructions, but for some unknown reason the pattern wont fold as yoshimura mountains and valleys.
How can I mange the direction of foldings? because the solver rolls the crease in wrong direction and I cannot define the axis in grasshopper? and also fold it not create a cylinder. if someone know how its done please inform me.
The exploration below involves using goran pleats and heavy modification. I do not always start with a standard solid polygon. The pleating is deconstructed and the edges expanded to create organic shapes. The first paper is some Italian paper that has a lovely memory to it and the second is a sheet of oiled lotka, which has a lovely pattern and was a pleasure to work with, although has less tension in the finished product.
At the Symposium on Computational Geometry in July, Demaine and Tomohiro Tachi of the University of Tokyo will announce the completion of a quest that began with that 1999 paper: a universal algorithm for folding origami shapes that guarantees a minimum number of seams.
Crease design is crucial to the function and application scope of origami projects, yet for the Yoshimura origami pattern, the connection between origami two-dimensional (2D) creases and three-dimensional (3D) forms has not been established, which greatly limits the research and application of origami structures. In this paper, a crease design theory based on the Yoshimura origami pattern is proposed to create 3D foldable origami structures. Afterwards, the flat origami folding process is described, and the corresponding end trajectory equations are derived from the crease chain folding analysis performed on the element block and the expansion block. Next, the positional and angular constraint equations for single-variable, double-variable, and triple-variable foldable forms with only element blocks are systematically discussed. Finally, a detailed folding simulation analysis is performed based on the positional and angular constraint equations, and the foldable form family diagrams with the corresponding angular eigenvalue intersection curve constraints are summarized. This work provides an effective theory for the design of origami creases and provides extensive guidance for the study of Yoshimura-based tubular origami engineering structures.
Origami-inspired engineering design is increasingly used in the development of self-folding structures. The majority of existing self-folding structures either use a bespoke crease pattern to form a single structure, or a universal crease pattern capable of forming numerous structures with multiple folding steps. This paper presents a new approach whereby multiple distinct, rigid-foldable crease patterns are superimposed in the same sheet such that kinematic independence and 1-DOF mobility of each individual pattern is preserved. This is enabled by the cross-crease vertex, a special configuration consisting of two pairs of collinear crease lines, which is proven here by means of a kinematic analysis to contain two independent 1-DOF rigid-foldable states. This enables many new origami-inspired engineering design possibilities, with two explored in depth: the compact folding of non-flat-foldable structures and sequent folding origami that can transform between multiple states without unfolding.
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