@article{3986,
abstract = {The motion of a biomolecule greatly depends on the engulfing solution, which is mostly water. Instead of representing individual water molecules, it is desirable to develop implicit solvent models that nevertheless accurately represent the contribution of the solvent interaction to the motion. In such models, hydrophobicity is expressed as a weighted sum of atomic surface areas. The derivatives of these weighted areas contribute to the force that drives the motion. In this paper we give formulas for the weighted and unweighted area derivatives of a molecule modeled as a space-filling diagram made up of balls in motion. Other than the radii and the centers of the balls, the formulas are given in terms of the sizes of circular arcs of the boundary and edges of the power diagram. We also give inclusion-exclusion formulas for these sizes.},
author = {Bryant, Robert and Herbert Edelsbrunner and Koehl, Patrice and Levitt, Michael},
journal = {Discrete & Computational Geometry},
number = {3},
pages = {293 -- 308},
publisher = {Springer},
title = {{The area derivative of a space-filling diagram}},
doi = {10.1007/s00454-004-1099-1},
volume = {32},
year = {2004},
}
@article{3987,
abstract = {We consider scientific data sets that describe density functions over three-dimensional geometric domains. Such data sets are often large and coarsened representations are needed for visualization and analysis. Assuming a tetrahedral mesh representation, we construct such representations with a simplification algorithm that combines three goals: the approximation of the function, the preservation of the mesh topology, and the improvement of the mesh quality. The third goal is achieved with a novel extension of the well-known quadric error metric. We perform a number of computational experiments to understand the effect of mesh quality improvement on the density map approximation. In addition, we study the effect of geometric simplification on the topological features of the function by monitoring its critical points.},
author = {Natarajan, Vijay and Herbert Edelsbrunner},
journal = {IEEE Transactions on Visualization and Computer Graphics},
number = {5},
pages = {587 -- 597},
publisher = {IEEE},
title = {{Simplification of three-dimensional density maps}},
doi = {10.1109/TVCG.2004.32},
volume = {10},
year = {2004},
}
@inproceedings{3988,
abstract = {We give an algorithm that locally improves the fit between two proteins modeled as space-filling diagrams. The algorithm defines the fit in purely geometric terms and improves by applying a rigid motion to one of the two proteins. Our implementation of the algorithm takes between three and ten seconds and converges with high likelihood to the correct docked configuration, provided it starts at a position away from the correct one by at most 18 degrees of rotation and at most 3.0Angstrom of translation. The speed and convergence radius make this an attractive algorithm to use in combination with a coarse sampling of the six-dimensional space of rigid motions.},
author = {Choi, Vicky and Agarwal, Pankaj K and Herbert Edelsbrunner and Rudolph, Johannes},
pages = {218 -- 229},
publisher = {Springer},
title = {{Local search heuristic for rigid protein docking}},
doi = {10.1007/978-3-540-30219-3_19},
volume = {3240},
year = {2004},
}
@inproceedings{3989,
abstract = {We introduce local and global comparison measures for a collection of k less than or equal to d real-valued smooth functions on a common d-dimensional Riemannian manifold. For k = d = 2 we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for which they ace easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets.},
author = {Herbert Edelsbrunner and Harer, John and Natarajan, Vijay and Pascucci, Valerio},
pages = {275 -- 280},
publisher = {IEEE},
title = {{Local and global comparison of continuous functions}},
doi = {10.1109/VISUAL.2004.68},
year = {2004},
}
@article{3990,
abstract = {The writhing number measures the global geometry of a closed space curve or knot. We show that this measure is related to the average winding number of its Gauss map. Using this relationship, we give an algorithm for computing the writhing number for a polygonal knot with n edges in time roughly proportional to n(1.6). We also implement a different, simple algorithm and provide experimental evidence for its practical efficiency.},
author = {Agarwal, Pankaj K and Herbert Edelsbrunner and Wang, Yusu},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {37 -- 53},
publisher = {Springer},
title = {{Computing the writhing number of a polygonal knot}},
doi = {10.1007/s00454-004-2864-x},
volume = {32},
year = {2004},
}