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arXiv · 2603.06420

On the Rigid-Ruling Folding of Curved Creases: Conjugate-Net Preserving Isometric Deformations of Semi-Discrete Globally Developable Conjugate-Nets

Klara Mundilova
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Abstract

In this paper, we investigate rigid-ruling folding motions of crease-rule patterns, that is, conjugacy-preserving isometries of developable semi-discrete conjugate nets. We derive two conditions for the rigid-ruling foldability of pairs of curves and consider two applications. First, we introduce computations that enable the sequential construction of rigid-ruling foldable crease-rule patterns. Second, we examine combinations of planar and constant fold-angle creases. In particular, we show that constant fold-angle creases are only compatible with other constant fold-angle creases, and we provide a characterization of rigid-ruling foldable combinations of planar and constant fold-angle creases.

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Klara Mundilova. 2026-03-06. On the Rigid-Ruling Folding of Curved Creases: Conjugate-Net Preserving Isometric Deformations of Semi-Discrete Globally Developable Conjugate-Nets. https://arxiv.org/abs/2603.06420

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