Higher-Order Level-Set Method and Its Application in Biomolecular Surfaces Construction

We present a general framework for a higher-order spline level-set (HLS)method and apply this to biomolecule surfaces construction. Startingfrom a first order energy functional, we obtain a general level setformulation of geometric partial differential equation, and provide anefficient approach to solving this partial differential equation using aC^2 spline basis. We also present a fast cubic spline interpolationalgorithm based on convolution and the Z-transform, which exploits thelocal relationship of interpolatory cubic spline coefficients withrespect to given function data values. One example of our HLS method isdemonstrated, which is the construction of biomolecule surfaces (animplicit solvation interface) with their individual atomic coordinatesand solvated radii as prerequisites.