Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Multigrid solution of the Poisson-Boltzmann equation
Journal of Computational Chemistry
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
NURBS based B-rep models for macromolecules and their properties
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
A PDE-based fast local level set method
Journal of Computational Physics
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Dynamic maintenance and visualization of molecular surfaces
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
TexMol: Interactive Visual Exploration of Large Flexible Multi-Component Molecular Complexes
VIS '04 Proceedings of the conference on Visualization '04
Quality meshing of implicit solvation models of biomolecular structures
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
Hierarchical molecular interfaces and solvation electrostatics
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
SIAM Journal on Scientific Computing
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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.