Construction and deformation of P-hedra using control polylines

TL;DR

This paper explores P-hedra, a flexible surface class controlled by three polylines, enabling shape manipulation and deformation analysis for design and computational purposes.

Contribution

It introduces an intuitive control method for P-hedra, enabling efficient shape deformation computation and analysis of their geometric properties.

Findings

P-hedra can be constructed from three control polylines.

The method allows for efficient computation of isometric deformations.

Various geometric properties like flexion limits and developability are discussed.

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.