We present a general framework for a higher-order spline level-set (HLS) method and apply this to biomolecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formulation of geometric partial differential equation, and provide an efficient approach to solving this partial differential equation using a C2 spline basis. We also present a fast cubic spline interpolation algorithm based on convolution and the Z-transform, which exploits the local relationship of interpolatory cubic spline coefficients with respect to given function data values. One example of our HLS method is demonstrated, which is the construction of biomolecule surfaces (an implicit solvation interface) with their individual atomic coordinates and solvated radii as prerequisites.

中文翻译：

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高阶水平集方法及其在生物分子表面构建中的应用

我们提出了高阶样条水平集（HLS）方法的一般框架，并将其应用于生物分子表面构建。从一阶能量泛函开始，我们获得了几何偏微分方程的一般水平集公式，并提供了一种使用 C2 样条基求解该偏微分方程的有效方法。我们还提出了一种基于卷积和 Z 变换的快速三次样条插值算法，该算法利用了插值三次样条系数相对于给定函数数据值的局部关系。演示了我们的 HLS 方法的一个例子，即构建生物分子表面（一种隐式溶剂化界面），以其各自的原子坐标和溶剂化半径作为先决条件。