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We introduce an improved version of the discrete bijective reflection proposed in [Andres 2019] and we show that this new reflection is almost always identical to the reflection based on the quasi shear rotation for integer centers. The difference between the two reflections is restricted to a discrete set of angles of the form \(\arctan (k+\frac{1}{2})\) , where \(k\in \mathbb {N}\) . The quasi shear rotation (QSR) based reflection yields among the lowest errors compared to the continuous reflection. Our improved pivot reflection (IPR) provides the same error in most cases and is easier to compute. Our new approach therefore offers a promising direction for the computation of nD rotations.

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A Discrete Bijective Reflection with Near-Equivalence to Shear Rotation Based Reflection

  • 会议论文

  • 发表日期：

    2026年

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  • Gaëlle Largeteau-Skapin,
  • Lidija Čomić,
  • Rita Zrour,
  • Eric Andres

摘要

We introduce an improved version of the discrete bijective reflection proposed in [Andres 2019] and we show that this new reflection is almost always identical to the reflection based on the quasi shear rotation for integer centers. The difference between the two reflections is restricted to a discrete set of angles of the form \(\arctan (k+\frac{1}{2})\) , where \(k\in \mathbb {N}\) . The quasi shear rotation (QSR) based reflection yields among the lowest errors compared to the continuous reflection. Our improved pivot reflection (IPR) provides the same error in most cases and is easier to compute. Our new approach therefore offers a promising direction for the computation of nD rotations.