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.

翻译：在第十九届机器人运动学进展国际研讨会上，作者提出了一类新型的连续柔性离散曲面，并指出这类被称为P-hedron（或P-net）的曲面可通过三条控制多边形直接调控其空间形态。在本后续研究中，我们深入探讨了这一直观方法，该方法借助交互工具使这类柔性平面四边形曲面适用于可变形设计任务。基于控制多边形构建P-hedron的方法同样可用于其等距形变的高效算法计算。此外，我们讨论了弯曲极限、分岔构型、可展/可平折模式以及管状P-hedron等特性。