TY - JOUR
AB - 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.
AU - Natarajan, Vijay
AU - Herbert Edelsbrunner
ID - 3987
IS - 5
JF - IEEE Transactions on Visualization and Computer Graphics
TI - Simplification of three-dimensional density maps
VL - 10
ER -
TY - CONF
AB - 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.
AU - Choi, Vicky
AU - Agarwal, Pankaj K
AU - Herbert Edelsbrunner
AU - Rudolph, Johannes
ID - 3988
TI - Local search heuristic for rigid protein docking
VL - 3240
ER -
TY - CONF
AB - 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.
AU - Herbert Edelsbrunner
AU - Harer, John
AU - Natarajan, Vijay
AU - Pascucci, Valerio
ID - 3989
TI - Local and global comparison of continuous functions
ER -
TY - JOUR
AB - 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.
AU - Agarwal, Pankaj K
AU - Herbert Edelsbrunner
AU - Wang, Yusu
ID - 3990
IS - 1
JF - Discrete & Computational Geometry
TI - Computing the writhing number of a polygonal knot
VL - 32
ER -
TY - CHAP
AU - Harold Vladar
AU - Cipriani, Roberto
AU - Scharifker, Benjamin
AU - Bubis, Jose
ED - Hanslmeier,A.
ED - Kempe,S.
ED - Seckbach,J.
ID - 4230
T2 - Life in the Universe From the Miller Experiment to the Search for Life on Other Worlds
TI - A mechanism for the prebiotic emergence of proteins
ER -