Box splines provide smooth spline spaces as shifts of a single generating function on a lattice and so generalize tensor-product splines. Their elegant theory is laid out in classical papers and a summarizing book. This compendium aims to succinctly but exhaustively survey symmetric low-degree box splines with special focus on two and three variables. Tables contrast the lattices, supports, analytic and reconstruction properties, and list available implementations and code.

翻译：箱样条通过在格点上平移单个生成函数来提供光滑样条空间，从而推广了张量积样条。其优雅理论已在经典论文及总结性专著中阐明。本简编旨在简明但全面地综述对称低次箱样条，特别聚焦于二元和三元情形。表格对比了格点结构、支撑域、解析性质与重建特性，并列出了现有实现方法与代码资源。