Nawratil, G. (2024). From Axial C-Hedra to General P-Nets. In J. Lenarcic & M. Husty (Eds.), Advances in Robot Kinematics 2024 (pp. 340–347). https://doi.org/10.1007/978-3-031-64057-5_39
We give a full classification of continuous flexible discrete axial cone-nets, which are called axial C-hedra. The obtained result can also be used to construct their semi-discrete analogs. Moreover, we identify a novel subclass within the determined class of (semi-)discrete axial cone-nets, whose members are named axial P-nets as they fulfill the proportion (P) of the intercept theorem. Known special cases of these axial P-nets are the smooth and discrete conic crease patterns with reflecting rule lines. By using a parallelism operation one can even generalize axial P-nets. The resulting general P-nets constitute a rich novel class of continuous flexible (semi-)discrete surfaces, which allow direct access to their spatial shapes by three control polylines. This intuitive method makes them suitable for transformable design tasks using interactive tools.
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Project title:
Advanced Computational Design: F 77 (FWF - Österr. Wissenschaftsfonds)