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arXiv · 2512.18869

Construction and deformation of P-hedra using control polylines

Georg Nawratil
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Abstract

In the 19th International Symposium on Advances in Robot Kinematics the author introduced a novel class of continuous flexible discrete surfaces and mentioned that these so-called P-hedra (or P-nets) allow direct access to their spatial shapes by three control polylines. In this follow-up paper we study this intuitive method, which makes these flexible planar quad surfaces suitable for transformable design tasks by means of interactive tools. The construction of P-hedra from the control polylines can also be used for an efficient algorithmic computation of their isometric deformations. In addition we discuss flexion limits, bifurcation configurations, developable/flat-foldable pattern and tubular P-hedra.

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Georg Nawratil. 2025-12-21. Construction and deformation of P-hedra using control polylines. https://arxiv.org/abs/2512.18869

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