Exponential polynomials are essential in subdivision for the reconstruction of specific families of curves and surfaces, such as conic sections and quadric surfaces. It is well known that if a linear subdivision scheme is able to reproduce a certain space of exponential polynomials, then it must be level-dependent, with rules depending on the frequencies (and eventual multiplicities) defining the considered space. This work discusses a general strategy that exploits annihilating operators to locally detect those frequencies directly from the given data and therefore to choose the correct subdivision rule to be applied. This is intended as a first step towards the construction of self-adapting subdivision schemes able to locally reproduce exponential polynomials belonging to different spaces. An application of the proposed strategy is shown explicitly on an example involving the classical butterfly interpolatory scheme. This particular example is the generalization of what has been done for the univariate case in Donat and López-Ureña (2019), which inspired this work.

指数多项式在细分中对于重建特定的曲线和曲面族（例如圆锥形截面和二次曲面）至关重要。众所周知，如果线性细分方案能够再现一定数量的指数多项式空间，则它必须与级别相关，并且规则取决于定义所考虑空间的频率（以及最终的多重性）。这项工作讨论了一种通用策略，该策略利用an灭性运算符直接从给定数据中本地检测那些频率，从而选择要应用的正确细分规则。这是迈向构建能够局部复制属于不同空间的指数多项式的自适应细分方案的第一步。在涉及经典蝴蝶插值方案的示例中明确显示了所提出策略的应用。这个特定的例子是对Donat和López-Ureña（2019）中单变量案例所做的概括，这激发了这项工作。