Miura-ori · Yoshimura · Kresling · Animated folding · Crease highlights
Rigid origami studies how flat sheets can be folded along crease lines so that the flat panels between creases remain rigid (do not bend). This simulation implements four classic patterns:
Miura-ori was used on Japan's Space Flyer Unit (1995) to deploy a solar array from a compact folded state. The James Webb Space Telescope's sun-shield uses origami-inspired folding to pack a tennis-court-sized sheet into a rocket fairing. Medical stents, foldable electronics and even airbag packaging all use origami geometry. Robert Lang, a pioneer of computational origami, uses tree-theory and circle packing to design incredibly complex single-sheet figures.
This simulation visualises rigid origami, in which a flat sheet folds along crease lines while the panels between creases stay rigid. It builds four classic tessellations and bases — Miura-ori, Yoshimura, Kresling and the waterbomb base — as collections of triangular and quadrilateral facets. Each facet's vertices are lifted out of the plane by a fold angle that scales with sin(foldPct), then rotated and projected onto the 2D canvas using a simple perspective transform.
Use the Pattern dropdown to switch between the four crease designs, and the Fold angle slider (0–100%) to animate from flat to fully collapsed. Grid size (3–12) sets the number of tiles, while Rotation and mouse-dragging tilt the view. Toggles control crease lines, face shading and auto-fold. These space-saving folds inspire deployable solar arrays, packable telescope shields and self-folding robots.
What is rigid origami?
Rigid origami studies how a sheet can fold along straight crease lines while the flat panels between those creases remain perfectly stiff and never bend. Only the creases act as hinges. This is the model used for engineering folds, since real panels of metal, plastic or solar cells cannot curve.
What are the four patterns shown?
The simulator offers Miura-ori, a tessellation of parallelograms; Yoshimura, a diamond pattern from buckling cylinders; Kresling, a triangulated cylinder that twists as it collapses; and the waterbomb base, a radial mountain-and-valley fold. You select between them with the Pattern dropdown.
What does the fold angle slider do?
The Fold angle slider runs from 0 to 100%, representing the sheet going from flat to fully folded. Internally this value is converted to an angle and the out-of-plane height of each crease scales with its sine, so the structure deepens smoothly as you raise the slider.
Miura-ori, devised by Koryo Miura, folds and unfolds with a single degree of freedom, so pulling two opposite corners deploys the whole sheet at once. This made it ideal for unfurling compact solar panels in space, and it appears in maps, packaging and metamaterials.
When crease lines are enabled, the simulation colours mountain folds in red and valley folds in blue. A mountain crease points the paper up toward you, a valley crease folds it away. Alternating mountain and valley creases is what lets these patterns collapse flat.
The Kresling pattern wraps triangular facets around a cylinder, and each layer is offset by a twist angle. As the fold increases, the cylinder both shortens and rotates helically, which is why it is popular for deployable masts, antennas and twisting soft-robot actuators.
It is a clear geometric approximation rather than a rigorous kinematic solver. The facet shapes and the mountain/valley layout match each real pattern, and the fold motion is plausible, but the vertex heights are driven by simple sine terms instead of solving the exact rigid-fold constraints, so panel rigidity is not strictly enforced.
The Grid size slider sets how many tiles make up the pattern, from 3 to 12 per side. More tiles produce a finer tessellation with many small panels; fewer tiles give a coarse, easy-to-read structure. The Stats panel reports the resulting panel count.
When a thin-walled tube is squeezed lengthwise, it cannot stay perfectly round and instead buckles into a regular diamond network of folds. That natural buckling shape is the Yoshimura pattern, which is why it is seen in crushed cans, drinking straws and collapsing structural shells.
Folding geometry packs large structures into small volumes. The James Webb Space Telescope's sunshield, deployable solar arrays, expandable medical stents, foldable electronics and airbag packing all draw on origami principles, and computational designers such as Robert Lang use circle packing to fold complex single-sheet figures.