Smooth piecewise quadric surfaces
Mathematical methods in computer aided geometric design
Modeling arbitrary smooth objects with algebraic surfaces
Modeling arbitrary smooth objects with algebraic surfaces
Cubicoids: Modeling and visualization
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG)
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
Hierarchical multiresolution reconstruction of shell surfaces
Computer Aided Geometric Design
TexMol: Interactive Visual Exploration of Large Flexible Multi-Component Molecular Complexes
VIS '04 Proceedings of the conference on Visualization '04
Guaranteed Quality Triangulation of Molecular Skin Surfaces
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
Kernel modeling for molecular surfaces using a uniform solution
Computer-Aided Design
Topologies of surfaces on molecules and their computation in O(n) time
Computer-Aided Design
Fast Molecular Solvation Energetics and Forces Computation
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Accelerated visualization of dynamic molecular surfaces
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
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In this paper, we describe a new method to generate a smooth algebraic spline (AS) model approximation of the molecular surface (MS), based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold Ps covering the PDB structure, and then generates piecewise polynomial Bernstein-Bezier (BB) spline function approximation F within Ps, which are nearly C1 everywhere. Approximation error and point sampling convergence bounds are also computed. An implicit AS model of the MS which is free of singularity, is extracted as the zero contours of F. Furthermore, we generate a polynomial parametrization of the implicit MS, which allows for an efficient point sampling on the MS, and thereby simplifies the accurate estimation of integrals needed for electrostatic solvation energy calculations.