Programming curvature using origami tessellations.

Area of Science:

• Computational geometry
• Materials science
• Origami engineering

Background:

• Origami principles govern folding flat sheets into structures but lack methods for designing patterns for specific target shapes.
• Existing origami design methods do not prescribe how to generate patterns for arbitrary surfaces.

Purpose of the Study:

• To develop a computational method for designing origami patterns that approximate given target surfaces.
• To assess the energetic cost and folding effort associated with the designed origami structures.

Main Methods:

• Utilized scale-independent geometric constructions and constrained optimization algorithms.
• Applied these methods to derive spatially modulated patterns for surfaces of constant and varying curvature.
• Quantified the energetic barrier between flat and folded states to assess folding difficulty.

Main Results:

• Demonstrated the feasibility of designing origami patterns for target surfaces using computational methods.
• Paper models confirmed the practical realization of calculated patterns.
• Characterized the trade-off between pattern accuracy and the effort required for folding.

Conclusions:

• The developed approach enables the tailoring of origami patterns to drape complex surfaces irrespective of scale.
• Provides a quantitative measure of the energetic and material costs associated with creating complex folded structures.