We present a general framework for a higher-order spline level-set (HLS) method and apply this to smooth surface constructions. 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 solve 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. We provide two demonstrative smooth surface construction examples of our HLS method. The first is the construction of a smooth surface model (an implicit solvation interface) of bio-molecules in solvent, given their individual atomic coordinates and solvated radii. The second is the smooth surface reconstruction from a cloud of points generated from a 3D surface scanner.
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