论文标题
快速立方样条插值
Fast Cubic Spline Interpolation
论文作者
论文摘要
数字食谱系列书籍是一个有用的资源，但是它们所包含的所有算法不能在开源项目中使用。在本文中，我们开发了用于立方样条插值的两种算法的替代方法，显示了我们尽可能多的工作以进行复制或评论。将新算法的输出与旧算法进行比较，并且在浮点精度施加的限制内发现没有什么不同。所有这些算法的基准，以及在某些情况下可能会更快运行的变体。通常，当在功能丰富的英特尔处理器上具有很少的控制点的插值曲线时，所有这些算法的执行时间大致相同。随着控制点的数量增加或删除处理器功能，新算法的始终始终比旧算法更快。探索了该概括以创建实施指南的例外，例如何时期望除法比乘法更快。
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline interpolation, showing as much of our work as possible to allow for replication or criticsm. The output of the new algorithms is compared to the old, and found to be no different within the limits imposed by floating-point precision. Benchmarks of all these algorithms, plus variations which may run faster in certain instances, are performed. In general, all these algorithms have approximately the same execution time when interpolating curves with few control points on feature-rich Intel processors; as the number of control points increases or processor features are removed, the new algorithms become consistently faster than the old. Exceptions to that generalization are explored to create implementation guidelines, such as when to expect division to be faster than multiplication.
