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ORIGAMI SIMULATOR
webxmaza cc hot This app allows you to simulate how any origami crease pattern will fold. It may look a little different from what you typically think of as "origami" - rather than folding paper in a set of sequential steps, this simulation attempts to fold every crease simultaneously. It does this by iteratively solving for small displacements in the geometry of an initially flat sheet due to forces exerted by creases. You can read more about it in our paper:

Fast, Interactive Origami Simulation using GPU Computation by Amanda Ghassaei, Erik Demaine, and Neil Gershenfeld (7OSME)

All simulation methods were written from scratch and are executed in parallel in several GPU fragment shaders for fast performance. The solver extends work from the following sources:

Origami Folding: A Structural Engineering Approach by Mark Schenk and Simon D. Guest
Freeform Variations of Origami by Tomohiro Tachi

This app also uses the methods described in Simple Simulation of Curved Folds Based on Ruling-aware Triangulation to import curved crease patterns and pre-process them in a way that realistically simulates the bending between the creases. webxmaza cc hot

Originally built by Amanda Ghassaei as a final project for Geometric Folding Algorithms. Other contributors include Sasaki Kosuke, Erik Demaine, and others. Code available on Github. If you have interesting crease patterns that would make good demo files, please send them to me (Amanda) so I can add them to the Examples menu. My email address is on my website. Thanks!
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Instructions:

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Slide the Fold Percent slider to control the degree of folding of the pattern (100% is fully folded, 0% is unfolded, and -100% is fully folded with the opposite mountain/valley assignments).
Drag to rotate the model, scroll to zoom.
Import other patterns under the Examples menu.
Upload your own crease patterns in SVG or FOLD formats, following these instructions.
Export FOLD files or 3D models ( STL or OBJ ) of the folded state of your design ( File > Save Simulation as... ).

Visualize the internal strain of the origami as it folds using the Strain Visualization in the left menu of the Advanced Options.

If you are working from a computer connected to a VR headset and hand controllers, follow these instructions to use this app in an interactive virtual reality mode. (sorry I think this may be deprecated now!)

External Libraries:

All rendering and 3D interaction done with three.js
svgpath and path-data-polyfill helps with SVG path parsing
FOLD is used as the internal data structure, methods from the FOLD API used for SVG parsing
Arbitrary polygonal faces of imported geometry are triangulated using the Earcut Library and cdt2d
numeric.js for linear algebra operations
GIF and WebM video export uses CCapture

You can find additional information in our 7OSME paper and project website. If you have feedback about features you want to see in this app, please see this thread.

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SIMULATION SETTINGS

This app uses a compliant dynamic simulation method to solve for the geometry of an origami pattern at a given fold angle. The simulation sets up several types of constraints: distance constraints prevent the sheet from stretching or compressing, face constraints prevent the sheet from shearing, and angular constraints fold or flatten the sheet. Each of these constraints is weighted by a stiffness - the stiffer the constraint, the better it is enforced in the simulation.

Axial Stiffness is the stiffness of the distance constraints. Increasing axial stiffness will decrease the stretching/compression (strain) in the simulation, but it will also slow down the solver. Face Stiffness is the stiffness of the face constraints, which help the axial constraints prevent deformation of the sheet's surface between the creases.

Fold and facet stiffnesses correspond to two types of angular constraints. Fold Stiffness is the stiffness of the mountain and valley creases in the origami pattern. Facet Stiffness is the stiffness of the triangulated faces between creases in the pattern. Increasing facet stiffness causes the faces between creases to stay very flat as the origami is folded. As facet stiffness becomes very high, this simulation approaches a rigid origami simulation, and models the behavior of a rigid material (such as metal) when folded.

Internally, constraint stiffnesses are scaled by the length of the edge associated with that constraint to determine its geometric stiffness. For Axial constaints, stiffness is divided by length and for angular constraints, stiffness is multiplied by length.

Since this is a dynamic simulation, vertices of the origami move with some notion of acceleration and velocity. In order to keep the system stable and help it converge to a static solution, damping is applied to slow the motion of the vertices. The Damping slider allows you to control the amount of damping present in the simulation. Decreasing damping makes the simulation more "springy". It may be useful to temporarily turn down damping to help the simulation more quickly converge towards its static solution - especially for patterns that take a long time to curl.

A Numerical Integration technique is used to integrate acceleration into velocity and position for each time step of the simulation. Different integration techniques have different associated computational cost, error, and stability. This app allows you to choose between two different integration techniques: Euler Integration is the simplest type of numerical integration (first order) with large associated error, and Verlet Integration is a second order integration technique with lower error and better stability than Euler.