What I want to improve next
Handle more general shapes, reduce fold count in real-world constraints, and make the app easier for other people to experiment with.
Studies • 3-year independent project
My Pathways
This page is a written overview of what I learned, built, and tested while exploring the mathematics of the “fold-and-cut” problem. I started from paper experiments, moved to CAD-based precision, and eventually implemented an app that generates crease patterns.
At a glance
Theme: fold-and-cut / one straight cut • Geometry + algorithms + implementation.
Computational geometry
Graph thinking
SVG
Python
UI prototyping
Highlights
The project is one story told from three angles: the problem itself, what I built, and what changed in how I think.
The question
Given a polygon (or a set of polygons), can a single straight cut remove it exactly after folding the paper?
The output
Crease patterns (SVG) that I can test with real paper — and a small app that generates them from polygon data.
The learning
Turning theory into something runnable taught me about edge cases, numerical stability, and designing tools people can actually use.
Timeline
A simple year-by-year map. Each year had a different “main skill” I wanted to gain.
Year 1
Theory & paper experiments
- Learned the definition of the fold-and-cut problem.
- Reproduced small examples by hand to understand why each fold exists.
- Started drawing crease patterns for letters and symbols.
Year 2
Precision with CAD
- Used CAD to place crease lines accurately and compare constructions.
- Connected “paper drawings” with algorithmic ideas (skeleton-like structure).
- Noticed patterns become cleaner when based on angle bisectors / structure.
Year 3
Implementation (Origami App)
- Represented polygons/segments/vertices as objects (OOP).
- Generated crease patterns as SVG output.
- Built a small GUI so users can draw shapes and run the pipeline.
Tools & skills I used
A compact list, grouped the way I think about building projects.
Math / CS
Geometry
Angle bisectors
Graphs
Algorithm design
Edge cases
Implementation
Python
SVG
Data modeling
GUI prototyping
Readable code