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We show that if a singly-periodic bar-joint framework in the Euclidean plane is derived from a pointed pseudotriangulation on the flexible flat cylinder, then it has a one-parameter deformation, which is expansive, i.e. the motion does not decrease the distance between any pair of joints. For the proof, we consider singly-periodic versions of Maxwell-Cremona liftings and adapt the proof of C. Borcea and I. Streinu for the doubly-periodic version of this statement.

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Singly-periodic Pointed Pseudotriangulations Have an Expansive Motion

  • 会议论文

  • 发表日期：

    2026年

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  • Jack Esson,
  • Eleftherios Kastis,
  • Bernd Schulze

摘要

We show that if a singly-periodic bar-joint framework in the Euclidean plane is derived from a pointed pseudotriangulation on the flexible flat cylinder, then it has a one-parameter deformation, which is expansive, i.e. the motion does not decrease the distance between any pair of joints. For the proof, we consider singly-periodic versions of Maxwell-Cremona liftings and adapt the proof of C. Borcea and I. Streinu for the doubly-periodic version of this statement.