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94
Morse-Smale Complexes for Piecewise Linear 3-Manifolds
, 2003
"... We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3-dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatori ..."
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Cited by 130 (24 self)
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We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3-dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatorial algorithm for constructing such complexes for piecewise linear data.
On the Definition and the Construction of Pockets in Macromolecules
, 1995
"... The shape of a protein is important for its functions. This includes the location and size of identifiable regions in its complement space. We formally define pockets as regions in the complement with limited accessibility from the outside. Pockets can be efficiently constructed by an algorithm base ..."
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Cited by 103 (26 self)
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The shape of a protein is important for its functions. This includes the location and size of identifiable regions in its complement space. We formally define pockets as regions in the complement with limited accessibility from the outside. Pockets can be efficiently constructed by an algorithm based on alpha complexes. The algorithm is implemented and applied to proteins with known three-dimensional conformations.
Aspects of Unstructured Grids and FiniteVolume Solvers for Euler and Navier-Stokes Equations,
- [VKI/NASA/AGARD Special Courses on Unstructured Grid Methods for Advection Dominated Flows AGARD Publication R-787],
, 1995
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Arrangements and Their Applications
- Handbook of Computational Geometry
, 1998
"... The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arr ..."
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Cited by 81 (17 self)
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The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arrangements to problems in motion planning, visualization, range searching, molecular modeling, and geometric optimization. Some results involving planar arrangements of arcs have been presented in a companion chapter in this book, and are extended in this chapter to higher dimensions. Work by P.A. was supported by Army Research Office MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.-Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR-91-22103 and CCR-93-11127, by a Max-Planck Research Award, and by grants from the U.S.-Israeli Binational Science Foundation, the Israel Science Fund administered by the Israeli Ac...
Representation and Visualization of Terrain Surfaces at Variable Resolution
, 1997
"... We present a new approach for managing the multiresolution representation of discrete topographic surfaces. A Triangulated Irregular Network (TIN) representing the surface is built from sampled data by iteratively refining an initial triangulation that covers the whole domain. The refinement process ..."
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Cited by 76 (11 self)
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We present a new approach for managing the multiresolution representation of discrete topographic surfaces. A Triangulated Irregular Network (TIN) representing the surface is built from sampled data by iteratively refining an initial triangulation that covers the whole domain. The refinement process generates triangulations of the domain corresponding to increasingly finer approximations of the surface. Such triangulations are embedded into a structure in a three dimensional space. The resulting representation scheme encodes all intermediate representations that were generated during refinement. We propose a data structure and traversal algorithms that are oriented to the efficient extraction of approximated terrain models with an arbitrary precision, either constant or variable over the domain. 1. Introduction The search for multiresolution representation schemes has recently become very popular. Major applications involve generic surfaces embedded in 3D space 16;8;27 , terrains i...
an optimal algorithm for intersecting three-dimensional convex polyhedra,”
- SIAM J. Comput.,
, 1992
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Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations
- Computational Geometry—Theory and Applications
, 1999
"... This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point by simply “walking through ” the triangulation, after selecting a “good starting point ” by random sampling. The analysis generalizes an ..."
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Cited by 63 (4 self)
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This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point by simply “walking through ” the triangulation, after selecting a “good starting point ” by random sampling. The analysis generalizes and extends a recent result for d D 2 dimensions by proving this procedure takes expected time close to O.n1=.dC1/ / for point location in Delaunay triangulations of n random points in d D 3 dimensions. Empirical results in both two and three dimensions show
