Kami

🦢 A (very) W.I.P. library for computational origami.

Description

After studying computational origami for the last 6-8 months and making a variety of rather disjoint projects, I am working towards creating a unified codebase for future origami work. This is very much a work-in-progress, and it will be a few months before the library is even remotely usable. It's my hope that this repo becomes a sort of "diary" / "scratch pad" for future studies: I will add more robustness and functionality as I continue to learn more about origami design, kinematics, and computational geometry. Pretty much all of the ideas here are taken from Robert Lang's books, Twists, Tilings, and Tessellations and/or Origami Design Secrets, so I claim no ownership over any of this knowledge.

Initially, I set out to build this library using geometric (or Clifford) algebra: a unified mathematical framework that includes "traditional" linear algebra, quaternions, complex numbers, and many other mathematical phenomena, all in one "package." This is still a goal of mine, but for now, I've decided to focus on some of the other higher-level functionality, deferring to the already wonderful nalgebra library for basic mathematical operations.

Because the Rust GUI story isn't great yet (although several libraries, like Iced and Druid are getting there), I've opted to create visualizations using the browser. This pretty straightforward with WASM and the websys crate. Regardless, this library is meant to be used within other projects that have a graphical interface - it isn't a front-end application itself.

In other words, you would use this library internally to build things like:

A crease pattern editor
A tessellation generator
Algorithmic origami designs
Rigid origami simulations

I'm using Rust because of its awesome type / ownership system, tooling, and community 🦀.

Roadmap

Graphs
- Planar graphs
  - Add new vertex (while maintaining planarity)
  - Add new edge (while maintaining planarity)
  - Delete an existing vertex (and all incident edges - optional)
  - Delete an existing edge (and any stray vertices - optional)
  - Determine 2-colorability
  - Graph neural networks (GNNs)?
  - Search (for a particular node, edge, or face)
  - Traversal
    - Grab all reference points (i.e. nodes)
    - Grab all fold vectors (i.e. vectors oriented along each edge of the graph)
    - Grab all interior fold intersections with outward facing, sorted edges emanating from each
    - Grab face boundaries (i.e. CCW sorted edges that form each face)
    - Angle of each fold vector w.r.t. +x-axis
    - Grab all face corner angles
    - Grab all face corner points
    - Construct fold paths
    - Construct fold map (matrix transformations accumulated by traversing a fold path)
- I/O formats
  - Graphviz output format (.dot)
  - .FOLD import / export
  - .oripa import / export
  - .svg import / export
Origami
- Crease
  - Specify assignment
  - Specify fold angle (target, upper bound, lower bound)
- Crease pattern
  - Maintains a (mutable) planar graph
  - Compute the stacking order (Oripa "translucent" preview)
  - Calculate vertex properties
    - Degree
    - Iso / anto
    - Majority type (mountain-like or valley-like)
    - Sector angles
  - Flat-foldability checks
    - Big-little-big-angle theorem (BLBA)
    - Kawasaki-Justin theorem (KJT)
    - Algebraic KJT (AKJT) - same as KJT but with matrices
    - Maekawa-Justin theorem (MJT)
    - Single vertex flat-foldable test (SVFFT) - accumulation of the previous 3 theorems
  - Calculate Justin path (similar to fold map from "Active Origami"?)
  - Apply a sequence of Huzita-Hatori axioms, starting from a blank sheet of "paper"
- Misc.
  - Universal molecule
  - Tree theory
  - Box pleating
  - 22.5 design
Geometry
- Read "Computational Geometry in C"
- Polygons (regular, irregular)
  - Compute area
  - Compute perimeter
  - Compute interior angles
  - Compute exterior angles
  - Apply transforms (rotate, scale, translate, etc.)
  - Calculate incenter, circumradius, etc.
  - Calculate bounding box
  - Degeneracy tests
  - Calculate angle bisectors
  - "Slicing" operations (fracture polygon into one or more sub-polygons)
  - Polygon to polyline conversion
  - Calculate "skeleton" (see ODS)
- Lines (segments, infinite)
- Polylines
  - Add / remove points
  - Resample / refine operations
  - Smoothing operations
  - Calculate length
  - Calculate tangents
- Tilings (Archimedean)
  - Vertex figures
  - Lattice vectors
  - Array of polygons with offsets and rotations
- Algorithms / utilities
  - Triangulate an arbitrary polygon
  - Compute the convex hull of a set of 2D points
  - Circle packing (bindings to Python SciPy (SLSQP) optimization)
  - Intersection routines
    - Line-line
    - Line-polygon
    - Segment-segment
    - Segment-polygon
    - Polygon-polygon
  - Misc.
    - Perpendicular bisector
    - Point-on-segment test
    - Point-on-line test
    - Point adjacency
    - Point sorting
Math
- Vectors (2D and 3D)
- Matrices (primarily 2x3, 3x3, 3x4, and 4x4)
- Linear algebra operations
  - Moore-Penrose pseudo-inverse
  - Inverse
  - Transpose
  - Determinant
- Revisit geometric / Clifford algebra
- Implement HH axioms using geometric algebra

References

Keeping track of interesting articles, ideas, blogs, and books:

mwalczyk / kami

Kami

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