Box Pleating

A Python library for creating and validating box-pleating origami patterns.

Installation

pip install box-pleating

Quick Start

from box_pleating import BoxPleatingPattern, Point, CreaseType
from box_pleating.fold import FoldConverter

# Create a new pattern with a 10x10 grid
pattern = BoxPleatingPattern(grid_size=10)

# Add creases
pattern.add_crease(
    Point(0, 0),
    Point(5, 5),
    CreaseType.MOUNTAIN
)

# Check if pattern is valid and flat-foldable
is_valid, report = pattern.is_valid_pattern()

# Convert to FOLD format
converter = FoldConverter()
fold_data = converter.to_fold(pattern)

Features

Box-Pleating Pattern Creation

• Create patterns on a customizable grid
• Add mountain, valley and border folds
• Automatic intersection and overlap handling
• Grid-based validation ensuring 45° and 90° angles (No Pythagorean Stretches, unfortunately)

Pattern Validation

• Local flat-foldability checking using:
  • Kawasaki's theorem (alternating angles sum to 180°)
  • Maekawa's theorem (mountain/valley crease difference is 2)
• Crease intersection detection
• Grid alignment verification, kind of

FOLD Format Support

• Import from FOLD format
• Export to FOLD format
• Automatic grid size optimization, kind of
• Redundant vertex removal

Coming Soon (Maybe)

• Crease removal/changing

Detailed Usage

Creating a Pattern

from box_pleating import BoxPleatingPattern, Point, CreaseType

# Create a pattern with a 10x10 grid
pattern = BoxPleatingPattern(grid_size=10)

# Add a mountain fold
pattern.add_crease(
    Point(0, 0),  # Start point
    Point(5, 5),  # End point
    CreaseType.MOUNTAIN
)

# Add a valley fold
pattern.add_crease(
    Point(5, 5),
    Point(10, 5),
    CreaseType.VALLEY
)

Converting FOLD Format

from box_pleating.fold import FoldConverter

converter = FoldConverter()

# Load from FOLD file
pattern = converter.load_fold("input.fold")

# Save to FOLD file
converter.save_fold(pattern, "output.fold")

Validating Patterns

# Check flat-foldability
is_foldable, violations = pattern.is_flat_foldable()
if not is_foldable:
    print("Violations found:")
    for violation in violations:
        print(f"Vertex at ({violation['vertex']['x']}, {violation['vertex']['y']})")
        print(f"Maekawa satisfied: {violation['maekawa_satisfied']}")
        print(f"Kawasaki satisfied: {violation['kawasaki_satisfied']}")

# Check overall pattern validity
is_valid, report = pattern.is_valid_pattern()

Pattern Cleanup

# Remove redundant vertices (vertices where parallel creases of the same type meet)
pattern.remove_redundant_vertices()

Contributing

Contributions are welcome.

License

This project is licensed under the MIT License - see the LICENSE file for details.

References

1. FOLD file documentation
2. Toshikazu Kawasaki's Theorem on flat-foldability
3. Jun Maekawa's Theorem on mountain-valley assignments
4. My Graph Theory notes

Authors

• Coleman Lai

Acknowledgments

• The FOLD file project contributors
• Claude AI by Anthropic (for debugging/generation of some code)